# Children's Guild DC

Part II of the application

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 11 Homework 3 Name Date 1. The rectangles below have the same area. Move the ( ) to find the missing side lengths. Then solve. 36 cm 1 cm b. Area: 1 × 36 = ______ sq cm ______ cm 9 cm 4 cm 2 cm b. Area: 4 × 9 = (2 × 2) × 9 =2×2×9 a. Area: 4 × _____ = ______sq cm _____ cm = _____ × _____ = ______ sq cm _____ cm _____ cm _____ cm d. Area: 12 × 3 = (6 × 2) × 3 c. Area: 4 × 9 = 4 × (3 × 3) =4×3×3 = _____ × _____ = ______ sq cm =6×2×3 = _____ × _____ = ______ sq cm 2. Does Problem 1 show all the possible whole number side lengths for a rectangle with an area of 36 square centimeters? How do you know? Lesson 11: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Demonstrate possible whole number side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.C.33 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 11 Homework 3 3. a. Find the area of the rectangle below. 6 cm 8 cm b. Hilda says a 4 cm by 12 cm rectangle has the same area as the rectangle in Part (a). Place ( ) in the equation to find the related fact and solve. Is Hilda correct? Why or why not? 4 × 12 = 4 × 2 × 6 =4×2×6 = _____ × _____ = _____ sq cm cm c. Use the expression 8 × 6 to find different side lengths for a rectangle that has the same area as the rectangle in Part (a). Show your equations using ( ). Then estimate to draw the rectangle and label the side lengths. Lesson 11: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Demonstrate possible whole number side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.C.34 New York State Common Core GRADE 3 Mathematics Curriculum GRADE 3 • MODULE 4 Topic D Applications of Area Using Side Lengths of Figures 3.MD.6, 3.MD.7, 3.MD.5 Focus Standards: 3.MD.6 3.MD.7 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Addition and Subtraction of Length Units Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10 Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10 Multi-Digit Multiplication and Division Exploring Multiplication Instructional Days: Coherence -Links from: 5 G2–M2 G3–M1 G3–M3 -Links to: G4–M3 G4–M7 Topic D requires students to synthesize and apply their knowledge of area. Lesson 12 begins the topic with an emphasis on real world applications by providing students with opportunities to apply their understanding of area to solving word problems. Students may practice unknown product, group size unknown, and number of groups unknown types of problems. (See examples of problem types in the chart on page 19 of the Geometric Measurement progression.) The word problems provide a stepping stone for the real world project based application with composite shapes and the area floor plan in Topic D. Lessons 13 and 14 introduce students to finding the area of composite shapes. They learn to find the missing measurements Topic D: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Applications of Area Using Side Lengths of Figures 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported.License. 4.D.1 NYS COMMON CORE MATHEMATICS CURRICULUM Topic D 3• 4 using the given side lengths and then make decisions about whether to decompose the tiled region into smaller rectangles and add the areas (3.MD.7c), or complete the composite figures and then subtract. In Lessons 15 and 16, students apply their work with composite shapes from the previous two lessons to a real word application to determine areas of rooms in a given floor plan. A Teaching Sequence Towards Mastery of Applications of Area Using Side Lengths of Figures Objective 1: Solve word problems involving area. (Lesson 12) Objective 2: Find areas by decomposing into rectangles or completing composite figures to form rectangles. (Lessons 13–14) Objective 3: Apply knowledge of area to determine areas of rooms in a given floor plan. (Lessons 15–16) Topic D: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Applications of Area Using Side Lengths of Figures 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported.License. 4.D.2 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 3 Lesson 12 Objective: Solve word problems involving area. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (15 minutes) (5 minutes) (30 minutes) (10 minutes) (60 minutes) Fluency Practice (15 minutes) Group Counting 3.OA.1 Multiply by 7 3.OA.7 Find the Side Length 3.MD.7 (3 minutes) (7 minutes) (5 minutes) Group Counting (3 minutes) Note: Group counting reviews interpreting multiplication as repeated addition. Direct students to count forward and backward, occasionally changing the direction of the count. Fours to 40 Sixes to 60 Eights to 80 Nines to 90 Multiply by 7 (7 minutes) Materials: (S) Multiply by 7 Pattern Sheet (6–10) Note: This activity builds fluency with multiplication facts using units of 7. It works toward students knowing from memory all products of two one-digit numbers. See G3–M4–Lesson 2 for the directions for administration of a Multiply By pattern sheet. T: S: T: S: (Write 7 × 7 = .) Let’s skip-count up by sevens. (Count with fingers to 7 as students count.) 7, 14, 21, 28, 35, 42, 49. Let’s see how we can skip-count down to find the answer, too. (Show 10 fingers.) Start at 70. (Count down with your fingers as students say numbers.) 70, 63, 56, 49. Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.3 © 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 3 Continue with the following possible sequence: 9 × 7, 6 × 7, and 8 × 7. T: (Distribute Multiply by 7 Pattern Sheet.) Let’s practice multiplying by 7. Be sure to work left to right across the page. Find the Side Length (5 minutes) Materials: (S) Personal white boards Note: This fluency reviews the relationship between side lengths and area. T: S: T: S: T: (Project a rectangle with a width of 2 units and an unknown length. Inside the rectangle, write Area = 10 square units.) Say the area of the rectangle. ____ units 10 square units. What’s the width of the rectangle? 2 units Area = 10 square units 2 units. (Write 2 units × __ units = 10 square units.) On your boards, complete the equation, filling in the unknown length. (Write 2 units × 5 units = 10 square units.) S: Continue with the following possible sequence: 1 unit × __ units = 8 square units, 5 units × __ = 15 square units, 3 units × __ units = 18 square units, and 6 units × __ units = 24 square units. Application Problem (5 minutes) a. Find the area of a 6 m by 9 m rectangle. b. Use the side lengths, 6 m × 9 m, to find different side lengths for a rectangle that has the same area. Show your equations using parentheses. Then estimate to draw the rectangle and label the side lengths. Note: This problem reviews using the associative property to generate whole number side lengths of rectangles with a given area. Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.4 © 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 3 Concept Development (30 minutes) Materials: (S) Personal white boards Problem 1: Solve area word problems with 1 side length unknown. Write or project the following problem: The area of Theo’s banner is 42 square feet. If the length of his banner measures 4 feet, how wide is his banner? T: S: T: S: T: T: S: MP.6 T: S: T: S: T: S: T: S: T: S: T: S: What information is known? The area and length of Theo’s banner. What information is unknown? The width. 4 ft I’ll draw an area model and use a letter for the unknown. (Draw an incorrectly scaled model like the one shown at right.) If the length is 4 feet and the area is 32 square feet, can the Area = 32 sq ft w width be less than 4 feet? No, the width needs to be more than 4 feet. The width should be more than 4 feet because 4 times 4 only equals 16, but the area is 32 square feet. Talk to your partner: Is the area model I drew an accurate representation of the rectangle in the problem? How do you know? No, because the width should be much longer than the length. Work with your partner to correctly redraw my area model on your board. (Draw as shown at right.) 4 ft How can we find the value of w? Divide 32 by 4! Write a division equation to find the value of w. (Write 32 ÷ 4 = w.) Area = 32 sq ft w What is the value of w? 8! So the width of Theo’s banner is just 8? 8 what? 8 feet! The area of a piece of paper is 72 square inches. Margo measures the length of the paper and says it is 8 inches. What is the width of the piece of paper? Jillian needs to draw a rectangle with an area of 56 square centimeters and a width of 7 inches. What is the length of the rectangle that Jillian needs to draw? Repeat the process with the following suggestions: Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.5 © 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 3 Problem 2: Choose a strategy to find the area of a larger rectangle. Write or project the following problem: Amir is getting carpet in his bedroom, which measures 7 feet by 15 feet. How many square feet of carpet will Amir need? T: Draw an area model to represent Amir’s bedroom. Write an expression that shows how to find the area. 7 ft (Draw as shown at right.) Talk to your partner: How can we find the area of Amir’s bedroom since the measurements are so large? We can break the room up into two smaller rectangles and add their areas together. We can also break apart one of the factors in 7 × 15 to come up with a multiplication sentence that is easier to solve. Decide with your partner which strategy you’ll use to find the area. Then solve. (Decide on a strategy and solve.) What is the area of Amir’s bedroom? 105 square feet! 15 ft Area: 7 × 15 S: T: S: T: S: T: S: NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: Offer planning and strategy development support to learners if needed. Some learners may use a method simply because they are not fluent in an alternative method. Model a think-aloud in which you consider two or more strategies, reason about your selection, and solve. This may take more time than allotted here. You may want to pre-teach to preserve the pace of the lesson and to maximize every student’s participation. Invite students to share which strategy they chose and why, and to articulate how they used the strategy to solve the problem. For the break apart and distribute strategy, students may have broken the rectangle apart several different ways. Continue with the following suggested examples, encouraging students to try different strategies: Maya helps her family tile the bathroom wall. It measures 12 feet by 11 feet. How many square-foot tiles does Maya need to cover the wall? Francis washes all of the windows outside his parents’ bookstore. There are 5 windows, each one is 6 feet wide and 8 feet high. What is the total area of the windows that Francis washes? NOTES ON MULTIPLE MEANS OF ENGAGEMENT: During the Problem Set, extend Problem 4 for students working above grade level. Have students model all possible rectangles with an area of 64. Or, have students model up to eight ways of breaking their rectangle (Part b) into two smaller rectangles. Make it an exciting, perhaps timed, competition. Always offer challenges and extensions to learners as alternatives, rather than additional “busy” work. Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems. Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.6 © 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 3 Student Debrief (10 minutes) Lesson Objective: Solve word problems involving area. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion. What shape is the sticky note in Problem 1? How do you know? Share student explanations to Problem 2(b). What is another way the artist’s mural in Problem 3 could have been broken apart? How did you identify Alana’s pattern in Problem 4? Discuss how you found the area of two pieces of Jermaine’s paper in Problem 5. Why was it necessary to find the missing side length first? Are there any other ways to find the area of the two pieces of paper? (81 – 27 = 54 sq cm.) How were all of today’s word problems related? Does the unknown in a problem change the way you solve it? Why or why not? Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.7 © 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 Pattern Sheet 3 Multiply. Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.8 ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 Problem Set 3 Name Date 1. Each side on a sticky note measures 9 centimeters. What is the area of the sticky note? 2. Stacy tiles the rectangle below using her square pattern blocks. Find the area of Stacyâ€™s rectangle in square units. Then draw and label a different rectangle with whole number side lengths and having the same area. b. Can you draw another rectangle with different whole number side lengths and having the same area? Explain how you know. Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.9 ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 Problem Set 3 3. An artist paints a 4 × 16 foot mural on a wall. What is the total area of the mural? Use the break apart and distribute strategy. 10 ft 4 ft 6 ft 4. Alana tiles the 3 figures below. She says, “I’m making a pattern!” a. Find the area of the Alana’s 3 figures and explain her pattern. b. Draw the next 2 figures in Alana’s pattern and find their areas. 5. Jermaine glues 3 identical pieces of paper as shown below and makes a square. Find the missing side length of 1 piece of paper. Then find the total area of 2 pieces of paper. 9 cm ? cm 9 cm Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.10 © 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 Exit Ticket 3 Name Date 1. A painting has an area of 63 square inches. One side length is 9 inches. What is the other side length? 9 inches Area = 63 square inches 2. Judyâ€™s mini dollhouse measures 4 inches by 16 inches. What is the total area of the dollhouse? Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.11 ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 Homework 3 Name Date 1. A square calendar has sides that are 9 inches long. What is the calendar's area? 2. Each is 1 square unit. Sienna uses the same square units to draw a 6 Ă— 2 rectangle and says that it has the same area as the rectangle below. Is she correct? Explain why or why not. 3. The surface of an office desk has an area of 15 square feet. Its length is 5 feet. How wide is the office desk? Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.12 ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 Homework 3 4. A rectangular garden has a total area of 48 square yards. Draw and label two possible rectangular gardens with different side lengths having the same area. 5. Lila makes the pattern below. Find and explain her pattern. Then draw the fifth figure in her pattern. Lesson 12: Date: Solve word problems involving area. