4th Grade Math Curriculum Date 8-4-11 I can: 8-8-12, 2011

I can: • •

Math Lesson

Concept

1.1 Student Ref. Book

1.1 Introduce the Student Reference Book

1.2 Points, Line Segments, Lines, and Rays 1.3 Angles, Triangles, and Quadrangles 1.4 Parallelograms 1.5 Polygons

1.2 Introduce tools for geometry; and to review points, line segments, lines, and rays. 1.3 Construct angles, triangles, and quadrangles, and to classify quadrangles. 1.4 Classify quadrangles based on their properties. 1.5 Identify properties of polygons and distinguish between convex and nonconvex (concave) polygons; and to explore geometric definitions and classification.

KCAS

4.G.1 4.G.2 4.MD.5.A,B

Flashback s

1-4

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines in two-dimensional figures. • Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. • An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. • An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 8-15-19, 1.6 Drawing Circles 1.6 Explore regular polygons; and practice 4.MD.5 5-8 2011 with a Compass using a compass. Aug. 12-½ 1.7 Circle 1.7 Define a circle; and to explore designs day Constructions with circles. 1.8 Hexagon and 1.8 Construct figures with a compass and a Triangle Constructions straightedge. 1.9 Review and Assess 1.9 Review and Assess • I can…. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. • Identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines in two-dimensional figures. • Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. • An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 8-22-26, 2.1 A Visit to 2.1 Review and find examples of the 4.NBT.1 9-12 2011 Washington, D.C. various ways in which numbers are used; 4.NBT.2 2.2 Many Names for and to introduce the World Tour Project. Numbers 2.2 To find equivalent names for numbers. 2.3 Place Value in 2.3 Name values of digits in numbers up to Whole Numbers hundred-millions; and to read and write 2.4 Place Value with a numbers up to hundred-millions. Calculator 2.4 Practice place-value skills through a 2.5 Organizing and calculator routine; and to read and write Displaying Data large numbers. 2.5 Organize and display data with a tally chart; and to determine the maximum, minimum, range, and mode of a set of data. I can… • Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. e.g. 700 / 70 = 10. • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. • Compare two multi-digit numbers based on meanings of the digits in each place, using >, <, or =. symbols.

Aug. 29 -Sept. 2, 2011

2.6 Review how to display a set of data with a line plot; and review how to find the median of a set of data. 2.7 Review the partial-sums method for addition; and introduce a column-addition method similar to the traditional addition algorithm. 2.8 Measure length to the nearest ½ cm; and to make and use bar graphs for a set of data. I can… Add or subtract multi-digit whole numbers using the standard algorithm. Sept. 6-9, 2.9 Subtraction of 2.9 Review the trade-first and counting-up 2011 Multidigit #s methods for subtraction; introduce the 2.10 Review and partial-differences method for subtraction. Assess 2.10 Review and Assess 3.1 Multiplication Facts 3.1 Review strategies for multiplication 3.2 Multiplication Facts facts; and to work toward instant recall of Practice the multiplication facts. 3.2 Establish a 50-facts test routine; and to practice multiplication facts. I can… Add or subtract multi-digit whole numbers using the standard algorithm. Sept. 12-16, 3.3 More Multiplication 3.3 To give a 50-facts test and record 2011 Facts Practice results; and to practice multiplication facts.

4.NBT.4

13-16

4.NBT.4

17-20

Sept. 19-23, 2011

4.MD.2

I can… •

2.6 The Median 2.7Addition of Multidigit #’s 2.8 Displaying Data with a Bar Graph

3.4 Multiplication, Division, and Fractions 3.5 World Tour: Flying to Africa 3.6 Finding Air Distances 3.7 A Guide for Solving Number Stories

3.4 Explore the relationship between multiplication and division and between division and fractions; and to practice division facts. 3.5 Continue World Tour Project 3.6 To find air distances. 3.7 Introduce a simplified approach to solving number stories; and to solve # stories.

