Core Skills Activities - the activities within each mission progresses from DOK 1 to DOK 3 to master each standard. Each Core Skills Activity is a set of standards-based basic skills practice questions.
Practice Drill Questions - practice problems requiring the application of skills and real-world problem-solving. Each set of mission questions progresses from DOK 1 to DOK 3.
DIGITAL COMPONENT:
Five-Star Challenge - standards-based assessments that measure students’ depth of knowledge including their ability to reason abstractly, create models, write arguments and critique strategies.
MATH BOOTCAMP® - SMART TO THE CORE STUDENT BOOKLET - GRADE 5 (FLORIDA)
Publisher: J&J Educational Boot Camp, Inc. Content Development: Educational Bootcamp
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MISSION 1
Understanding Place Value
MISSION 2
Reading and Writing Multi-Digit Numbers with Decimals
MISSION 3
Composing and Decomposing MultiDigit Numbers
MISSION 4
Plotting and Ordering Multi-Digit Numbers
MISSION 5
MA.5.NSO.1.1
Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right.
MA.5.NSO.1.3
Compose and decompose multi-digit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions or equations.
MA.5.NSO.1.4 Plot, order and compare multi-digit numbers with decimals up to the thousandths.
Rounding Multi-Digit Numbers MA.5.NSO.1.5
MISSION 6
Multiplying Multi-Digit Whole Numbers
MISSION 7
Dividing Multi-Digit Whole Numbers
MISSION 8
MA.5.NSO.2.1
MA.5.NSO.2.2
Adding and Subtracting Multi-Digit Numbers MA.5.NSO.2.3
MISSION 9
Multiplying and Dividing Multi-Digit Numbers with Decimals
MISSION 10
Dividing Two Whole Numbers as a Fraction
MISSION 11
Adding and Subtracting Fractions with Unlike Denominators
MA.5.NSO.2.5
Round multi-digit numbers with decimals to the thousandths to the nearest hundredth, tenth or whole number.
Multiply multi-digit whole numbers including using a standard algorithm with procedural fluency.
Divide multi-digit whole numbers, up to five digits by two digits, including using a standard algorithm with procedural fluency. Represent remainders as fractions.
Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.
Multiply and divide a multi-digit number with decimals to the tenths by one-tenth and one-hundredth with procedural reliability.
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MA.5.NSO.2.4
MA.5.FR.1.1
MA.5.FR.2.1
Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value.
Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction.
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Add and subtract fractions with unlike denominators, including mixed numbers and fractions greater than 1, with procedural reliability. 81 - 88
MISSION 12
Multiplying Fractions by Fractions
MISSION 13
Predicting the Relative Size of the Product
MISSION 14
Dividing Unit Fractions by Whole Numbers
MISSION 15
Solve Multi-Step Real-World Problems
MISSION 16
Solve Real-World Problems Involving Fractions
MA.5.FR.2.2
MA.5.FR.2.3
MA.5.FR.2.4
MA.5.AR.1.1
MA.5.AR.1.2
Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.
When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.
Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.
Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context.
Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1.
MISSION 17 Solve Real-World Problems Involving Division MA.5.AR.1.3 Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
MISSION 18
Translate Real-World Problems Into Numerical Expressions MA.5.AR.2.1
Translate written real-world and mathematical descriptions into numerical expressions and numerical expressions into written mathematical descriptions.
MISSION 19 Using the Order of Operations MA.5.AR.2.2 Evaluate multi-step numerical expressions using order of operations.
MISSION 20 True or False Equations and Determining the Unknown
MISSION 21 Writing Equations to Determine the Unknown
MISSION 22 Rules for Describing Patterns as an Expression
MISSION 23 Mean, Median, Mode, and Range
MA.5.AR.2.3
MA.5.AR.2.4
MA.5.AR.3.1
Determine and explain whether an equation involving any of the four operations is true or false.
Given a mathematical or real-world context, write an equation involving any of the four operations to determine the unknown whole number with the unknown in any position.
Given a numerical pattern, identify and write a rule that can describe the pattern as an expression.
MA.5.AR.3.2 Given a rule for a numerical pattern, use a two-column table to record the inputs and outputs.