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.13 ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 3 Lesson 13 Objective: Find areas by decomposing into rectangles or completing composite figures to form rectangles. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (12 minutes) (6 minutes) (32 minutes) (10 minutes) (60 minutes) Fluency Practice (12 minutes) Group Counting 3.OA.1 Find the Common Products 3.OA.7 (4 minutes) (8 minutes) Group Counting (4 minutes) Note: Group counting reviews interpreting multiplication as repeated addition. Direct students to count forward and backward, occasionally changing the direction of the count. Threes to 30 Sixes to 60 Eights to 80 Nines to 90 Find the Common Products (8 minutes) Materials: (S) Blank paper Note: This fluency reviews multiplication patterns. After listing the multiples of 4 and 8, guide students through the following steps. T: S: Draw a line to match the numbers that appear in both columns. (Match 8, 16, 24, 32, and 40.) Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.14 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 3 T: S: T: S: T: S: T: S: T: (Write 2 × 4 = 8, etc., next to each matched number on the left half of the paper.) Write the rest of the number sentences like I did. (Write number sentences.) (Write 8 = 1 × 8, etc., next to each matched number on the right half of the paper.) Write the rest of the number sentences like I did. (Write number sentences.) (Write 2 × 4 = __ × 8.) Say the true number sentence. 2 × 4 = 1 × 8. (Write 2 × 4 = 1 × 8.) Write the remaining equal facts as number sentences. (Write 4 × 4 = 2 × 8, 6 × 4 = 3 × 8, 8 × 4 = 4 × 8, and 10 × 4 = 5 × 8.) Discuss the patterns in your number sentences. Application Problem (6 minutes) Anil finds the area of a 5 inch by 17 inch rectangle by breaking it into 2 smaller rectangles. Show one way that he could have solved the problem. What is the area of the rectangle? NOTES ON MULTIPLE MEANS OF ENGAGEMENT: Students who solve the Application Problem quickly may enjoy comparing their solution strategy with others. They may discuss or journal about their reasoning. Note: This problem reinforces the strategy of breaking a larger shape apart into 2 smaller shapes to find the total area. Concept Development (32 minutes) Materials: (S) Personal white boards, grid template Problem 1: Add using the break apart strategy to find area of a composite shape. Distribute one grid template to each student. Draw or project the shape shown at right. T: S: T: S: Draw and shade the shape on your grid template. (Draw and shade.) How do you find the area of a rectangle? Multiply the side lengths! Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.15 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 3 Talk to your partner: Can we find the area of the shaded figure by multiplying side lengths? How do you know? S: No, because it isn’t a rectangle. We can count the unit squares inside, though. T: In the Application Problem, we used the break apart and distribute strategy to find the area of a larger rectangle by breaking it into smaller rectangles. Turn and talk to your partner: How might we use a strategy like that to find the area of the shaded figure? S: We can break it into a square and a rectangle. We can break it into three squares. T: Draw a dotted line to show how to break the shaded figure apart into a square and rectangle. S: (Draw.) T: (Model as shown at right.) What equation tells you the area of the square on top? S: 2 × 2 = 4! T: What equation tells you the area of the rectangle on bottom? S: 2 × 4 = 8! T: How do we use those measurements to find the area of the shaded figure? S: Add them together! MP.7 T: What is the sum of 8 and 4? S: 12. T: What is the area of the shaded figure? S: 12 square units! Draw or project the shape shown at right. T: We can also find the area of the shaded figure by thinking about a 4 × 4 square with missing units. Turn and talk to your partner: How can we find the shaded area using our square? S: The area of the square is 16 square units. Since the entire square isn’t shaded, we need to subtract the 4 units that are unshaded. 16 – 4 = 12 square units. T: There are different strategies of finding the area of a figure. It just depends on how you choose to look at it. Continue with the following suggested examples: T: Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.16 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 3 Problem 2: Subtract to find area of a composite shape. 6 cm Draw or project the shape shown at right. T: This figure shows a small rectangle cut out of a larger, shaded rectangle. How can we find the area of the shaded figure? 6 cm 4 cm S: We can break apart the shaded part. Or we can subtract the unshaded area from the shaded square. 2 cm T: (Shade in the white shape.) We now have a large, shaded square. Write a number sentence to find the area of the large square. S: (Write 6 × 6 = 36.) T: What is the area of the square? S: 36 square centimeters. T: (Erase the shading inside the white rectangle.) Beneath the number sentence you just wrote, write a number sentence to find the area for the shape we “cut out.” S: (Write 2 × 4 = 8.) T: What is the area of the white shape? S: 8 square centimeters. T: The area of the square is 36 square centimeters. We cut out, or took away, 8 square centimeters of shading. Turn and talk to you partner. How can we find the area of the shaded region? S: Subtract 8 square centimeters from 36 square centimeters! T: Write a number sentence to find the area of the shaded region. S: (Write 36 – 8 = 28.) Continue with the following example: 6 in 3 in 4 in 2 in Problem 3: Subtract to find area of a composite shape with missing side lengths. Draw or project the shape shown at right. T: S: T: This figure also shows a small rectangle cut out of a larger, shaded rectangle, but what is missing? The side lengths of the smaller rectangle. Do we have enough information to find the side lengths of the smaller rectangle? 4 ft 11 ft 9 ft _____ ft _____ ft 5 ft Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.17 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 3 S: T: S: T: S: T: S: T: S: T: S: T: No, I don’t think so. We know the side lengths of the larger rectangle. Maybe we can subtract to the find the missing side lengths. Opposite sides of a rectangle are equal. Since we know the length of the rectangle is 9 feet, what is the opposite side length? 9 feet. You can then find the missing lengths by subtracting the total, 9 feet, from the known length, 4 feet. The missing length is 5 feet! Use the same strategy to find the missing width. (Write 11 – 5 = 6.) What is the missing width? 6 feet! Can we now find the area of the shaded figure? Yes! With your partner, find the area of the shaded figure. NOTES ON MULTIPLE MEANS OF ENGAGEMENT: Extend Problem 3 for students working above grade level. Challenge students to think about a real life scenario in which this model might be used and to write a word problem to match. Always offer challenges and extensions to learners as alternatives. Here, a student might be given the option of solving one other problem in addition to this extension. Another option would be to direct students to solve the problem you intend to discuss in the Student Debrief. Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems. Student Debrief (10 minutes) Lesson Objective: Find areas by decomposing into rectangles or completing composite figures to form rectangles. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.18 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 3 You may choose to use any combination of the questions below to lead the discussion. How did you break apart the rectangles in Figure 4?. Did anyone break apart the rectangles in a different way? (A rectangle of 10 by 2). In Problem 2, a 4-cm by 3-cm rectangle was cut out of a bigger rectangle. What other measurements could have been cut out to keep the same area for the shaded region? How did you find the unknown measurements in Problem 3? How were today’s strategies examples of using what we know to solve new types of problems? Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.19 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Problem Set 3 Name Date 1. Each of the following figures is made up of 2 rectangles. Find the total area of each figure. Figure 1 Figure 2 A C B D E Figure 3 F Figure 4 G H 18 Figure 1: Area of A + Area of B: ________ + _________ = _________ sq units Figure 2: Area of C + Area of D: ________ + _________ = __________ sq units Figure 3: Area of E + Area of F: ________ + _________ = __________ sq units Figure 4: Area of G + Area of H: ________ + _________ = __________ sq units Lesson 13: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.20 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Problem Set 3 2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded region. 9 cm 10 cm 3 cm 4 cm Area of the shaded region: ______ – ______ = ______ sq cm 3. The figure shows a small rectangle cut out of a big rectangle. 4 cm _____ cm 7 cm _____ cm a. Label the missing measurements. 3 cm 9 cm b. Area of the big rectangle: ______ × ______ = ______ sq cm c. Area of the small rectangle: ______ × ______ = ______ sq cm d. Find the area of the shaded region. Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.21 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Exit Ticket 3 Name Date The following figure is made up of 2 rectangles. Find the total area of the figure. A B Area of A + Area of B: ________ + _________ = _________ sq units Lesson 13: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.22 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Homework 3 Name Date 1. Each of the following figures is made up of 2 rectangles. Find the total area of each figure. Figure 1 Figure 2 A C B D Figure 3 Figure 4 E F G H Figure 1: Area of A + Area of B: ________ + _________ = _________ sq units Figure 2: Area of C + Area of D: ________ + _________ = __________ sq units Figure 3: Area of E + Area of F: ________ + _________ = __________ sq units Figure 4: Area of G + Area of H: ________ + _________ = __________ sq units Lesson 13: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.23 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Homework 3 2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded region. 7 cm 8 cm 3 cm 3 cm Area of the shaded region: ______ - ______ = ______ sq cm 3. The figure shows a small rectangle cut out of a big rectangle. _____ cm 6 cm a. Label the missing measurements. _____ cm 8 cm b. Area of the big rectangle: ______ × ______ = ______ sq cm c. Area of the small rectangle: ______ × ______ = ______ sq cm 4 cm 9 cm d. Find the area of the shaded region. Lesson 13: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.24 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 Template 3 Lesson 13: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.25 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 3 Lesson 14 Objective: Find areas by decomposing into rectangles or completing composite figures to form rectangles. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (15 minutes) (5 minutes) (30 minutes) (10 minutes) (60 minutes) Fluency Practice (15 minutes) Group Counting 3.OA.1 Multiply by 8 3.OA.7 Find the Area 3.MD.7 (3 minutes) (7 minutes) (5 minutes) Group Counting (3 minutes) Note: Group counting reviews interpreting multiplication as repeated addition. Direct students to count forward and backward, occasionally changing the direction of the count. Fours to 40 Sixes to 60 Sevens to 70 Nines to 90 Multiply by 8 (7 minutes) Materials: (S) Multiply By 8 Pattern Sheet (6–10) Note: This activity builds fluency with multiplication facts using units of 8. It works toward students knowing from memory all products of two one-digit numbers. See G3–M4–Lesson 2 for the directions for administration of a Multiply By pattern sheet. T: S: (Write 6 × 8 = .) Let’s skip-count up by eights to solve. (Count with fingers to 6 as students count.) 8, 16, 24, 32, 40, 48. Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.26 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 3 T: S: T: S: T: Let’s skip-count down to find the answer, too. Start at 80. (Count down with fingers as students count.) 80, 72, 64, 56, 48. Let’s skip-count up again to find the answer, but this time start at 40. (Count up with fingers as students count.) 40, 48. (Distribute Multiply by 8 pattern sheet.) Let’s practice multiplying by 8. Be sure to work left to right across the page. Figures for Find the Area Continue with the following possible sequence: 8 × 8, 7 × 8, and 9 × 8. Find the Area (5 minutes) Materials: (S) Personal white boards Note: This fluency reviews the relationship between side lengths and area and supports the perception of the composite shapes by moving from part to whole using a grid. T: S: T: S: T: (Project the first figure on the right.) On your boards, write a number sentence to show the area of the shaded rectangle. (Write 5 × 2 = 10 square units or 2 × 5 = 10 square units.) Write a number sentence to show the area of the unshaded rectangle. (Write 3 × 2 = 6 square units or 2 × 3 = 6 square units.) (Write __ sq units + __ sq units = __ sq units.) Using the areas of the shaded and unshaded rectangle, write an addition sentence to show the area of the entire figure. (Write 10 sq units + 6 sq units = 16 sq units or 6 sq units + 10 sq units = 16 sq units.) S: Continue with the other figures. Application Problem (5 minutes) a. Break apart the shaded figure into 2 rectangles. Then add to find the area of the shaded figure below. MP.7 b. Subtract the area of the unshaded rectangle from the area of the large rectangle to check your answer in Part (a). Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.27 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 3 MP.7 Note: This problem reviews G3–M4–Lesson 13’s concept of finding area of composite shapes. Students may choose to break apart their rectangles in different ways for Part (a). Concept Development (30 minutes) Materials: (S) Personal white boards, Problem Set Problem 1: Choose an appropriate method for finding the area of a composite shape. Distribute one Problem Set to each student. Project the shape to the right. T: S: What two strategies did we learn yesterday to find the area of a non-rectangular shape? We can break the shape apart into smaller rectangles and then add the areas of the smaller rectangles together. Or, find the area of the larger rectangle and subtract the area of the “missing” part. Look at the figure in Problem 1(a). What is the unknown width? 