21-24

25-28

Use addition, subtraction, multiplication, and division to solve word problems involving distance, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. • Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Sept. 26-30, Fall Break Fall Break Fall Fall Break 2011 Break Oct. 10-14, 3.8 True or False # 3.8 Review the meanings of # sentences; 4.NBT.2 29-32 2011 Sentences and to determine whether # sentences are 3.9 Parentheses in # true or false. Sentences 3.9 Review the use of parentheses in # 3.10 Open Sentences sentences. 3.11 Logic Problems 3.10 Introduce vocabulary and notation for 3.12 Review and open sentences; and to solve open Assess sentences. 3.11 To develop reasoning skills. 3.12 Review and Assess • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. • Compare two multi-digit numbers based on meanings of the digits in each place, using >, <, or =. Oct. 17-21, 4.1 Decimals: Review 4.1 Review basic concepts and notation for 4.NF.5 33-36 2011 of Basic Concepts decimals through hundredths. 4.NF.7 4.2 Comparing and 4.2 Compare and order decimals in tenths Ordering Decimals and hundredths. 4.3 Estimating with 4.3 To learn why decimals are useful; and to Decimals estimate sums and differences of decimals. 4.4 Decimal Addition 4.4 To extend methods for whole-# addition and Subtraction and subtraction to decimals. I can… • Express a fraction with a denominator 10 as an equivalent fraction with denominator 100, and use this

technique to add two fractions with respective denominators 10 and 100. e.g., 3/10 = 30/100 and add 3/10 + 4/100 = 34/100 because 3/10 = 30/100. • Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, <, or =, and justify the conclusions, e.g, by using a visual model. Oct. 24-28, 4.5 Decimals in Money 4.5 To compute balances in savings 4.NF.6 37-40 2011 4.6Thousandths account. Oct. 26-1/2 4.7 Metric Units of 4.6 To extend basic concepts and notation day Length for decimals to thousandths. 4.8 Personal 4.7 To review the relationships among References for Metric metric units of length; and to work with Length metric measurements. 4.8 To establish personal references for metric units of length. • Use decimal notation for fractions with denominators 10 or 100. e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters, locate 0.62 on a number line diagram. Oct. 314.9 Measuring in 4.9 Measure lengths to the nearest 4.MD.1 41-44 Nov. 4, 2011 Millimeters millimeter; and to convert measurements 4.10 Decimal Place between mm and cm. Value 4.10 To summarize the concepts presented 4.11 Review and in this unit by extending the base-ten Assess place-value system to decimals. 4.11 Review and Assess I can… • Know relative sizes of measurement units within one system of units including km, m, cm, kg,g, lb, oz, l, ml, hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. e.g., know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1,12), (2,24) (3,36),…. Nov. 7-11, 5.1 Extended 5.1 Extend basic multiplication facts to 4.NBT.3 45-48 2011 Multiplication Facts products of ones and tens and products of *Nov. 8th No 5.2 Multiplication tens and tens. School Wrestling 5.2 Practice the extended multiplication 5.3 Estimating Sums facts; and to introduce the basic principles 5.4 Estimating of multiplication with multidigit numbers. Products 5.3 Examine situations in which it is appropriate to make an estimate; and to estimate sums. 5.4 Estimate whether a product is in the tens, hundreds, thousands, or more. I can…. • Use place value understanding to round multi-digit whole numbers to any place. Nov. 14-18, 5.5 The Partial5.5 To learn and practice the partial4.NBT.5 DB 4th 2011 Products Algorithm for products algorithm for 1-digit multipliers. 23,24,25,26 Multiplication (Part 1) 5.6 To learn and practice the partial5.6 The Partialproducts algorithm for 2-digit multipliers. Products Algorithm for 5.7 To learn and practice the lattice Multiplication (Part 2) method for multiplication. 5.7 Lattice 5.8 To read, write, and compare large Multiplication numbers using patterns in the base-ten 5.8 Big Numbers place-value system. I can… • Multiply a 4 digit whole number by a 1 digit whole number. • Multiply 2 2 digit whole numbers. • Illustrate and explain my calculations by using equations, rectangular arrays, and/or area models. Nov. 21-25, Thanksgiving Math To review math skills 4.NBT.4 2011 *Nov. 23-25, No School I can… Add or subtract multi-digit whole numbers using the standard algorithm. Nov. 285.9 Powers of 10 5.9 Introduce exponential notation for 4.NBT.3 49-52 Dec. 2, 2011 5.10 Rounding and powers of 10 as a way of naming the Reporting Large values of places in our base-ten system. Numbers 5.10 To discuss sensible ways of reporting a 5.11 World Tour: count when a large number of items has