- 184
MISSION 24 Converting Measurement Units
MISSION 25
Solving Real-World Problems Involving Money
MISSION 26
Classifying Triangles and Quadrilaterals
MISSION 27
Classifying ThreeDimensional Figures
MISSION 28
Finding the Perimeter and Area of a Rectangle
MISSION 29
Using Volume as an Attribute of ThreeDimensional Figures
MISSION 30
Finding the Volume of a Right Rectangular Prism
MISSION 31
Solving Real-World Problems Involving Volume
MISSION 32
Plotting and Labeling Ordered Pairs
MISSION 33 Plotting Points Representative of Real-World Problems
MISSION 34
Creating Tables, Graphs, and Line Plots
MISSION 35
Classifying ThreeDimensional Figures
MA.5.M.1.1
MA.5.M.2.1
MA.5.GR.1.1
MA.5.GR.1.2
Solve multi-step real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement.
Solve multi-step real-world problems involving money using decimal notation.
MA.5.GR.2.1
MA.5.GR.3.1
Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category.
Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres.
Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas.
Explore volume as an attribute of three-dimensional figures by packing them with unit cubes without gaps. Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes.
MA.5.GR.3.2
MA.5.GR.3.3
MA.5.GR.4.1
MA.5.GR.4.2
Find the volume of a right rectangular prism with wholenumber side lengths using a visual model and a formula.
Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem.
Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane.
Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.
MA.5.DP.1.1
MA.5.DP.1.2
Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots.
Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range.
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There are three Core Skills practice activities in each mission that help students in build confidence while improving their math skills. They include 20 basic questions worth 5 points each, challenging students' thinking while facilitating their growth. These practice activities increase in difficulty from Depth of Knowledge level 1 to 3, promoting daily progress in math.
Practice Drills are critical components of the Smart to the Core curriculum. These five-question sets provide students with ample opportunities to hone their assessment skills. After completing the Core Skills activities, students should move on to the Practice Drills, progressing towards mastery. Each set of Practice Drills is carefully designed to simulate the types of questions that students may encounter on assessments.
The Five-Star Challenge is an end-of-mission, 10-question assessment that responds to the Math Bootcamp Intervention. The Five-Star Challenge Drill indicates that a customized learning plan is needed for students who have not yet mastered the standard. Students who earn a rating of 1, 2, or 3 stars should be placed in lessons within ED Basecamp, our virtual learning platform.
COMPOSING AND DECOMPOSING MULTI-DIGIT NUMBERS
MA.5.NSO.1.3
Compose and decompose multi-digit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions or equations.
To compose a number, we combine the values of its individual digits in their respective places. Each digit in a multi-digit number represents a specific place value such as ones, tens, hundreds, thousandths, and so on. By adding these values together, we can create a complete number.
Example: Compose the number 0.735. The digit 7 is in the tenths place, representing 7 tenths (0.7). The digit 3 is in the hundredths place, representing 3 hundredths (0.03). Finally, the digit 5 is in the thousandths place, representing 5 thousandths (0.005).
TENS
By adding these values together, we compose the number 0.735.
Each digit represents a specific place value, such as ones, tens, hundreds, thousandths, and so on. Understanding the value of each digit in its respective place is essential to effectively decompose numbers.
Example: When decomposing the number 3.725, we can identify the value of each digit in terms of its place value. The digit 3 represents three whole units (3), the digit 7 represents seven tenths (0.7), the digit 2 represents two hundredths (0.02), and the digit 5 represents five thousandths (0.005).
Breaking down the number into its individual place values, we decompose it into: 3 + 0.7 + 0.02 + 0.005 HUNDREDS TENS
DIRECTIONS:
Decompose 8.397 in four different ways.
IN WORD FORM
NOTE: There are additional ways to decompose 8.397.
DIRECTIONS: Decompose 47.25 in four different ways.
VALUE IN WORD FORM
NOTE: There are additional ways to decompose 47.25.
DIRECTIONS: Decompose 36.714 in four different ways.
# VALUE IN WORD FORM
NOTE: There are additional ways to decompose 36.714.
DIRECTIONS:
Decompose 32.435 in four different ways.
# VALUE IN WORD FORM
NOTE: There are additional ways to decompose 32.435.
DIRECTIONS: Decompose 523.76 in four different ways.
# VALUE IN WORD FORM
NOTE: There are additional ways to decompose 523.76.
DIRECTIONS: Decompose 745.23 in four different ways.
# VALUE IN WORD FORM
NOTE: There are additional ways to decompose 745.23.
Which of the following is the standard form of 71 hundreds + 40 ones + 19 thousandths?
Which of the following is one way to express 1,408.026?
Which of the following is represented by the model below?
300 ones + 47 hundredths
3 ones + 47 hundredths
30 ones + 47 hundredths
3 ones + 47 tenths
What decimal is represented by the model below?
Which of the following is represented by the model below?
Which of the following is not the same as the rest?