5 centimeters! 2 centimeters plus 3 centimeters is 5 centimeters. Label that on your figure. Then write the equation used to find the area of each of the smaller rectangles. (Record on Problem Set.) What is the area of the top rectangle? 10 square centimeters! What is the area of the bottom rectangle? 9 square centimeters! On your Problem Set, write the number sentence used to find the area of the whole figure. Be sure to answer 2 cm 3 cm 2 cm 3 cm T: T: S: T: S: T: S: T: S: T: NOTES ON MULTIPLE MEANS OF ENGAGEMENT: Students working below grade level may benefit from sentence frames to assist their writing the equations to find the area in Problem 1. You may provide the following: ____ ×____=____square centimeters ____ ×____=____square centimeters ____ sq cm + ____ sq cm =____square centimeters The area is ____square centimeters. Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.28 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 3 T: S: in a complete sentence! What is the total area of the figure? 19 square centimeters! Continue with Problem 1(b) from the Problem Set. Problem 2: Solve a word problem involving area of nonrectangular shapes. Write or project the following problem: Fanny has a piece of fabric 8 feet long and 5 feet wide. She cuts out a rectangular piece that measures 3 feet by 2 feet. How many square feet of fabric does Fanny have left? T: T: S: T: S: T: S: T: S: T: T: S: T: S: T: S: T: S: NOTES ON MULTIPLE MEANS OF ENGAGEMENT: Adjust the numbers in Problem 2 of the Concept Development to challenge students working above grade level. Or, offer an alternative challenge, such as scripting and recording the steps to find the area of a non-rectangular shape that they can refer back to when needed. Draw and label Fanny’s fabric. How big is the piece that Fanny cuts out? 3 ft by 2 ft. Work with your partner to draw the piece of fabric that Fanny cuts out. Label the measurements of the piece being cut out. (Draw as shown at right. Note: The 3 ft by 2 ft piece can be taken out of any part of the original rectangle, including at an angle.) What’s the best way for us to find the area of the remaining fabric? Find the area of the original piece, then subtract the area of what was cut out. Write an equation to find the area of the original piece of fabric. (Write 8 × 5 = 40 sq ft.) Beneath what you just wrote, write a number sentence to find the area of the piece of fabric Fanny cuts out. What is the area of the piece that is cut out? 6 square feet! What expression tells us the area of the remaining fabric? 40 – 6. 40 – 6 equals? 34! How much fabric does Fanny have left? 34 square feet! 5 ft 8 ft 5 ft 3 ft 8 ft 2 ft Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems. Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.29 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 3 Student Debrief (10 minutes) Lesson Objective: Find areas by decomposing into rectangles or completing composite figures to form rectangles. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion. Lead a discussion about the strategy choice for Problems 1(a) and 1(b). Could the strategies have been reversed for these two problems? What steps did you need to follow to solve Problem 2? How were you able to find the area of the smaller rectangle? Invite students to share their drawings for Problem 3. In what ways are they similar? In what ways are they different? Why did Tila and Evan wind up with the same amount of paper in Problem 4? If they both cut their rectangles from the corners of their papers, would they both be able to cut out a 4 cm by 8 cm rectangle with their remaining paper? (Guide students to reason that even though they both have 42 sq cm left and the 4 × 8 rectangle only measures 32 sq cm, only Evan can cut out such a rectangle from his remaining paper.) Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.30 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 3 Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the studentsâ€™ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 14: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.31 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 Pattern Sheet 3 Multiply. Lesson 14: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.32 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 Problem Set 3 Name Date 1. Find the area of each of the following figures. All figures are made up of rectangles. a. 2 cm 3 cm 2 cm 3 cm b. 1m 4m 1m 2m 1m 2. The figure below shows a small rectangle in a big rectangle. Find the area of the shaded part of the figure. 1m 5m 2m 1m 2m 6m Lesson 14: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.33 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 Problem Set 3 3. A paper rectangle has a length of 6 inches and a width of 8 inches. A square with a side length of 3 inches was cut out of it. What is the area of the remaining paper? 4. Tila and Evan both have paper rectangles measuring 6 cm by 9 cm. Tila cuts a 3 cm by 4 cm rectangle out of hers and Evan cuts a 2 cm by 6 cm rectangle out of his. Tila says she has more paper left over. Evan says they have the same amount. Who is correct? Show your work below. Lesson 14: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.34 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 Exit Ticket 3 Name Date Mary draws an 8 cm by 6 cm rectangle on her grid paper. She shades a square with a side length of 4 cm inside her rectangle. What area of the rectangle is left unshaded? Lesson 14: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.35 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 Homework 3 Name Date 1. Find the area of each of the following figures. All figures are made up of rectangles. 6 feet a. 3 feet 8 feet 3 feet 8 inches b. 5 inches 3 inches 2 inches 4 inches Lesson 14: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.36 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 Homework 3 2. The figure below shows a small rectangle cut out of a big rectangle. 10 feet 2 feet 7 feet 3 feet 2 feet 2 feet a. Label the side lengths of the unshaded region. b. Find the area of the shaded region. Lesson 14: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Find areas by decomposing into rectangles or completing composite figures to form rectangles. 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.37 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 3• 4 Lesson 15 Objective: Apply knowledge of area to determine areas of rooms in a given floor plan. Suggested Lesson Structure Fluency Practice Concept Development Student Debrief Total Time (15 minutes) (35 minutes) (10 minutes) (60 minutes) Fluency Practice (15 minutes) Group Counting 3.OA.1 Multiply by 9 3.OA.7 Find the Area 3.MD.7 (3 minutes) (7 minutes) (5 minutes) Group Counting (3 minutes) Note: Group counting reviews interpreting multiplication as repeated addition. Direct students to count forward and backward, occasionally changing the direction of the count. Threes to 43 Sixes to 60 Sevens to 70 Eights to 80 Multiply by 9 (7 minutes) Materials: (S) Multiply by 9 Pattern Sheet (1–5) Note: This activity builds fluency with multiplication facts using units of 9. It works toward students knowing from memory all products of two one-digit numbers. See G3–M4–Lesson 2 for the directions for administration of a Multiply By pattern sheet. T: S: T: (Write 5 × 9 = .) Let’s skip-count by nines to find the answer. (Count with fingers to 5 as students count.) 9, 18, 27, 36, 45. (Record on the board as students count.) (Circle 45 and write 5 × 9 = 45 above it. Write 3 × 9 = .) Let’s skip-count up by nines again. (Count with fingers to 3 as students count.) Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.38 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 3• 4 S: T: S: T: 9, 18, 27. Let’s see how we can skip-count down to find the answer, too. Start at 45 with 5 fingers, 1 for each nine. (Count down with your fingers as students say numbers.) 45 (5 fingers), 36 (4 fingers), 27 (3 fingers). (Distribute Multiply by 9 Pattern Sheet.) Let’s practice multiplying by 9. Be sure to work left to right across the page. Repeat the process for 4 × 9. Find the Area (5 minutes) Materials: (S) Personal white boards Note: This fluency reviews the relationship between side lengths and area and supports the perception of the composite shapes by moving from part to whole using a grid. T: S: T: S: T: S: (Project the figure on the right.) On your boards, write a number sentence to show the area of the shaded rectangle. (Write 4 × 2 = 8 square units or 2 × 4 = 8 square units.) Write a number sentence to show the area of the unshaded rectangle. (Write 3 × 2 = 6 square units or 2 × 3 = 6 square units.) (Write __ sq units + __ sq units = __ sq units.) Using the areas of the shaded and unshaded rectangles, write an addition sentence to show the area of the entire figure. (Write 8 sq units + 6 sq units = 14 sq units or 6 sq units + 8 sq units = 14 sq units.) Continue with the figures below: Concept Development (35 minutes) Materials: (S) Problem Set, ruler T: For the next two days, you are going to be architects. Today you are going to use a floor plan that your clients designed to find the area in square centimeters of each room in the house. Look at the floor plan. What will you need to do before you can find the areas? A NOTE TO THE TEACHER: This lesson is designed to be completed in two days. For early finishers, please refer to the optional activities suggested in G3–M4–Lesson 16. Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.39 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 3• 4 S: T: S: T: S: T: S: T: S: T: S: T: We need to find the side lengths of each room. We need to know the lengths and widths of the rooms. Use your ruler to measure the side lengths of Bedroom 1 in centimeters. What is the length? 5 cm. What is the width? 12 cm. Write an expression to show how to find the area of Bedroom 1. (Write 5 × 12.) (Write Multiply Side Lengths on a chart labeled Strategies We Can Use to Find Area.) What strategy can you use to find the area since this fact is so large? The break apart and distribute strategy! (Add the strategy to the chart.) What about the rooms that aren’t rectangles, how will you find their areas? We can find the areas of smaller rectangles and add them together to get the area of a room that isn’t rectangular. Yeah, that’s the break apart and add strategy we just learned. Or, we might be able to find the area of a large rectangle and then subtract the area of a smaller rectangle. (Add the strategies to the chart.) Look at the floor plan and use what we’ve learned about area to help you answer Problem 1. (Allow students time to answer Problem 1.) Work with a partner to find the areas of the rooms and the hallway in the floor plan. Record the areas and the strategy you use to find each area in the chart in Problem 2. NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: Some students may benefit from a review of how to use a ruler to measure. Have them try the following: Place the zero end of the ruler against the line to be measured. Make sure the zero tick mark is lined up against the beginning of the side length. Read the last number on the ruler that is by the end of the side length. To make measuring easier, try the tips below: Darken the lines to be measured. Outline the lines with glue to make a tactile model. Provide large print rulers. Give the option of using centimeter blocks to measure. NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: To ease the task of constructing a response for Problems 3–5 of the Problem Set, allow English language learners and others to discuss their reasoning prior to writing. Discussions can be in first languages, if beneficial. Also provide English language learners with sentence frames, such as those given below. The _____ has the biggest area. My prediction was right/wrong because_____. There are/aren’t enough tiles because _____. Problem Set (20 minutes) Students should do their personal best to complete the Problem Set within the allotted 20 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems. Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.40 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 3• 4 Student Debrief (10 minutes) Lesson Objective: Apply knowledge of area to determine areas of rooms in a given floor plan. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion. Explain to a partner your choice for the prediction you made in Problem 1. What have you learned about area that helped you make your prediction? What strategy did you use to find the area of the living room? Is there more than one way to break apart the living room into smaller rectangles? Explain two different ways to a partner. How many more tiles do your clients need to have enough tiles for the bathroom floor? If they buy another box of tiles, how many will be left over? Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.41 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 3• 4 Exit Ticket (5 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.42 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 Pattern Sheet 3• 4 Multiply. Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.43 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 Problem Set 3• 4 Name 1. Make a prediction: Which room looks like it has the biggest area? Date 2. Record the areas and show the strategy you used to find each area. Room Area Strategy Bedroom 1 _______ sq cm Bedroom 2 _______ sq cm Kitchen _______ sq cm Hallway _______ sq cm Bathroom _______ sq cm Dining Room _______ sq cm Living Room _______ sq cm Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.44 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 Problem Set 3â€˘ 4 3. Which room has the biggest area? Was your prediction right? Why or why not? 4. Your clients buy 3 boxes of square centimeter tiles. Each box has 8 tiles. Are there enough tiles to cover the entire bathroom floor? Explain your answer. 