Traveling to Europe 5.12 Review and Assess

been counted. 5.11 To look up and compare numerical data, including geographical measurements. 5.12 Review and Assess I can… Use place value understanding to round multi-digit whole numbers to any place. Dec. 5-9, 6.1 A Multiple Strategy 6.1 To solve equal-grouping division stories 4.NBT.6 53-56 2011 for Division by using a multiples-of-10 strategy. 6.2 The Partial6.2 To introduce and practice a “low stress” Quotients Division division algorithm. Algorithm 6.3 To solve multiplication and division 6.3 Multiplication and number stories, using diagrams to organize Division # Stories information. 6.4 Expressing and 6.4 To express remainders in division as Interpreting fractions or decimals, and answers as Remainders mixed numbers or decimals; and to interpret remainders in problem contexts. I can… • Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Dec. 12-16, 2011 Dec. 17Jan. 1, 2012 Jan. 2-6, 2012

Christmas Play

Christmas Play

Christmas Break

Christmas Break

6.5 Rectangular Coordinate Grids for Maps 6.6 Rotations and Angles 6.7 Using a Circular Protractor

6.5 To use letter-number pairs and ordered pairs of numbers to locate points on a rectangular grid; and to use a map scale. 6.6 To review rotations; and to make and use a circular protractor. 6.7 To use a circular protractor to measure and draw angles less than 360º.

57-60 Christma s Break 4.MD.6

Christmas Break 61-64

I can… • Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Jan. 9-13, 6.8 The Half-Circle 6.8 To classify angles as acute, right, 4.MD.6 65-68 2012 Protractor obtuse, straight, and reflex; and to use a 6.9 The Global Grid half-circle protractor to measure angles. System 6.9 To introduce the partitioning of the 6.10 Latitude and globe using circles of latitude and Longitude semicircles of longitude; and to use a half6.11 Review and circle protractor to draw angles. Assess 6.10 To find the latitude and longitude of given places using a globe and a map; and to identify places for which the latitude and longitude are given. 6.11 Review and Assess I can… Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Jan. 16-20, 7.1 Review of Basic 7.1 To review fractions as parts of a whole 4.NF.1 69-72 2012 Fraction Concepts (ONE), fractions on number lines, and uses *Jan. 16th 7.2 Fractions of Sets of fractions. No School 7.3 Pattern-Block 7.2 To find fractional parts of sets. Fractions 7.3 To find fractional parts of polygonal 7.4 Fraction Addition regions. and Subtraction 7.4 To use pattern blocks to help add and subtract fractions. I can… Explain why a fraction a/b is equivalent to a fraction (n • a)/(n • b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Jan. 23-27, 7.4 Fraction Addition 7.4 To use pattern blocks to help add and 4.NF.3.a, 73-76 2012 and Subtraction subtract fractions. b,c,d 7.5Clock Fractions 7.5 To model fractions on a clock face; and

to use a clock face to help add and subtract fractions. I can…. Understand a fraction a/b with a>1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g. by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. Jan. 30 -Feb. 3, 2011

7.6 Many Names for Fractions 7.7 Equivalent Fractions 7.8 Fractions and Decimals 7.9 Comparing Fractions

7.6 To identify equivalent fractions. 7.7 To develop and use a rule for generating equivalent fractions. 7.8 To rename fractions as decimals and decimals as fractions; and to explore the relationship between fractions and division. 7.9 To order sets of fractions.

4.NF.1 4.NF.2

77-80

I can…

Explain why a fraction a/b is equivalent to a fraction (n • a)/(n • b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. • Compare two fractions with different numerators and different denominators, e.g. by creating common denominators or numerators, or by comparing to a benchmark fraction such as •••. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <, >, =, and justify the conclusion, e.g. by using a visual fraction model. Feb. 6-10, 7.10 The ONE for 7.10 To find the whole, or ONE, for given 4.NF.3 81-84 2012 Fractions fractions. 7.11 Probability, 7.11 To review basic ideas of probability, Fractions, and including fairness and expected results; Spinners and to apply knowledge of fractions to 7.13 Review and spinners. Assess 7.13 Review and Assess I can… Understand a fraction a/b with a>1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Feb. 13-17, 2012

7.12 Cube-Drop Experiment 8.1 Kitchen Layouts and Perimeter 8.2 Scale Drawings 8.3 Area 8.4 What is the Area of My Skin?

7.12 To compare predicted and actual results from an experiment with random outcomes. 8.1 To measure and add distances in feet and inches; to find the medians and other landmarks of sets of measurements; and to find the perimeters of triangles. 8.2 To measure distances to the nearest foot; and to use measurements and a given scale to create a scale drawing on a grid. 8.3 To review basic area concepts; to estimate the area of a polygon by counting unit squares; and to use a scale drawing to find area. 8.4 To estimate the area of a surface having a curved boundary; and to convert measurements from one unit to another.