34 tens + 8 tenths
MA.5.NSO.1.4
PLOTTING AND ORDERING MULTI-DIGIT NUMBERS
Plot, order and compare multi-digit numbers with decimals up to the thousandths.
Use plotting techniques on a number line to order and compare multi-digit numbers. Start by selecting an appropriate scale for the number line or coordinate plane, placing the whole number part of the decimal in its corresponding position. Then, determine the location of the decimal part by dividing the remaining space between whole numbers into equal intervals based on the place value of the decimal.
Example: Plot the number 625.75 on a number line.
To plot the number 625.75 on a number line, determine the whole numbers that come before and after the number. Place those two numbers on opposite sides of the number line.
Next, find the midpoint between the numbers. Plot the number in the middle of the number line.
Then, find the midpoints between these numbers. Plot the numbers on the number line. In this instance, the number 625.75 can be found between 625.5 and 626.
In addition to using place value to compare the values of digits in each place, you can also use the number line. The number line is a visual representation of numbers that can help you compare their values. To use the number line to compare two numbers, plot them on the line, then look at their relative positions. The number to the right is always greater than the number to the left.
Example: To compare 625.75 to 625.67, first plot both points on a line using units that are close to the numbers being compared. Next, locate each point on the line and determine which is farther to the right. In this case, 625.75 is farther to the right than 625.67, so it is greater.
DIRECTIONS:
Compare each pair of numbers below using comparison symbols (>, <, or =).
DIRECTIONS: Select all the numbers as indicated below.
DIRECTIONS:
Use the number line below to compare (>, <, or =).
DIRECTIONS:
Compare each pair of numbers below using comparison symbols (>, <, or =).
DIRECTIONS: Select all the numbers as indicated below.
DIRECTIONS:
Three decimals are plotted on the number line. They are represented by the letters A, B, and C. Which of the following decimals could not be located between A and B on the number line?
Which
Augustus measured the daily temperature last week and recorded his data on the table. Which day had the highest recorded temperature?
Compare each pair of numbers below using comparison symbols (>, <, or =).
DIRECTIONS: Select all the numbers as indicated below.
DIRECTIONS:
Use the number line below to compare (>, <, or =).
Select the symbol that makes the following statement true.
Which of the following sets of decimals is listed in descending order?
Which of the following sets of decimals is listed in ascending order?
The table below shows the thickness of Susan’s books. Which one of Susan’s books is the thinnest?
During a science experiment, Zayn measured the weight of four rocks. The table on the right shows the weight of the four rocks. Which rock was the heaviest?
1
The table on the right shows the prices of school supplies. Which item has the highest price?
2
The table on the right shows the length of ribbons Carmi found in her drawer. What is the color of the shortest ribbon that Carmi found?
3
The table on the right shows the hair length of four students. Who has the longest hair?
Which of the following sets of decimals is listed in descending order?
Which
The table on the right shows the mass of different fruits. Which fruit has the greatest mass?
The table on the right shows the heights of different buildings. Which building is the second tallest?
MA.5.FR.2.2
MULTIPLYING FRACTIONS BY FRACTIONS
Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.
Multiplication to multiply a fraction by a fraction often requires converting mixed numbers to improper fractions.
Example:
STEP 1: If you have mixed numbers, convert them to improper fractions. Multiply the whole number by the denominator, then add the numerator. The result becomes the new numerator, and the denominator remains the same.
STEP 2: Simplify the fractions before multiplying to make calculations easier. Divide the numerator and denominator by their greatest common divisor.
STEP 3: Multiply the numerators of the fractions together to get the new numerator, and multiply the denominators together to get the new denominator.
STEP 4: If possible, simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor.
STEP 5: When multiplying a fraction greater than 1 by another fraction, follow the same steps. The resulting product will be greater than the original fractions.
STEP 6: When dealing with mixed numbers, first convert them to improper fractions (Step 2). Then follow the same steps for multiplying fractions. Remember to simplify if needed.
NOTE: The final answer should be written as a simplified mixed number, unless otherwise requested as an improper number.
DIRECTIONS:
Multiply the proper fractions below.
DIRECTIONS: Multiply the mixed fractions below.
DIRECTIONS:
Multiply the proper fractions below.
DIRECTIONS: Multiply the mixed fractions below.
Florence has cup of flour in her pantry. She uses of the flour for her banana bread recipe. How much flour does she use?
4
Frank has 1 pints of hot sauce in his fridge. He uses of the sauce for his buffalo chicken recipe. How much sauce does he have left?