5. Find the side lengths of the house without using your ruler to measure them and explain the process you used. Side lengths: __________ centimeters and __________ centimeters 6. What is the area of the whole floor plan? How do you know? Area = __________ square centimeters Lesson 15: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.45 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 Problem Set 3• 4 The rooms in the floor plan below are rectangles or made up of rectangles. Bedroom 1 Bathroom Kitchen Hallway Bedroom 2 Dining Room Living Room Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.46 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 Exit Ticket 3• 4 Name Date Jack uses grid paper to create a floor plan of his room. Label the missing measurements and find the area of the items listed below. Desk Table Bed Dresser Name a. Jack’s Room b. Bed c. Table d. Dresser e. Desk Equations Total Area ________ square units ________ square units ________ square units ________ square units ________ square units Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.47 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 15 Homework 3• 4 Name Date Use a ruler to measure the side lengths of each lettered room in centimeters. Then find the area. Use the measurements below to match and label the rooms with the correct areas. Kitchen - 28 square centimeters Porch – 32 square centimeters Bathroom – 24 square centimeters Garage – 72 square centimeters Bedroom – 56 square centimeters Hallway – 12 square centimeters A B D C E F Lesson 15: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.48 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 3• 4 Lesson 16 Objective: Apply knowledge of area to determine areas of rooms in a given floor plan. Suggested Lesson Structure Fluency Practice Concept Development Student Debrief Total Time (15 minutes) (35 minutes) (10 minutes) (60 minutes) Fluency Practice (15 minutes) Group Counting 3.OA.1 Multiply by 9 3.OA.7 Find the Area 3.MD.7 (3 minutes) (7 minutes) (5 minutes) Group Counting (3 minutes) Note: Group counting reviews interpreting multiplication as repeated addition. Direct students to count forward and backward, occasionally changing the direction of the count. Sixes to 60 Sevens to 70 Eights to 80 Multiply By 9 (7 minutes) Materials: (S) Multiply By 9 Pattern Sheet (6–10) Note: This activity builds fluency with multiplication facts using units of nine. It works toward students knowing from memory all products of two one-digit numbers. See G3–M4–Lesson 2 for the directions for administration of a Multiply By pattern sheet. T: S: T: S: (Write 6 × 9 = .) Let’s skip-count up by nine to solve. (Count with fingers to 6 as students count.) 9, 18, 27, 36, 45, 54. Let’s skip-count down to find the answer, too. Start at 90. (Count down with fingers as students count.) 90, 81, 72, 63, 54. Lesson 16: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.49 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 3• 4 T: S: T: Let’s skip-count up again to find the answer, but this time start at 45. (Count up with fingers as students count.) 45, 54. (Distribute Multiply By 9 pattern sheet.) Let’s practice multiplying by 9. Be sure to work left to right across the page. 7 in 4 in 5 in 2 in Continue with the following possible sequence: 8 × 9, 7 × 9, and 9 × 9. Find the Area (5 minutes) Materials: (S) Personal white boards Note: This fluency reviews G3–M4–Lesson 14. T: (Project the first figure on the right.) Find the areas of the large rectangle and the unshaded rectangle. Then subtract to find the area of the shaded region. (Write Area = square inches.) (Students work and write Area = 27 square inches.) 6 in 6 in 2 in 3 in S: Continue with other figures. 9 in 8 in 4 in 4 in Concept Development (35 minutes) Materials: (S) G3–M4–Lesson 15 Problem Set, ruler T: Today you will continue to find the area in square centimeters of each room in the house. Materials: (S) Optional Problem Set, centimeter grid paper, construction paper, glue Optional: Create a floor plan with different side lengths for given areas. If students finish early on the second day, they may work with a partner to create a floor plan with the areas of the rooms that they found. The task is for students to find new side lengths for each room. Students should use their answers from the Problem Set to ensure that they find different side lengths with the same area. After they find new side lengths, they mark each room on centimeter grid paper and then cut the rooms out. They will use these centimeter grids to fit the rooms together to make their floor plan. They will glue their final arrangement of rooms onto a piece of construction paper. Allow students a few minutes to do a gallery walk of the completed floor plans. Lesson 16: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.50 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 3• 4 Optional: Review strategies to find new side lengths of given areas. T: Yesterday you found the areas of the rooms in a floor plan that your clients designed. They like the area of each room, but they want to change the way the rooms look. Your job today is to create rooms with the same areas, but with different side lengths. Are you up for the challenge architects? Yes! Look at the Problem Set. What is the area of the hallway? 24 square centimeters. What are possible side lengths you can have for the hallway and still have the same area? 3 and 8. 1 and 24. 2 and 12. 6 and 4. Talk to a partner: Which of these choices was used in the floor plan? 8 and 3. The numbers are just switched. So when you redesign the floor plan today, be sure you don’t use that combination! S: T: S: T: S: T: S: T: Problem Set (25 minutes) Students should do their personal best to complete the Problem Set within the allotted 25 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems. Student Debrief (10 minutes) Lesson Objective: Apply knowledge of area to determine areas of rooms in a given floor plan. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be Lesson 16: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.51 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 3• 4 addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion. Explain to a partner how you found the side lengths of the whole house without using your ruler to measure. Can you multiply the side lengths of the house to find the area of the house? Why or why not? How did you find the area of the whole house? Do we usually measure rooms in centimeters? What unit might each centimeter in this picture represent on a real house? (Yards, feet, or meters.) Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 16: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.52 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 Pattern Sheet 3• 4 Multiply. Lesson 16: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.53 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 Problem Set 3â€˘ 4 Name Date Optional: Record the new side lengths you have chosen for each of the rooms and show that these side lengths equal the required area. For non-rectangular rooms, record the side lengths and areas of the small rectangles. Then show how the areas of the small rectangles equal the required area. Room New Side Lengths Bedroom 1: 60 sq cm Bedroom 2: 56 sq cm Kitchen: 42 sq cm Lesson 16: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.54 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 Problem Set 3• 4 Room New Side Lengths Hallway: 24 sq cm Bathroom: 25 sq cm Dining Room: 28 sq cm Living Room: 88 sq cm Lesson 16: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.55 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 Exit Ticket 3• 4 Name Date Find the area of the shaded region. Then draw and label a rectangle with the same area. 7 cm 4 cm 7 cm 4 cm Lesson 16: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.56 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 Homework 3â€˘ 4 Name Date Jeremy plans and designs his own dream playground on grid paper. His new playground will cover a total area of 72 square units. The chart shows how much space he gives for each piece of equipment, or area. Use the information in the chart to draw and label a possible way Jeremy can plan his playground. Basketball Court Jungle Gym Slide Soccer Area 10 square units 9 square units 6 square units 24 square units Lesson 16: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Apply knowledge of area to determine areas of rooms in a given floor plan. 9/30/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.D.57 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment TaskLesson 3• 4 2• 3 Date Name 1. Jasmine and Roland each use unit squares to tile a piece of paper. Their work is shown below. Jasmine’s Array Roland’s Array a. Can one of the arrays be used to correctly measure the area of the piece of paper? If so, whose array would you use? Explain why. b. What is the area of the piece of paper? Explain your strategy for finding the area. c. Jasmine thinks she can skip-count by sixes to find the area of her rectangle. Is she correct? Explain why or why not. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.1 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson New York State Common Core 2. Jaheim says you can create three rectangles with different side lengths using 12 unit squares. Use numbers, equations, and words to show what Jaheim is saying. 3. The area of a rectangle is 72 square units. One side has a length of 9 units. What is the other side length? Explain how you know using pictures, equations, and words. Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.2 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson New York State Common Core 4. Jax started to draw a grid inside the rectangle to find its area. a. Use a straight edge to complete the drawing of the grid. b. Write both an addition and a multiplication equation that you could use to find the area, then solve. 5. Half of the rectangle below has been tiled with unit squares. a. How many more unit squares are needed to fill in the rest of the rectangle? b. What is the total area of the large rectangle? Explain how you found the area. Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.3 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson New York State Common Core Mid-Module Assessment Task Standards Addressed Topics A–B Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. a. b. 3.MD.6 3.MD.7 A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Relate area to the operations of multiplication and addition. a. b. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. d. Evaluating Student Learning Outcomes A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing understandings that students develop on their way to proficiency. In this chart, this progress is presented from left (Step 1) to right (Step 4). The learning goal for each student is to achieve Step 4 mastery. These steps are meant to help teachers and students identify and celebrate what the student CAN do now and what they need to work on next. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.4 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment TaskLesson 3• 4 2• 3 A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. STEP 2 Evidence of some reasoning without a correct answer. (1 Point) 1 3.MD.5 3.MD.6 Response demonstrates little evidence of reasoning without a correct answer. (2 Points) Response shows limited reasoning with at least one correct answer. STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) Response includes evidence of some reasoning with three correct answers, or evidence of solid reasoning with an incorrect answer. STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) Student correctly answers: a. Jasmine’s array, giving strong evidence of understanding that tiling must have no gaps or overlaps. b. The area is 24 tiles. Provides appropriate explanation of the calculation including counting or skipcounting strategies. c. Yes, there are 4 rows of 6 squares so it is possible to skipcount by six. 2 3.MD.7b Response demonstrates little evidence of reasoning without a correct answer. Response shows limited reasoning with at least one correct answer. Student identifies at least two of three rectangles correctly. Response includes evidence of accurate reasoning with pictures, numbers, or words. Student correctly identifies three rectangles: 1 × 12 or 12 × 1 2 × 6 or 6 × 2 3 × 4 or 4 × 3 Response shows evidence of solid reasoning using pictures, numbers, and words. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.5 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson New York State Common Core A Progression Toward Mastery 3 3.MD.7b Response demonstrates little evidence of reasoning without a correct answer. Response shows limited reasoning without a correct answer. Student finds the missing side length of 8 units but may not show enough work to clearly justify the answer. Student correctly finds the missing side length of 8 units. Response shows evidence of solid reasoning using pictures, numbers, and words. Student correctly: a. Completes the array with 8 columns and 6 rows. b. Writes an addition equation (repeated addition of 8 sixes or 6 eights); writes a multiplication equation (6 × 8 or 8 × 6); and gives an area of 48 sq cm. Student correctly: a. Identifies that 16 tiles are needed to fill the remaining area. b. Says the area of the large rectangle is 32 square units. Explanation gives evidence of solid reasoning to support answer. 4 3.MD.5 3.MD.6 3.MD.7a Response demonstrates little evidence of reasoning without a correct answer. Response shows evidence of some reasoning in attempt to write equations and complete the array, but work may not include a correct answer. Student accurately completes the array and finds the area of 48 sq cm, but may not accurately provide both addition and multiplication equations. 5 3.MD.5a 3.MD.5b 3.MD.7a 3.MD.7d Response demonstrates little evidence of reasoning without a correct answer to either part. Response shows limited reasoning with a correct answer in one part. Student slightly miscalculates the number of tiles needed to fill the remaining area, but the explanation shows evidence of solid reasoning. Part (b) is correct based on the student’s slight miscalculation but not the correct answer of 32 units. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.6 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson New York State Common Core Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.7 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson New York State Common Core Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.8 NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Task Lesson New York State Common Core Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.9 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment TaskLesson 3• 4 2• 3 Date Name 1. Sarah says the rectangle on the left has the same area as the sum of the two on the right. Pam says they do not have the same areas. Who is correct? Explain using numbers, pictures, or words. 2. Draw three different arrays that you could make with 36 square-inch tiles. Label the side lengths on each of your arrays. Write multiplication sentences for each array to prove that the area of each array is 36 square inches. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.10 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Task Lesson New York State Common Core 3. Mr. and Mrs. Jackson are buying a new house. They are deciding between the two floor plans below. House A House B 3m 3m 3m 6m 10 m 10 m 3m 4m 4m 12 m 12 m Which floor plan has the greater area? Show how you found your answer on the drawings above. Show your calculations below. Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.11 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment TaskLesson 3• 4 2• 3 4. Superior Elementary School uses the design below for their swimming pool. 10 m C 6m 3m A 17 m B a. Label the side lengths of Rectangles A and B on the drawing. b. Find the area of each rectangle. c. Find the area of the entire pool. Explain how you found the area of the pool. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.12 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Task Lesson New York State Common Core End-of-Module Assessment Task Standards Addressed 3.MD.5 Topics A–D Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement. a. b. 3.MD.6 3.MD.7 A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Relate area to the operations of multiplication and addition. a. b. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. c. d. Evaluating Student Learning Outcomes A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing understandings that students develop on their way to proficiency. In this chart, this progress is presented from left (Step 1) to right (Step 4). The learning goal for each student is to achieve Step 4 mastery. These steps are meant to help teachers and students identify and celebrate what the student CAN do now and what they need to work on next. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.13 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment TaskLesson 3• 4 2• 3 A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. STEP 2 Evidence of some reasoning without a correct answer or with a partially correct answer in a multi-step question. (2 Points) Student identifies that Sarah is correct, demonstrating evidence of limited reasoning to support the answer. STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. STEP 4 Evidence of solid reasoning with a correct answer. (1 Point) 1 3.MD.7c 3.MD.7d Response demonstrates little or no evidence of reasoning without a correct answer. (3 Points) Student identifies that Sarah is correct. Response shows evidence of accurate reasoning to support the answer using at least one representation. Student correctly draws and labels two different arrays. Side lengths are labeled in inches. Multiplication sentences are shown for those two arrays. (4 Points) Student identifies that Sarah is correct. Explanation shows evidence of solid reasoning using multiple representations. Student correctly draws and labels three different arrays. Side lengths are labeled in inches. Possible arrays: 1 × 36 2 × 18 3 × 12 4×9 6×6 Correct multiplication sentences are shown for each array drawn. 2 3.MD.5b 3.MD.6 3.MD.7a 3.MD.7b Student attempts, but is unable to draw any correct arrays with labels. Multiplication sentences are not shown. Student correctly draws and labels one array. Side lengths are labeled without units. A multiplication sentence is shown. 3 3.MD.7d 3.MD.7b Response demonstrates little or no evidence of reasoning without a correct answer. Student miscalculates one area. Student may identify that House A has the greater area with limited reasoning. Response demonstrates correct calculations and area. Student identifies that House A has the greater area. Student demonstrates correct area calculations with answers: House A = 102 sq meters House B = 84 sq meters Explanation identifies that House A has the greater area. Response provides evidence of solid reasoning. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.14 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Task Lesson New York State Common Core A Progression Toward Mastery 4 3.MD.5 3.MD.7b 3.MD.7d Attempts, but is unable to answer any part of the question correctly. Student: a. Labels length and width correctly, but without units. b. Calculates at least two areas correctly. c. May miscalculate the total area. Student answers Parts (a) and (b) correctly, but may miscalculate the total area. Student correctly: a. Labels length and width of rectangles A and B, including units: A=3m×7m B = 3 m × 10 m b. Calculates the area of each rectangle as: A = 21 sq meters B = 30 sq meters C = 60 sq meters c. Calculates the total area as 111 sq meters. Module 4: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.15 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Task Lesson New York State Common Core Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.16 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Task Lesson New York State Common Core Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.17 NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Task Lesson New York State Common Core Module 4: Date: ÂŠ 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication and Area 10/1/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 4.S.18 2/28/14 To whom it may concern: I am excited about the prospect of a Children’s Guild charter school in DC. We need more positive school in DC, that supports our children’s learning experience. My daughter has been attending the guild for the past 3 years. She has been able to make progress with the help and support of her teachers and counselors. There patience and dedication to my daughter and our family, has allowed her to love learning again. My daughter loves going to school every day. She wakes up extra early to make sure that she doesn’t miss her bus. It is The Children’s Guild that was able to help my daughter get excited about learning again, to help her see that she could learn, and instill confidence in her, showing her that she has the potential to be successful. I fully support the development of a school run by this organization in Washington D.C. Phillina Thompson 46 Galveston St. SW Apt. 302 Washington, DC 20032 204 Oklahoma Ave NE Apt. 1 Washington DC 20002 MONARCH ACADEMY BALTIMORE CAMPUS, INC. FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 CONTENTS Page INDEPENDENT ............................................................................................................................................................................. AUDITORS' REPORT 1-2 FINANCIAL STATEMENTS ............................................................................................................................................................................. Statements of Financial Position 3 ............................................................................................................................................................................. Statements of Activities 4 ............................................................................................................................................................................. Statements of Cash Flows 5-6 ............................................................................................................................................................................. Notes to Financial Statements 7 - 14 INDEPENDENT AUDITORS' REPORT ON INTERNAL CONTROL OVER FINANCIAL REPORTING AND ON COMPLIANCE AND OTHER MATTERS BASED ON AN AUDIT OF FINANCIAL STATEMENTS PERFORMED IN ACCORDANCE ............................................................................................................................................................................. WITH GOVERNMENT AUDITING STANDARDS 15 - 16 Certified Public Accountants and Consultants INDEPENDENT AUDITORS' REPORT Board of Directors Monarch Academy Baltimore Campus, Inc. Report on the Financial Statements We have audited the accompanying financial statements of Monarch Academy Baltimore Campus, Inc. (MABC), which comprise the statements of financial position as of June 30, 2013 and 2012, and the related statements of activities and cash flows for the years then ended, and the related notes to the financial statements. Management's Responsibility for the Financial Statements Management is responsible for the preparation and fair presentation of these financial statements in accordance with accounting principles generally accepted in the United States of America; this includes the design, implementation, and maintenance of internal control relevant to the preparation and fair presentation of financial statements that are free from material misstatement, whether due to fraud or error. Auditors' Responsibility Our responsibility is to express an opinion on these financial statements based on our audit. We conducted our audit in accordance with auditing standards generally accepted in the United States of America and the standards applicable to financial audits contained in Government Auditing Standards, issued by the Comptroller General of the United States. Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements are free from material misstatement. An audit involves performing procedures to obtain audit evidence about the amounts and disclosures in the financial statements. The procedures selected depend on the auditors' judgment, including the assessment of the risks of material misstatement of the financial statements, whether due to fraud or error. In making those risk assessments, the auditor considers internal control relevant to MABC's preparation and fair presentation of the financial statements in order to design audit procedures that are appropriate in the circumstances, but not for the purpose of expressing an opinion on the effectiveness of MABC's internal control. Accordingly, we express no such opinion. An audit also includes evaluating the appropriateness of accounting policies used and the reasonableness of significant accounting estimates made by management, as well as evaluating the overall presentation of the financial statements. We believe that the audit evidence we have obtained is sufficient and appropriate to provide a basis for our audit opinion. TIMONIUM 9690 Deereco Road, Suite 500 Timonium, MD 21093 410 - 828 - CPAS (2727) | 410-828-9512 (FAX) COLUMBIA 9881 Broken Land Parkway, Suite 220 Columbia, MD 21046 410 - 290-3288 | 410-381-7795 (FAX) BEL AIR 109 N. Main Street, Suite C Bel Air, MD 21014 410 - 838-5717 | 410-838-2579 (FAX) www.KatzAbosch.com Members of: American Institute of Certified Public Accountants / Maryland Association of Certified Public Accountants / The Leading Edge Alliance Certified Public Accountants and Consultants Board of Directors Monarch Academy Baltimore Campus, Inc. Page 2 Opinion In our opinion, the financial statements referred to above present fairly, in all material respects, the financial position of MABC as of June 30, 2013 and 2012, and the changes in its net assets and its cash flows for the years then ended in accordance with accounting principles generally accepted in the United States of America. Other Reporting Required by Government Auditing Standards In accordance with Government Auditing Standards, we have also issued our report dated November 5, 2013, on our consideration of MABCâ€™s internal control over financial reporting and on our tests of its compliance with certain provisions of laws, regulations, contracts, and grant agreements and other matters. The purpose of that report is to describe the scope of our testing of internal control over financial reporting and compliance and the results of that testing, and not to provide an opinion on the internal control over financial reporting or on compliance. That report is an integral part of an audit performed in accordance with Government Auditing Standards in considering MABCâ€™s internal control over financial reporting and compliance. Timonium, Maryland November 5, 2013 MONARCH ACADEMY BALTIMORE CAMPUS, INC. STATEMENTS OF FINANCIAL POSITION JUNE 30, 2013 AND 2012 2013 ASSETS ASSETS Cash Grants and tuition receivable Prepaid expenses Deposits Property and equipment - net TOTAL ASSETS $ 830,477 17,507 0 0 10,845,994 $ 191,413 104,451 43,883 20,697 267,676 628,120 2012 $ 11,693,978 LIABILITIES AND NET ASSETS $ LIABILITIES Accounts payable and accrued expenses Due to related entity Note payable - net Debt TOTAL LIABILITIES $ 2,128,974 70,555 3,661,349 5,059,689 10,920,567 $ 350,134 142,084 0 0 492,218 NET ASSETS Unrestricted TOTAL LIABILITIES AND NET ASSETS 773,411 $ 11,693,978 $ 135,902 628,120 The Accompanying Notes are an Integral Part of the Financial Statements -3- MONARCH ACADEMY BALTIMORE CAMPUS, INC. STATEMENTS OF ACTIVITIES FOR THE YEARS ENDED JUNE 30, 2013 AND 2012 2013 SUPPORT AND REVENUE Program Revenue: Tuition Public Support: Fundraising and grants TOTAL SUPPORT AND REVENUE EXPENSES Functional expenses: Program: Charter School Management and general TOTAL EXPENSES Change in Net Assets Net Assets - Beginning of the Year Net Assets - End of the Year $ 2012 $ 6,086,304 $ 446,517 6,532,821 3,057,093 532,612 3,589,705 5,249,335 645,977 5,895,312 637,509 135,902 773,411 $ 2,941,410 327,626 3,269,036 320,669 (184,767) 135,902 The Accompanying Notes are an Integral Part of the Financial Statements -4- MONARCH ACADEMY BALTIMORE CAMPUS, INC. STATEMENTS OF CASH FLOWS FOR THE YEARS ENDED JUNE 30, 2013 AND 2012 2013 CASH FLOWS FROM OPERATING ACTIVITIES Change in net assets Adjustments to reconcile change in net assets to net cash provided by operating activities: Depreciation Contributed property Changes in operating assets and liabilities: Grants and tuition receivable Prepaid expenses Accounts payable and accrued expenses Net Cash Provided by Operating Activities $ 637,509 264,873 (191,475) 86,944 43,883 202,539 1,044,273 $ 2012 320,669 2,028 0 (81,770) (34,250) 342,634 549,311 CASH FLOWS FROM INVESTING ACTIVITIES Deposits made Purchases of property and equipment Net Cash Used in Investing Activities 0 (333,680) (333,680) (20,697) (263,124) (283,821) CASH FLOWS FROM FINANCING ACTIVITIES Net activity in amounts due to related entity Net Cash Used in Financing Activities NET CHANGE IN CASH CASH AT THE BEGINNING OF THE YEAR CASH AT THE END OF THE YEAR $ (71,529) (71,529) 639,064 191,413 830,477 $ (74,077) (74,077) 191,413 0 191,413 The Accompanying Notes are an Integral Part of the Financial Statements -5- 2013 Supplemental Schedule of Noncash Investing and Financing Activities: Construction in progress from proceeds of debt Acquisition of land and building via issuance of note payable Application of deposit to property and equipment Construction in progress in accounts payable