4.MD.3

85-88

I can… Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Feb. 20-24, 2012 Feb. 20th No School

8.5 Formula for the Area of a Rectangle 8.6 Formula for the Area of a Parallelogram 8.7 Formula for the Area of a Triangle

8.5 To develop and use a formula for the area of a rectangle. 8.6 To review the properties of parallelograms; and to develop and use a formula for the area of a parallelogram. 8.7 To develop and use a formula for the area of a triangle.

4.MD.3

89-92

I can… Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Feb. 27 8.8 Geographical 8.8 To examine how geographical areas 4.MD.3 93-96 -March 2, Area Measurements are measured; and to use division to 2012 8.9 Review and Assess compare two quantities with like units. 8.9 Review and Assess I can… Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. March 5-9, G-Made G-Made G-Made 2012 7th ½ day March 129.1 Fractions, 9.1 To use percents to describe real-life 4.NF.1 97-100 16, 2012 Decimals, and situations; and to practice naming Percents equivalencies among fractions, decimals, 9.3 Using a Calculator and percents. to Convert Fractions 9.2 To rename “easy” fractions (fourths, to Decimals fifths, and tenths) as decimals and 9.4 Using a Calculator percents; and to solve percent problems to Convert Fractions by using equivalent fractions. to Percents 9.3 To rename any fraction as a decimal by using a calculator; and to memorize fractions/percent equivalencies for “easy” fractions (fourths, fifths, and tenths). 9.4 To rename fractions as percents using a calculator; and to solve number stories involving discounts expressed as percents. I can… Explain why a fraction a/b is equivalent to a fraction (n • a)/(n • b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. March 199.5 Conversions 9.5 To look up and record numerical data; 4.NF.7 101-104 23, 2012 among Fractions, to rename fractions as percents using a Decimals, and calculator; and to rename decimals as Percents percents. 9.6 Comparing the 9.6 To organize and tabulate survey data; Results of a Survey and to use percents to compare quantities 9.7 Comparing expressed as fractions with unlike Population Data denominators. 9.7 To rank and compare data that are reported as percents; and to display ranked data by coloring maps. I can… Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, <, or =, and justify the conclusions, e.g, by using a visual model. March 269.8 Multiplication of 9.8 To multiply decimals by whole numbers; Not 105-108 30, 2012 Decimals and to practice the partial-products and KCAS 9.9 Division of lattice methods for multiplication. Decimals 9.9 To divide decimals by whole numbers; 9.10 Review and and to practice the partial-quotients Assess division algorithm introduced in Unit 6. 9.10 Review and Assess I can… Multiply and divide decimals by whole numbers. April 2-6, Spring Spring Break Spring Break Spring Break

2012 April 9-13, 2012

10.1 Explorations with a Transparent Mirror 10.2 Finding Lines of Reflection 10.3 Properties of Reflections 10.4 Line Symmetry

10.1 To explore reflections of 2-dimensional figures. 10.2 To explore reflections; and to identify lines of reflection. 10.3 To discover basic properties of reflections. 10.4 To explore the connection between reflections and line symmetry.

Break 4.G.3

109-112

I can… •

Recognize a line of symmetry for a two-dimensional figure as a line across a figure such that the figure can be folded along the line into matching parts. • Identify line-symmetric figures and draw lines of symmetry. April 16-20 10.5 Frieze Patterns 10.5 To explore an application of Not 113-116 2012 10.6 Positive and reflections, rotations, and translations. KCAS Negative Numbers 10.6 To explore addition of integers. 10.7 Review and 10.7 Review and Assess. Assess I can… Use a number line to add positive and negative integers. April 23-27, Math Review Math Review 117-120 2012 April 30 -May 4, 2012 May 7-11, 2012 May 14-18, 2012

Testing

Testing

Testing

Testing

Testing

Testing

Testing

Testing

11.1 Weight 11.2 Geometric Solids 11.3 Constructing Geometric Solids

11.1 To review grams and ounces as units of weight; and to estimate and measure weights in grams and ounces. 11.2 To review properties of common geometric solids. 11.3 To identify geometric solids, given their properties; and to construct polyhedrons with straws and twist-ties.

4.MD.1

I can…. Know relative sizes of measurement units within one system of units including km, m, cm, kg,g, lb, oz, l, ml, hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. e.g., know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1,12), (2,24) (3,36),….