5
Which number makes the equation below true?
DIRECTIONS:
Multiply the proper fractions below.
DIRECTIONS: Multiply the mixed fractions below.
Stephanie multiplies × . Which of the following could not be her answer?
Harrison has of a jug of bubbles on the porch. He uses of his bubbles in his bubble machine. What fraction of the jug does Harrison use?
Luis has of a pizza left over. of the leftover pizza has mushrooms on it. How much mushroom pizza is there?
What is the product of × 5 ?
Sid cuts of a cake for himself and his friends. He gives of the cake to his cousin. How much cake does he have left for his other friends?
3 Which number makes the equation below true?
=
4 Henry bought pound of cupcake mix and pound of cake mix. What is the total weight of the cupcake and cake mixes that Henry bought?
6
What is the product of and ?
7
Nicholas has gallon of gasoline available. He uses of the gasoline for his new motorized invention. What fraction of gasoline did Nicholas use?
8
Jack has of a pizza left over. of the leftover pizza has olives on it. How much olive pizza is there?
MA.5.FR.2.3
PREDICTING THE RELATIVE SIZE OF THE PRODUCT
When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.
Make predictions about the relative size of the product without actually performing the multiplication.
STEP 1: Determine if the fraction is less than 1 or greater than 1. If the fraction is less than 1, the numerator is smaller than the denominator. For example, 1/2 or 3/4. If the fraction is greater than 1, the numerator is larger than the denominator. For example, 3/2 or 5/4.
STEP 2: Consider the effect of multiplying by a fraction less than 1. When you multiply a given number by a fraction less than 1, the product will be smaller than the given number. This is because you are taking a part of the given number, which is less than the whole.
STEP 3: Consider the effect of multiplying by a fraction greater than 1. When you multiply a given number by a fraction greater than 1, the product will be larger than the given number. This is because you are taking more than the whole, as the numerator of the fraction is larger than the denominator.
a check mark ( ) next to all
1
Which of the following expressions will have a product less than 24?
2
The product of × 109 will be ____________ 109. less than greater than equal to twice as much as
3
In the equation below, “n” will equal ________________. 4 × 67 = n a number greater than 67 a number less than 67 one-third of
4
Which of the following statements is true?
5
Alana wants to multiply 78 by a number to get an answer less than 78. Select all the answers that could be Alana’s number.
DIRECTIONS:
Kyler multiplies 32 by a number, and his answer is greater than 32. Which of the following could not be his number?
A number multiplied by a fraction greater than a whole will always have a product that is: equal to the original number one-tenth of the original number greater than the original number less than the original number 3
81 is multiplied by . Steve thinks the answer will be equal to 81, and Bailey thinks the answer will be less than 81. Who is correct?
Steve is correct because 81 and have the same digits, which means the product will be the same as the original number.
Bailey is correct because is less than a whole, which means the product will be less than the original number.
Bailey is correct because is greater than a whole, which means the product will be less than the original number.
Neither of them is correct because the product will actually be greater than 81.
4
Which of the following expressions will have a product greater than 157?
Which of the following makes the statement below true?
1
Which of the following expressions will have a product greater than 97?
Ms. Perez wrote the statement below on the board:
In the equation × 22 = m, “m” will equal _____.
What phrase makes this correct? a number greater than 22 a number lesser than 22 a number equal to 22 one-fourth of 22
Which of the following statements is true?
Anna wants to multiply a number by 65 to get an answer greater than 65. Select all of the possible answers that could be Anna’s number.
Kayla multiplies the number 45 by and says the answer will be the same as 45. Mike says the answer will be less than 45. Who is correct?
Mike is correct since is less than a whole, and will give an answer less than 45.
Kayla is correct since is same as 1 and the product will therefore be 45.
Mike is correct since is greater than a whole and will give an answer greater than 45.
Neither of them is correct since the answer is a number greater than 45.
Which of the following makes the statement below true?
× ______ = a number less than 6
The product of × 117 will be ____________ 117. less than greater than equal to twice as much as
In the equation below, “k” will equal ________________. 3 × × 56 = k
Product of a number and a fraction that is less than one will always be: equal to the original number one-tenth of the original number greater than the original number less than the original number
Abadi multiplies 17 by a number, and his answer is less than 17. Which of the following could be his number?
MA.5.FR.2.4
DIVIDING UNIT FRACTIONS BY WHOLE NUMBERS
Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.
Divide unit fractions by a whole number by multiplying its reciprocal.
STEP 1: Understand that a unit fraction is a fraction with a numerator of 1 (e.g., 1/2, 1/3, and 1/4).