and accrued expenses Supplemental Disclosures of Cash Flow Information: Interest paid, net of capitalized interest of approximately $36,000 and $0 for the years ended June 30, 2013 and 2012, respectively $ 5,059,689 3,661,349 20,697 1,576,301 $ 2012 0 0 0 0 $ 12,233 $ 9,855 The Accompanying Notes are an Integral Part of the Financial Statements -6- MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 1: SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES Nature of operations During the fiscal year ended June 30, 2011, Monarch Academy Baltimore Campus, Inc. (MABC) was incorporated as a Maryland non-stock, not-for-profit corporation. MABC was incorporated to operate a public charter school in Baltimore City (City) for students in kindergarten through eighth grade. MABC's first students enrolled in Spring 2011 for the instructional program which commenced in August 2011 for students enrolled in kindergarten through fourth grade. On November 9, 2010, the Baltimore City Board of School Commissioners granted a charter allowing MABC to operate a charter school in Baltimore City, MD. The Charter defines the City's and MABC's responsibilities in relation to the operation, management and administration of the school. The Charter has an initial term of five years, and MABC may apply for an additional five year term during the last year of the initial five year term. The Charter may be terminated by the City (subject to certain requirements), or by MABC on an annual basis (MABC must provide notice of intent to terminate by March 1 annually). Additionally, the Charter may be terminated by mutual agreement between MABC and the City. MABC's operations are funded based upon funds allocated to the school by the City in accordance with the Maryland State Department of Education approved funding model. The employees of the public charter school remain employees of the City, and the expenditures related to salaries and benefits are deducted by the City from the funded amounts provided to MABC quarterly. Additionally, other costs as negotiated, such as transportation costs, are deducted from the funded amounts provided to MABC quarterly. The revenues and the associated salaries, benefits and other costs have been reported within the accompanying financial statements on a gross basis, rather than net, in order to provide a complete picture of the school's operations and costs. Basis of accounting The financial statements are prepared on the accrual basis of accounting. Financial statement presentation MABC follows the Not-For-Profit Entities Presentation of Financial Statements Topic of the Financial Accounting Standards Board (FASB) Accounting Standards Codification which requires it to report information regarding its financial position and activities according to three classes of net assets: unrestricted net assets, temporarily restricted net assets and permanently restricted net assets. As of June 30, 2013 and 2012, there were no permanently or temporarily restricted net assets. -7- MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 1: SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Continued) Grants and tuition receivable Government and private grants are recognized based on the terms of the specific grant. Grant revenue received in advance of the grant period is recorded as deferred revenue or temporarily restricted support, depending on the nature of the transaction. Tuition receivable is recorded at the amount MABC expects to receive after year end from Baltimore City related to services provided. Accounting for contributions MABC follows the Not-For-Profit Entities Revenue Recognition Topic of the FASB Accounting Standards Codification. Under this topic of the FASB Accounting Standards Codification, MABC recognizes contributions when the donor makes a promise to give to MABC that is, in substance, unconditional. Contributions received are recorded as unrestricted, temporarily restricted, or permanently restricted support depending on the existence or nature of any donor restrictions. Contributions whose restrictions are met in the same reporting period are shown as unrestricted contributions. Property and equipment Property and equipment are recorded at cost if purchased and fair value if donated. It is MABCâ€™s policy to capitalize expenditures for property and equipment in excess of $1,000. Expenditures for repairs and maintenance are charged to expense as incurred. The cost of property and equipment is depreciated using the straight-line method over their estimated useful lives. Income taxes MABC is exempt from federal and state taxation under Section 501(c)(3) of the Internal Revenue Code, and is classified as other than a private foundation. MABC's Forms 990, Return of Organization Exempt from Income Tax, for the fiscal years ended June 30, 2013, 2012 and 2011 are subject to examination by the IRS, generally for three years after they were filed. Use of estimates Management uses estimates and assumptions in preparing financial statements in accordance with accounting principles generally accepted in the United States of America. Those estimates and assumptions affect the reported amounts of assets and liabilities, the disclosure of contingent assets and liabilities and the reported revenues and expenses. Actual results could differ from the estimates that were used. -8- MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 1: SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Continued) Functional expenses Expenses are charged directly to program, management and general or fundraising categories based on specific identification, when determinable. A reasonable allocation is made for costs not specifically identifiable. During the years ended June 30, 2013 and 2012, MABC did not expend significant resources related to fundraising. Subsequent events MABC has evaluated subsequent events through November 5, 2013, which is the date the financial statements were available to be issued. NOTE 2: PROPERTY AND EQUIPMENT The following is a summary of property and equipment at June 30, 2013 and 2012: 2013 Land Furniture and equipment Construction in progress Total Less: accumulated depreciation Total property and equipment - net $ $ 1,098,055 $ 447,178 9,567,662 11,112,895 (266,901) 10,845,994 $ 2012 0 11,316 258,388 269,704 (2,028) 267,676 $ Depreciation expense for the years ended June 30, 2013 and 2012 amounted to $264,873 and $2,028, respectively. NOTE 3: DEBT During the year ended June 30, 2013, MABC entered into a loan agreement to obtain financing necessary for the renovation of property acquired for the purpose of becoming MABC's permanent operational facility. The maximum amount available under the loan agreement is $8,900,000, and the loan is primarily funded by one financial institution in the amount of $7,150,000, however, a participating lender is funding the remaining $1,750,000. The loan requires interest only payments during the construction phase (ending April 2014), with first principal and interest payments to begin in May 2014. -9- MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 3: DEBT (Continued) The portion of the overall loan funded by the primary financial institution incurs interest during the construction phase at the greater of 5% or the sum of the prime rate plus 2%. At the conclusion of the construction phase, principal payments will commence and the interest rate will be adjusted to a fixed rate which will remain in effect until April 2019, at which time the fixed rate will be modified to a new fixed rate which will remain in effect until the maturity date (April 2024). The loan may be prepaid, however prepayment would require the payment of a fee which is dependent on the timing of the prepayment. The portion of the overall loan funded by the participating lender incurs interest during the construction phase and through April 2019 at the rate of 4.25%. At that time, the interest rate will be adjusted to a new fixed rate which will remain in effect through the maturity date (April 2024). Principal payments commence in May 2014. The loan may be prepaid, however prepayment would require the payment of a fee which is dependent on the timing of the prepayment. The loans are subject to certain financial and non-financial covenants, including a debt service coverage ratio (which will be effective upon substantial completion of the renovation project during the fiscal year ended June 30, 2014 and then will be reviewed annually thereafter), and a tangible net worth requirement, which is reviewed annually based upon the consolidated financial statements of the Children's Guild Institute, Inc. (Institute), a related entity (see Note 5). The loans are collateralized by a first deed of trust related to the improved property, a first priority lien in the rents related to a lease which exists for a portion of the acquired property (see Note 4), and essentially all other MABC assets. Additionally, the loans have been guaranteed by the Institute and the Children's Guild, Inc. (Guild) (see Note 5). However, the guarantees of the Institute and the Guild are subordinated to a different financial institution from which the Institute and the Guild have previously entered into debt agreements or provided other loan guarantees. MABC has entered into an agreement with the Institute which provides the Institute the option, subject to the approval of the primary financial institution, to purchase the land and property which was improved from the proceeds of the loans described above. The option expires in April 2025. - 10 - MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 3: DEBT (Continued) As of June 30, 2013, debt matures as follows (annual amounts below are presented under the assumption that all available loan funds will be borrowed during the construction phase, and reflect what will be repaid beginning in May 2014): Fiscal year 2014 2015 2016 2017 2018 2019 and thereafter Total $ 48,828 272,743 286,249 300,425 315,307 7,676,448 8,900,000 $ Total interest expense, including accrued interest related to the note payable described in Note 4 and interest on the intercompany line of credit described in Note 5, and net of interest which was capitalized during the year ended June 30, 2013, was $71,103 and $7,822 for the years ended June 30, 2013 and 2012, respectively. NOTE 4: ACQUISITION OF PROPERTY AND NOTE PAYABLE During the year ended June 30, 2013, MABC entered into an agreement with a seller to acquire property to be used as MABC's permanent operational facility beginning in August 2014. As a part of the agreement, MABC obtained property with an appraised fair value of $2,827,376, and additionally assumed a lease with an unrelated third party covering a small portion of the acquired property. MABC recorded an additional property value of $1,025,448 representing the present value of the future expected rental receipts from the lease, assuming an 8% discount rate and a lease term expiring in 2034. As such, the total asset recognized within property and equipment - net on the accompanying 2013 statement of financial position is $3,852,824. As consideration for the property, MABC entered into a note payable with the seller, and additionally agreed to remit to the seller the remaining rents under the lease as it existed at the time of the sale. The contractual balance of the note payable is $3,045,000 and MABC is required to make quarterly principal and interest payments of $65,320 beginning in October 2013. The note payable has a fixed interest rate of 8% and a maturity date of September 2047. However, MABC's obligations under the note will cease upon the occurrence of a termination event, as defined in the promissory note. A termination event occurs upon the later of (1) the death of the owner of the note holder, or (2) 144 months after the first payment date (September 30, 2025). MABC may prepay the balance outstanding on the note payable at any time. The note payable is subordinate to the debt described in Note 3. The Institute has guaranteed the note payable, however, the Institute's guarantee is subordinate to a different financial institution to whom the Institute had previously made guarantees. - 11 - MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 4: ACQUISITION OF PROPERTY AND NOTE PAYABLE (Continued) MABC has recognized the note payable in the accompanying 2013 statement of financial position at its present value, determined using a discount rate of 8%, and with an expected repayment period of 18.6 years (based on a life expectancy table). The repayment period was determined by a third party in accordance with a request to provide an independent valuation of the note payable as of the date of the purchase and sale agreement. The note payable has been recorded at its present value of $2,517,549 as of June 30, 2013. As MABC has committed to remit to the seller the certain rents described above, a liability for the present value of the future payments to the seller has been determined and recorded using a discount rate of 8% and an expected term through 2034. The present value of the anticipated lease payments of $1,143,800 has been added to the note payable balance. MABC has no obligation to remit any lease payments to the seller if the tenant does not extend the term of the lease or make its rental payments to MABC. The total of the present value of the note payable and the present value of the lease payment liability is $3,661,349 as of June 30, 2013. MABC recorded contribution income within public support on the accompanying 2013 statement of activities in the amount of $191,475 (representing the excess of the recorded value of the acquired property over the present value of the note payable and the present value of the lease payment liability). As of June 30, 2013, the note payable matures as follows: Fiscal year 2014 2015 2016 2017 2018 2019 and thereafter Sub-total Less: discount on note payable Plus: present value of excess lease payments Total note payable NOTE 5: RELATED PARTY TRANSACTIONS MABC has entered into transactions and/or agreements with the following related parties as of June 30, 2013 and 2012: $ 13,527 19,333 20,927 22,651 24,518 2,944,044 3,045,000 (527,451) 1,143,800 3,661,349 $ - 12 - MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 5: RELATED PARTY TRANSACTIONS (Continued) The Children's Guild Institute, Inc. (Institute) was incorporated during the year ended June 30, 2009 as a Maryland non-stock charitable supporting organization. The Institute was incorporated to provide planning and support for the causes of several organizations, including MABC. The Institute controls MABC through a majority voting interest on MABC's