STEP 2: When dividing, express the whole number as a fraction with a denominator of 1. For example, if you want to divide 1/3 by 2, rewrite 2 as 2/1.
STEP 3: Take the reciprocal of the whole number (flip it). For example, 1/3 ÷ 2/1 = 1/3 ÷ 1/2.
STEP 4: Next, change the division sign to multiplication and multiply the unit fraction by the reciprocal of the whole number. For example, 1/3 × 1/2 = 1/6.
Divide a whole number by a unit fractions by multiplying its reciprocal.
STEP 1: Express the whole number as a fraction with a denominator of 1 (e.g., 6 = 6/1).
STEP 2: When dividing a whole number by a unit fraction, take the reciprocal (flip) of the unit fraction. For example, if you want to divide 6/1 by 1/2, rewrite 1/2 as 2/1.
STEP 3: Change the division sign to multiplication and multiply the whole number by the reciprocal of the unit fraction. For example, 6/1 × 2/1 = 12/1.
DIRECTIONS:
DIRECTIONS:
Remi has 7 feet of string she is using to make bracelets. If each bracelet uses foot of string, how many bracelets will she be able to make?
What is the quotient of ÷ 4?
makes the equation below true?
Eli has of a pizza he needs to divide equally for his 5 friends. What fraction of a pizza will each friend receive?
Nora has 11 chocolate bars to share with her class. She divides each bar into bar pieces. If there are 24 kids in her class, will she have enough chocolate for each student to have a piece?
No, because she will only have bar.
Yes, because she will have 33 pieces.
Yes, because she will have exactly 24 pieces.
No, because she will only have 3 pieces
Zane has of a bowl of punch left at his party. He shares it equally in 10 cups for the party guests. What fraction of the bowl of punch does each of the guests receive?
Ethan is running on a 5-mile path by his school. He stops every mile to drink some water and runs the whole distance of the path. How many breaks does he take for water?
1
Finney marks the racing ground into tracks for an event. The width of the entire track is 235 feet. If he has to mark every 2 feet, how many tracks can he make?
2
What is the quotient of ÷ ?
3
Gwen wants to share of an apple pie with her 4 friends. What share of the pie will each of them get?
4
Bruce has carton of milk left after breakfast. He shares the milk equally among his 3 cats. What fraction of the carton of milk does each cat get? 5
Which number makes the equation below true ?
5 = _____
What is the quotient of ÷ ?
Emma wants to share of a box of candies with her 4 siblings. What share of the candies will each of them get? 9
Alex has of a watermelon left after lunch. He wants to share the watermelon equally among his 6 friends. What fraction of the watermelon does each friend get?
SOLVE REAL-WORLD PROBLEMS INVOLVING DIVISION
MA.5.AR.1.3
Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
When solving real-world problems involving a unit fraction by a whole number, it is important to multiply by the reciprocal of the divisor.
STEP 1: Carefully read and comprehend the information provided in the real-world problem.
STEP 2: When dividing real-world problems involving division, express the whole number as a fraction with a denominator of 1. For example, if you want to divide 1/3 by 2, rewrite 2 as 2/1.
STEP 3: Take the reciprocal of the whole number (flip it). For example, 1/3 ÷ 2/1 = 1/3 ÷ 1/2.
STEP 4: Next, change the division sign to multiplication and multiply the unit fraction by the reciprocal of the whole number. For example, 1/3 × 1/2 = 1/6.
When solving real-world problems involving a a whole number by a unit fraction, it is important to multiply by the reciprocal of the divisor.
STEP 1: To divide a whole number by a unit fraction, express the whole number as a fraction with a denominator of 1.
STEP 2: Take the reciprocal of the unit fraction (flip it). For example, 5/1 ÷ 1/10 = 1/3 ÷ 10/1.
STEP 3: Next, change the division sign to multiplication and multiply the unit fraction by the reciprocal of the whole number. For example, 5/1 × 10/1 = 50/1 = 50
DIRECTIONS:
Solve each word problem below.
Rachel has a rectangular pizza that is divided into 10 equal slices. If she ate of the pizza, how many slices did she eat?
Maria has a rope that is feet long. She needs to cut 3 equal pieces from the rope. How long will each piece of rope be?
Samantha baked a cake and divided it into 8 equal slices. She ate 3 slices. What fraction of the cake did Samantha eat?
A recipe for chocolate chip cookies calls for cup of sugar. If you want to make only half the recipe, how much sugar will you need?
DIRECTIONS:
Solve each word problem below.
A rectangular field has a perimeter of meters. If each side of the field has the same length, what is the length of each side?
Marta is creating 3 dresses that require yards of fabric to complete. If each dress is identical, how many yards of fabric are needed for each dress?
A recipe for a fruit smoothie requires cups of fruit salad. If you want to make of the recipe, how many cups of fruit salad do you need?
A group of friends went on a road trip and traveled a total distance of miles. If they drove for hours, what was their average speed in miles per hour?
1
A restaurant chef has four pounds of potatoes. How many servings of mashed potatoes can the chef make if each serving of mashed potatoes calls for one-eighth of a pound of potatoes?
2 servings 8 servings 16 servings
2
A group of six friends, including Miriam, went to dine in a restaurant. While waiting for their dishes to be served, the waiter served them a quarter of a bowl of peanuts. If they split the bowl of peanuts evenly, how much peanuts did Miriam get? of a bowl of a bowl of a bowl of a bowl
3
Carl spent a total of 2 hours to complete several tasks. If he spent of an hour to complete each task, how many tasks did Carl complete during those 2 hours?
2 tasks 3 tasks 6 tasks 12 tasks
4
Mr. Antonio equally divided half an acre of land among his three children. How many acres of land did each child receive?
5
Romaine prepared 20 sandwiches for a party. She cut each of the sandwiches into fourths and put the slices on a tray. How many slices of sandwiches did Romaine put on the tray? 5
DIRECTIONS:
Solve each word problem below.
3 4
A container holds gallons of water. If each person needs gallon of water, how many servings are there? 25 2 3
2
A farmer has acres of land where she grows sugar cane. If each sugar cane field covers acres, how many sugar cane fields can the farmer create?
1 3
A corner store received a shipment of pounds of apples. If they want to pack them into bags of pounds, how many bags can they fill?
3 4 1 1 2
1 2 2 3 4
A construction project requires feet of piping. If each section of piping is feet long except for the last section, how many sections of piping will the project have?
1
A bakery used of a bag of chocolate chips to make 5 batches of chocolate chip cookies. If the bakery used the same amount of chocolate chips in each batch, how much chocolate chips did the bakery use in each batch?
of a bag of a bag of a bag of a bag
2
A car wash uses one-sixth of a quart of soap to wash each car. If the car wash has 8 quarts of soap, how many cars can they wash?
cars
3
George needs to fill a 20-gallon aquarium with water. If George can only carry half a gallon of water each trip, how many trips will it take him to fill the aquarium?
trips
trips
4
trips
trips
A carpenter has a piece of log that is of a yard long. He cuts the log into 9 equal pieces. How long will each piece be? of a yard of a yard of a yard of a yard 5
Amanda served a 12-pound turkey last Thanksgiving. If she cut the turkey into one-third of a pound servings, how many servings of the turkey did she make?
1
A dressmaker used one-third of a yard of fabric to make four skirts. The dressmaker used the same amount of fabric to make each skirt. How much fabric did the dressmaker use to make one skirt? of a yard of a yard of a yard of a yard
2
A group of ten friends, including Sheila, equally shared half a bar of chocolate. Each friend got the same amount of chocolate. What fraction of a chocolate bar did Sheila get? of a chocolate bar of a chocolate bar of a chocolate bar of a chocolate bar
3
Jack bought 3 pounds of dog food for his dog. If his dog eats of a pound of dog food each day, how many days will the dog food that Jack bought last?
days
4
A painter has 6 liters of paint. If each wall requires liter of paint, how many walls can the painter paint?
5
A tailor has a roll of fabric that is 6 meters long. If he cuts fabric into pieces, each meter long, how many pieces will he get?
Mary is making lemonade and needs to fill a pitcher that holds 5 liters. She can only carry of lemonade at once. How many trips will she need to make to completely fill the pitcher?
trips
trips
trips
Tim is organizing a party and bought a 10-pound cake. If he plans to serve slices of the cake that each weigh a pound each, how many slices can he serve from the cake?
A farmer has 12 liters of pesticide to spray on his crops. If each field requires liter of pesticide, how many fields can he spray?
fields
A construction company has a cement mixer with a capacity of 1 cubic yards. If each foundation requires cubic yards of cement, how many foundations can they pour from 1 full load of the cement mixer?
A carpenter has 25 feet of wood. If each shelf requires 2 feet of wood, how many shelves can the carpenter make?
TRANSLATE REAL-WORLD PROBLEMS INTO NUMERICAL EXPRESIONS
MA.5.AR.2.1
Translate written real-world and mathematical descriptions into numerical expressions and numerical expressions into written mathematical descriptions.