board of directors. MABC is included in the annual financial statements of the Institute as a consolidated, wholly-owned subsidiary. The Children's Guild, Inc. (Guild) was formed in 1953 as a Maryland not-for-profit corporation to provide facilities and opportunities to help educate children and provide individual and family counseling. The Guild primarily serves central Maryland and has several major programs, the most significant of which, as defined by a percentage of revenues, is the Guild's Special Education School program. The Guild has assisted MABC in establishing MABC's program, obtaining funding and performing management and general activities on MABC's behalf. During the fiscal year ended June 30, 2011, the Guild extended an intercompany line of credit to MABC to provide working capital. Advances under this credit facility bear interest at a fixed rate of 6% and interest payments are due monthly. The intercompany line of credit is due on demand, has maximum available borrowings of $600,000, and has a stated maturity date of June 30, 2014. The amount due to the Guild as of June 30, 2013 and 2012 relating to the intercompany line of credit was $70,555 and $142,084, respectively. For the years ended June 30, 2013 and 2012, interest expense related to this facility was $12,233 and $7,822, respectively. Effective July 1, 2011, MABC entered into a management agreement with the Guild whereby the Guild will provide management and administrative services for MABC. Management fee expense for the years ended June 30, 2013 and 2012 was $606,804 and $245,996, respectively. NOTE 6: OPERATING LEASES During the years ended June 30, 2013 and 2012, MABC operated its program in facilities under short-term lease arrangements. In April 2013, MABC acquired property and commenced significant renovations to the acquired property in order to operate its program in a permanent facility beginning in August 2013. As a condition of acquiring the property discussed above, MABC assumed an existing lease with a third party, whereby MABC receives monthly rental payments. The lease was subsequently amended in July 2013. As amended, the lease has an initial expiration date in June 2014, however, the tenant has multiple renewal options, with each option for an additional 5 years. For the year ended June 30, 2014, MABC will receive approximately $84,000 in lease payments from the third party. Rent expense, including amounts charged for rental equipment, for the years ended June 30, 2013 and 2012 was $114,847 and $185,887, respectively. - 13 - MONARCH ACADEMY BALTIMORE CAMPUS, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 7: FAIR VALUE Fair value measurement accounting literature provides a framework for measuring fair value. The framework provides a fair value hierarchy that prioritizes the inputs to valuation techniques used to measure fair value. The hierarchy gives the highest priority to unadjusted quoted prices in active markets for identical assets (level 1 measurements), the next priority to other direct or indirect observable inputs (level 2 measurements), and the lowest priority to unobservable inputs (level 3 measurements). When available, MABC measures fair value using level 1 inputs because they generally provide the most reliable evidence of fair value. The fair value of the acquired land and building (See Note 4) was partially determined based upon an appraisal (level 2 measurement). The appraisal primarily used existing data from recent sales of property in the same metropolitan area, adjusted for factors such as financing terms, conditions of sale, market conditions, location, and physical characteristics to determine fair value. NOTE 8: SUBSEQUENT EVENT The Institute has initiated a plan to obtain additional debt and refinance substantially all outstanding debt, notes payable, and mortgages payable, including those reported on the accompanying 2013 statement of financial position. The refinance is expected to occur through a tax-exempt bond offering. The plan to obtain additional debt and refinance existing debt is expected to result in changes to property ownership, with the Institute becoming the primary owner of property. In concurrence with the tax-exempt bond issue, the Institute intends to exercise its option to purchase the land and property currently owned by MABC (per Note 3). Institute anticipates entering into an agreement to lease this facility to MABC. - 14 - INDEPENDENT AUDITORS' REPORT ON INTERNAL CONTROL OVER FINANCIAL REPORTING AND ON COMPLIANCE AND OTHER MATTERS BASED ON AN AUDIT OF FINANCIAL STATEMENTS PERFORMED IN ACCORDANCE WITH GOVERNMENT AUDITING STANDARDS Board of Directors Monarch Academy Baltimore Campus, Inc. We have audited, in accordance with auditing standards generally accepted in the United States of America and the standards applicable to financial audits contained in Government Auditing Standards issued by the Comptroller General of the United States, the financial statements of Monarch Academy Baltimore Campus, Inc. (MABC), which comprise the statement of financial position as of June 30, 2013, and the related statements of activities and cash flows for the year then ended, and the related notes to the financial statements, and have issued our report thereon dated November 5, 2013. Internal Control Over Financial Reporting In planning and performing our audit of the financial statements, we considered MABC's internal control over financial reporting (internal control) to determine the audit procedures that are appropriate in the circumstances for the purpose of expressing our opinion on the financial statements, but not for the purpose of expressing an opinion on the effectiveness of MABC's internal control. Accordingly, we do not express an opinion on the effectiveness of MABC's internal control. A deficiency in internal control exists when the design or operation of a control does not allow management or employees, in the normal course of performing their assigned functions, to prevent, or detect and correct, misstatements on a timely basis. A material weakness is a deficiency, or combination of deficiencies, in internal control, such that there is a reasonable possibility that a material misstatement of the entity's financial statements will not be prevented, or detected and corrected on a timely basis. A significant deficiency is a deficiency, or combination of deficiencies, in internal control that is less severe that a material weakness, yet important enough to merit attention by those charged with governance. Our consideration of internal control was for the limited purpose described in the first paragraph of this section and was not designed to identify all deficiencies in internal control that might be material weaknesses or significant deficiencies. Given these limitations, during our audit we did not identify any deficiencies in internal control that we consider to be material weaknesses. However, material weaknesses may exist that have not been identified. Compliance and Other Matters As part of obtaining reasonable assurance about whether MABC's financial statements are free from material misstatement, we performed tests of its compliance with certain provisions of laws, regulations, contracts, and grant agreements, noncompliance with which could have a direct and material effect on the determination of financial statement amounts. However, providing an opinion on compliance with those provisions was not an objective of our audit, and accordingly, we do not express such an opinion. The results of our tests disclosed no instances of noncompliance or other matters that are required to be reported under Government Auditing Standards. Purpose of this Report The purpose of this report is solely to describe the scope of our testing of internal control and compliance and the results of that testing, and not to provide an opinion on the effectiveness of MABC's internal control or on compliance. This report is an integral part of an audit performed in accordance with Government Auditing Standards in considering MABC's internal control and compliance. Accordingly, this communication is not suitable for any other purpose. Timonium, Maryland November 5, 2013 THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 CONTENTS Page INDEPENDENT ............................................................................................................................................................................. AUDITORS' REPORT 1-2 FINANCIAL STATEMENTS ............................................................................................................................................................................. Statements of Financial Position 3 ............................................................................................................................................................................. Statements of Activities 4 ............................................................................................................................................................................. Statements of Cash Flows 5-6 ............................................................................................................................................................................. Notes to Financial Statements 7 - 12 Certified Public Accountants and Consultants INDEPENDENT AUDITORS' REPORT Board of Directors The Monarch Academy Public Charter School, Inc. We have audited the accompanying financial statements of The Monarch Academy Public Charter School, Inc., which comprise the statements of financial position as of June 30, 2013 and 2012, and the related statements of activities and cash flows for the years then ended, and the related notes to the financial statements. Management's Responsibility for the Financial Statements Management is responsible for the preparation and fair presentation of these financial statements in accordance with accounting principles generally accepted in the United States of America; this includes the design, implementation, and maintenance of internal control relevant to the preparation and fair presentation of financial statements that are free from material misstatement, whether due to fraud or error. Auditors' Responsibility Our responsibility is to express an opinion on these financial statements based on our audits. We conducted our audits in accordance with auditing standards generally accepted in the United States of America. Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements are free from material misstatement. An audit involves performing procedures to obtain audit evidence about the amounts and disclosures in the financial statements. The procedures selected depend on the auditors' judgment, including the assessment of the risks of material misstatement of the financial statements, whether due to fraud or error. In making those risk assessments, the auditor considers internal control relevant to the MAPCS's preparation and fair presentation of the financial statements in order to design audit procedures that are appropriate in the circumstances, but not for the purpose of expressing an opinion on the effectiveness of the MAPCS's internal control. Accordingly, we express no such opinion. An audit also includes evaluating the appropriateness of accounting policies used and the reasonableness of significant accounting estimates made by management, as well as evaluating the overall presentation of the financial statements. We believe that the audit evidence we have obtained is sufficient and appropriate to provide a basis for our audit opinion. TIMONIUM 9690 Deereco Road, Suite 500 Timonium, MD 21093 410 - 828 - CPAS (2727) | 410-828-9512 (FAX) COLUMBIA 9881 Broken Land Parkway, Suite 220 Columbia, MD 21046 410 - 290-3288 | 410-381-7795 (FAX) BEL AIR 109 N. Main Street, Suite C Bel Air, MD 21014 410 - 838-5717 | 410-838-2579 (FAX) www.KatzAbosch.com Members of: American Institute of Certified Public Accountants / Maryland Association of Certified Public Accountants / The Leading Edge Alliance Certified Public Accountants and Consultants Board of Directors The Monarch Academy Public Charter School, Inc. Page 2 Opinion In our opinion, the financial statements referred to above present fairly, in all material respects, the financial position of The Monarch Academy Public Charter School, Inc. as of June 30, 2013 and 2012, and the changes in its net assets and its cash flows for the years then ended in accordance with accounting principles generally accepted in the United States of America. Timonium, Maryland November 5, 2013 THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. STATEMENTS OF FINANCIAL POSITION JUNE 30, 2013 AND 2012 2013 ASSETS ASSETS Cash Prepaid expenses and other current assets Deposits and advances Property and equipment - net TOTAL ASSETS $ 144,303 58,865 60,500 3,625,007 3,888,675 $ 889,608 77,007 150,702 2,944,875 4,062,192 2012 $ $ LIABILITIES AND NET ASSETS LIABILITIES Accounts payable and accrued expenses Due to related entity Debt TOTAL LIABILITIES $ 92,658 412,477 1,999,978 2,505,113 $ 152,476 796,531 2,342,854 3,291,861 NET ASSETS Unrestricted TOTAL LIABILITIES AND NET ASSETS $ 1,383,562 3,888,675 $ 770,331 4,062,192 The Accompanying Notes are an Integral Part of the Financial Statements -3- THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. STATEMENTS OF ACTIVITIES FOR THE YEARS ENDED JUNE 30, 2013 AND 2012 2013 REVENUE AND SUPPORT Program Revenue Tuition and other revenue Public Support Fundraising and grants TOTAL REVENUE AND SUPPORT EXPENSES Functional expenses: Program: Charter School Management and general TOTAL EXPENSES Change in Net Assets Net Assets - Beginning of the Year Net Assets - End of the Year $ 2012 $ 8,140,033 $ 154 8,140,187 6,072,368 41,280 6,113,648 6,686,875 840,081 7,526,956 613,231 770,331 1,383,562 $ 5,406,263 505,753 5,912,016 201,632 568,699 770,331 The Accompanying Notes are an Integral Part of the Financial Statements -4- THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. STATEMENTS OF CASH FLOWS FOR THE YEARS ENDED JUNE 30, 2013 AND 2012 2013 CASH FLOWS FROM OPERATING ACTIVITIES Change in net assets Adjustments to reconcile change in net assets to net cash provided by operating activities: Depreciation Changes in operating assets and liabilities: Grants and contracts receivable Prepaid expenses and other current assets Deposits and advances Accounts payable and accrued expenses Deferred revenue Net Cash Provided by Operating Activities $ 613,231 242,856 0 18,142 0 (59,818) 0 814,411 $ 2012 201,632 199,096 30,270 29,405 (70,909) 44,979 (30,270) 404,203 CASH FLOWS FROM INVESTING ACTIVITIES