Use keywords to help translate written real-world and mathematical descriptions into numerical expressions.
STEP 1: Determine which mathematical operations are involved in the mathematical description. Look for keywords or phrases that indicate specific operations.
STEP 2: Identify the quantities mentioned in the description and assign them variables or symbols. Use letters such as x, y, or z to represent unknown values or specific variables mentioned in the problem.
STEP 3: Write the expression using appropriate mathematical symbols and notation.
KEYWORD is times each row each shelf each ____ same as MEANING Equals (=)
Multiply (×)
Multiply (×) Multiply (×) Multiply (×) Equals (=)
KEYWORD of product of increased by all together more than per
MEANING Multiply (x)
Multiply (x) Add (+) Add (+) Add (+) Multiply (x)
KEYWORD sum total combined greater plus and MEANING Add (+) Add (+) Add (+) Add (+) Add (+) Add (+)
KEYWORD left take away how many more decreased by difference less than
MEANING Subtract ( )
Subtract ( )
Subtract ( ) Subtract ( )
Subtract ( )
Subtract ( )
KEYWORD quotient quarter remaining half out of out of
MEANING Divide (÷)
Divide (÷)
Divide (÷) by 4
Divide (÷)
Divide (÷) by 2
Use key words to help translate numerical expressions into mathematical descriptions.
Divide (÷)
STEP 1: Translate the mathematical operations in the numerical expression into written form. Use words such as "add," "subtract," "multiply," or "divide" to describe the operations being performed.
STEP 2: Describe the quantities involved using appropriate terms and units of measurement. Use words such as "number of," "amount of," or "value of" to specify the quantities involved.
STEP 3: Arrange the numerical descriptions of operations and quantities in a clear and concise manner.
DIRECTIONS:
Interpret the numerical expressions.
DIRECTIONS: Interpret the word expressions.
WORD EXPRESSION
Multiply 8 and 4, then subtract 6
Add 12 and 3, then multiply by 7
Subtract 16 from the sum of 47 and 26
6 times the quantity 25 divided by 5
Add 15, 28, and 121, then multiply by 23
Divide 16 by 4, then add 24
DIRECTIONS:
Interpret the numerical expressions.
DIRECTIONS: Interpret the word expressions.
Multiply 12 and 6, then subtract 7
Add 58 and 42, then multiply by 11
Subtract 64 from the sum of 125 and 37
12 times the quantity 72 divided by 9
Add 241, 34, and 87, then multiply by 19
Divide 99 by 11, then add 54
1
Which of the following expressions is the same as saying half the sum of fifteen and twentythree?
(15 + 23) ÷ 2 15 + 23 ÷ 2
15 + (23 ÷ 2) (15 ÷ 2) + 23
2
Which of the following expressions is the same as saying one-third the difference of twelve and six?
3
Which of the following expressions is the same as saying twice the sum of one-fourth and threeeighths?
Which of the following is the word form of the expression × (16 ÷ 4)?
Half the quotient of sixteen and four
Half of sixteen divided by four
Product of one-half and sixteen divided by four
Half of four divided by sixteen
5
Which of the following is the word form of the expression (24 ÷ 5) + ?
Four-fifths the quotient of twenty-four and five
Twenty-four divided by four-fifths more than five
The quotient of twenty-four and five plus four-fifths.
Twenty-four divided by the sum of five and four-fifths
Which of the following is the word form of the expression (3 × 9) − ?
Two-thirds less than the product of three and nine
Two-thirds less than the product of three and nine
The product of three, and nine less than two-thirds
The product of three, and nine less two-thirds
2
Amy bought three baskets of apples. Each basket contained six red apples and four green apples. Which expression represents the total number of apples Amy bought?
3 × 6 + 4 3 × (6 + 4) (3 × 6) + 4) 6 + (3 × 4)
3
Douglas bought eight boxes of marbles. Each box contains twenty-four marbles, six of which are green. Which expression represents the number of marbles Douglas bought that are not green?
8 × 24 (8 × 24) − 6
8 × 24 − 6 8 × (24 − 6)
4
A carpenter has a piece of wood seven feet and three-tenths of a foot long. He cuts the wood into two pieces of equal length. Which expression represents the length of each piece?
Patrick bought seven packs of trading cards. Each pack contains eight trading cards, five of which are baseball cards. Which expression represents the total number of trading cards Patrick bought that are not baseball cards?