Purchases of property and equipment Net Cash Used in Investing Activities (832,786) (832,786) (208,665) (208,665) CASH FLOWS FROM FINANCING ACTIVITIES Proceeds from debt - net of refinance Principal payments on debt Net repayments and advances to related entity Net Cash Provided by (Used in) Financing Activities NET INCREASE (DECREASE) IN CASH CASH AT THE BEGINNING OF THE YEAR CASH AT THE END OF THE YEAR $ 0 (342,876) (384,054) (726,930) (745,305) 889,608 144,303 $ 1,071,725 (314,586) (216,570) 540,569 736,107 153,501 889,608 The Accompanying Notes are an Integral Part of the Financial Statements -5- 2013 Supplemental Schedule of Noncash Investing and Financing Activities: Repayment of affiliate's note payable to a bank with proceeds from refinance note payable Application of deposit to fixed assets Leasehold improvements and equipment transferred from affiliate due to assumption of lease and repayment of affiliate note payable, net of depreciation of $118,277 recorded by affiliate prior to July 1, 2011 Supplemental Disclosures of Cash Flow Information: Interest paid $ 118,199 $ $ 0 90,202 $ 2012 435,715 0 0 988,278 93,138 The Accompanying Notes are an Integral Part of the Financial Statements -6- THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 1: SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES Nature of operations During the fiscal year ended June 30, 2008, The Monarch Academy Public Charter School, Inc. (MAPCS) was incorporated as a Maryland non-stock, not-for-profit corporation. MAPCS was incorporated to operate a public charter school in Anne Arundel County (County) for students in kindergarten through eighth grade. MAPCS's first students enrolled in Spring 2009 and the instructional program commenced in August 2009. MAPCS operates as a public charter school in connection with a Charter School Agreement with the County. The Charter School Agreement defines the County's and MAPCS's responsibilities in relation to the operation, management, and administration of the school. The school's operations are funded based upon a County determined "Per Pupil Expenditure Rate", which is established based upon the number of certified enrolled pupils at the charter school as of September 30th of each year. The employees of the public charter school remain employees of the County, and the expenditures related to salaries and benefits are deducted from the "Per Pupil Expenditure Rate", along with an administration fee withheld by the County, before the net funding proceeds are remitted to MAPCS monthly. The revenues and the associated salaries and benefits and fees have been reported within the accompanying financial statements on a gross basis, rather than net, in order to provide a complete picture of the charter school's operations and costs, and to comply with reporting requirements of the County. MAPCS has been awarded a contract with the County to operate a contract school. The contract school, to be known as Monarch Global Academy Public Contract School, is expected to enroll its first students during the year ended June 30, 2014, and commence its instructional program in August 2014. It is anticipated that the Children's Guild Institute, Inc. (Institute) will acquire and construct a facility to be leased by the MAPCS for use in its operations. As further described in Note 5, the Institute is a related entity. Additionally, in July 2013, the County approved a new charter school to be operated by MAPCS beginning in August 2015. Basis of accounting The financial statements are prepared on the accrual basis of accounting. Financial statement presentation MAPCS follows the Not-For-Profit Entities Presentation of Financial Statements Topic of the Financial Accounting Standards Board (FASB) Accounting Standards Codification. Under this topic of the FASB Accounting Standards Codification, MAPCS is required to report information regarding its financial position and activities according to three classes of net assets: unrestricted net assets, temporarily restricted net assets and permanently restricted net assets. During the years ended June 30, 2013 and 2012, there were no temporarily or permanently restricted net assets. -7- THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 1: SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Continued) Accounting for contributions MAPCS follows the Not-For-Profit Entities Revenue Recognition Topic of the FASB Accounting Standards Codification. Under this topic of the FASB Accounting Standards Codification, MAPCS recognizes contributions when the donor makes a promise to give to MAPCS that is, in substance, unconditional. Contributions received are recorded as unrestricted, temporarily restricted, or permanently restricted support depending on the existence or nature of any donor restrictions. Contributions whose restrictions are met in the same reporting period are shown as unrestricted contributions. Property and equipment and depreciation Property and equipment are recorded at cost if purchased and fair value if donated. It is MAPCSâ€™s policy to capitalize expenditures for property and equipment in excess of $1,000. Expenditures for repairs and maintenance are charged to expense as incurred. The cost of property and equipment is depreciated using the straight-line method over their estimated useful lives. Income taxes MAPCS is exempt from federal and state taxation under Section 501(c)(3) of the Internal Revenue Code, and is classified as other than a private foundation. MAPCS's Forms 990, Return of Organization Exempt from Income Tax, for the years ended June 30, 2013, 2012 and 2011 are subject to examination by the IRS, generally for three years after they were filed. Use of estimates Management uses estimates and assumptions in preparing financial statements in accordance with accounting principles generally accepted in the United States of America. Those estimates and assumptions affect the reported amounts of assets and liabilities, the disclosure of contingent assets and liabilities and the reported revenues and expenses. Actual results could differ from the estimates that were used. Functional expenses Expenses are charged directly to program, management and general or fundraising categories based on specific identification, when determinable. A reasonable allocation is made for costs not specifically identifiable. MAPCS, during the years ended June 30, 2013 and 2012, did not expend significant resources related to fundraising. Subsequent events MAPCS has evaluated subsequent events through November 5, 2013, which is the date the financial statements were available to be issued. -8- THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 2: PROPERTY AND EQUIPMENT The following is a summary of property and equipment at June 30, 2013 and 2012: 2013 Leasehold improvements Furniture and equipment Construction in progress Total Less: accumulated depreciation Total property and equipment - net $ $ 3,463,576 $ 724,420 2,296 4,190,292 (565,285) 3,625,007 $ 2012 2,820,578 428,775 203,724 3,453,077 (508,202) 2,944,875 Depreciation expense for the years ended June 30, 2013 and 2012 amounted to $242,856 and $199,096, respectively. NOTE 3: LINE OF CREDIT In July 2009, MAPCS obtained a revolving line of credit facility with a bank. Advances under the credit facility bear interest at the greater of the one-month LIBOR rate plus 1.90% or 2.75% (the interest rate floor), and interest payments are due monthly. The maximum amount which may be advanced is $250,000. Advances are due upon demand and are collateralized by a lien on all deposits of MAPCS held by the bank and other personal property. The Institute and The Children's Guild, Inc. (Guild) guarantee the line of credit. There were no outstanding borrowings on the line as of June 30, 2013 or 2012. NOTE 4: DEBT During the year ended June 30, 2012, MAPCS obtained a $2,400,000 loan with the bank with which they have the credit facility, refinancing $1,150,000 of debt. A portion of the loan proceeds were used to repay the remaining balance of bank debt related to leasehold improvements originally recorded on the financial statements of the Guild, as MAPCS, in July 2011, assumed the lease related to the improvements and has the benefit of the related improvements. The note bears interest at a fixed rate of 4.61% and matures in April 2019. The loan is being repaid, beginning in May 2012, through 84 monthly installments of principal and interest. The note is secured by a lien on all MAPCS deposits held by the bank and other personal property. The note payable is guaranteed by the Guild and the Institute. MAPCS is required to meet certain covenants in connection with the note payable with the bank, including a cash flow coverage ratio. -9- THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 4: DEBT (Continued) As of June 30, 2013, debt matures as follows: Fiscal Year 2014 2015 2016 2017 2018 2019 Total $ 342,876 342,876 342,876 342,876 342,876 285,598 1,999,978 $ Total interest expense, including interest on the intercompany line of credit described in Note 5, was $118,199 and $93,138 for the years ended June 30, 2013 and 2012, respectively. NOTE 5: RELATED PARTY TRANSACTIONS MAPCS has entered into transactions and/or agreements with the following related parties as of June 30, 2013 and 2012: The Guild was formed in 1953 as a Maryland not-for-profit corporation to provide facilities and opportunities to help educate children and provide individual and family counseling. The Guild primarily serves central Maryland and has several major programs, the most significant of which, as defined by a percentage of revenues, is the Guild's Special Education School program. The Guild has assisted MAPCS in establishing MAPCS's program, obtaining financing and performing management and general activities on MAPCS's behalf. During the fiscal year ended June 30, 2009, the Guild extended an intercompany line of credit to MAPCS to provide working capital. Advances under this credit facility bear interest at a fixed rate of 6% and interest payments are due monthly. The intercompany line of credit is due on demand and has a stated maturity date of June 30, 2014. The maximum amount that may be advanced under this credit facility at any one time is $1,000,000. The amount due to the Guild as of June 30, 2013 and 2012 relating to the intercompany line of credit was $412,477 and $796,531, respectively. For the years ended June 30, 2013 and 2012, interest expense related to this facility was $41,764 and $29,527, respectively. During the fiscal year ended June 30, 2009, the MAPCS entered into a management agreement with the Guild whereby the Guild will provide management and administrative services for MAPCS. Effective January 1, 2012, the Guild requested, and the MAPCS board approved, an amendment to the agreement increasing the annual management fee to 8% of tuition revenues. Management fee expense for the years ended June 30, 2013 and 2012 totaled $648,471 and $317,168, respectively. The agreement automatically renews each year unless properly terminated by either MAPCS or the Guild. - 10 - THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 5: RELATED PARTY TRANSACTIONS (Continued) Effective July 1, 2011, MAPCS assumed a certain lease obligation of the Guild related to a lease for program space, and MAPCS used this space in its program. Additionally, as previously described, MAPCS used a portion of its refinance loan proceeds to repay the Guild's remaining obligations on a note payable originally entered into by the Guild to finance the leasehold improvements to the space now used by MAPCS. Therefore, effective July 1, 2011, the Guild transferred to MAPCS the net book value of the leasehold improvements and related equipment, and MAPCS depreciates these leasehold improvements and equipment over the remaining useful lives. The net book value of the leasehold improvements and equipment on July 1, 2011 was $988,278. The Institute was incorporated during the year ended June 30, 2009 as a Maryland non-stock charitable supporting organization. The Institute was incorporated to provide planning and support for the causes of several organizations, including MAPCS. The Institute controls MAPCS through a majority voting interest on the MAPCS's board of directors. MAPCS will at times contract with the Institute to receive training services. MAPCS, along with the related entities described above, is considering a restructuring of operational and financial management strategies. It is currently anticipated that the related entities may realign property ownership, as well as any related debt, under the umbrella of the Institute. It is anticipated that during the fiscal year ended June 30, 2014, the Organization may enter into agreements with related entities and required third parties to document this restructuring, however, no formal agreements have been signed as of the date these financial statements were available to be issued. NOTE 6: OPERATING LEASES MAPCS entered into a five-year operating lease in March 2009 for space located in Glen Burnie, MD. The space rented is used for the operations of MAPCS. The lease includes four renewal options of five years each. During the year ended June 30, 2012, the lease was amended and the initial expiration date was adjusted to August 2019. As described previously, effective July 1, 2011, MAPCS assumed a lease obligation of the Guild, which allowed MAPCS to expand its program. The minimum future rental payments required under non-cancelable operating leases having terms in excess of one year as of June 30, 2013 are as follows: Fiscal Year Ended: 2014 2015 2016 2017 2018 2019 and thereafter Total $ 474,700 487,438 341,638 351,536 361,799 434,571 2,451,682 $ - 11 - THE MONARCH ACADEMY PUBLIC CHARTER SCHOOL, INC. NOTES TO FINANCIAL STATEMENTS JUNE 30, 2013 AND 2012 NOTE 6: OPERATING LEASES (Continued) Rent expense, including amounts charged by the landlord for operating expenses and other equipment rentals, for the years ended June 30, 2013 and 2012 was $586,796 and $457,733, respectively. NOTE 7: COMMITMENT During the fiscal year ended June 30, 2009, MAPCS entered into an agreement with a transportation company for bus services. During the fiscal year ended June 30, 2012, this agreement was renewed and extended through June 2017, with annually escalating rates. MAPCS may terminate the agreement with written notice in situations where the transportation company does not provide sufficient services, as specified in the agreement. For the years ended June 30, 2013 and 2012, the total amount of expense incurred by MAPCS under this agreement totaled $845,790 and $681,352, respectively. - 12 -