7 × 5 7 × 8 − 5 7 × 8 7 × (8 − 5) 2 3
1
Felicia ordered twelve boxes of pens from an online store. Each box contained twenty-four pens, a third of which were black. Which expression represents the total number of black pens that Felicia ordered online?
× 24
× 12
2
12 × (24 × )
12 + (24 × )
There are thirty-six animals on Uncle Henry’s farm, a quarter of which are goats. Of all the goats on the farm, two have horns. Which expression represents the number of goats with no horns?
4 − 2
36 ÷ (4 − 2)
36 ÷ 4 (36 ÷ 4) − 2
3
Five boxes contain a total of sixty tokens. Each box contains the same number of tokens. If each box has ten green tokens and the rest are yellow tokens, which expression represents the number of yellow tokens in each box?
60 − 5 × 10
60 − (5 × 10)
60 ÷ 5 − 10 (60 ÷ 5) − 10
4
Which of the following is the word form of the expression × ( + 3)?
Product of 5 and the sum of three-fourths and three
One-fifth of the sum of three-fourths and three
Sum of one-fifth and three-fourths and three
Product of three-fifths and three-fourths
5
Which of the following is the word form of the expression (7 ÷ ) 3?
Quotient of seven and two less than three
Quotient of seven less than three and one-half
Three less than quotient of seven and one-half
One-
seven and three
A hotel has 100 residents. 30 residents are Italian, 15 are French, 25 are German, and a third of the rest are Japanese. Which expression represents the number of Japanese residents?
(100 - 30 + 15 + 25) × 100 + (30 + 15 + 25) ×
100 - (30 + 15 - 25) × 100 - (30 - 15 + 25) × 7
Which of the following is the word form of the expression (12 ÷ 2) - 5?
Two over twelve minus five
Twelve divided by two plus five
Five less than the division of twelve over two
Five less the division of twelve over two 8
Marcus collects the cherries from 6 trees in the garden. From each tree, he takes 20 cherries. He then stores them in 4 equal containers. Which expression represents the number in each container?
Anne’s mom wants to make peanut butter, so she needs 1.1kg of peanuts for every 1.2kg of peanut butter. If she wants to make 4kg of peanut butter, which expression represents the amount of peanuts needed?
A beekeeper has 8 hives, each containing 200 bees except the last one which contains 600. Which expression represents the total number of bees?
RULES FOR DESCRIBING PATTERNS AS AN EXPRESSION
MA.5.AR.3.1
Given a numerical pattern, identify and write a rule that can describe the pattern as an expression.
To find a pattern in a series of numbers, look for a consistent difference or ratio between each number.
STEP 1: Study the given pattern of numbers. For example, 2, 4, 6, 8, 10.
STEP 2: Figure out how the numbers in the pattern are related. Check for a consistent difference or ratio between each number.
STEP 3: If the pattern has a consistent difference between each number (arithmetic sequence), subtract any number from the one before it to find the common difference. In our example, the common difference is 2 because each number is 2 more than the previous one.
STEP 4: If the series has a consistent ratio between each number (geometric sequence), divide any number by the one before it to find the common ratio. In our example, the common ratio is 2 because each number is twice the previous one.
STEP 5: Write a formula using variables to represent the pattern. For an arithmetic sequence, the formula will include the common difference (d) and the first term (a). For a geometric sequence, the formula will include the common ratio (r) and the first term (a).
STEP 6: For our example pattern (2, 4, 6, 8, 10), since it has a common difference of 2, we can write the formula as n = 2n, where “n” represents the nth term of the sequence.
STEP 7: If needed, simplify the formula or adjust it to fit the specific starting term or index of the pattern. For example, if the pattern starts with the term “a1” instead of “a0”, you may need to adjust the expression accordingly.
STEP 8: Check the formula by applying it to additional terms in the pattern to see if it correctly predicts the values. For our example, when we substitute “n” with 1, 2, 3, 4, and 5 in the formula (n) = 2n, we get the correct corresponding values of 2, 4, 6, 8, and 10, respectively.
Example:
Rule: Add 3 x 9 12 15 - ? 6 + 3 + 3 + 3 + 3 + 3 first second third fourth fifth
RULE: 3 + 3x, where x = 1, 2, 3, 4...
Therefore , the sixth term may be calculated with x = 6 3 + 3x
3 + (3 × 6)
3 + 18
DIRECTIONS:
Find the next 4 terms to create a pattern using the rules given below.
DIRECTIONS: Write the rule of the pattern as an expression.
No. THE FIRST FOUR TERMS
5, 10, 15, 20
9, 13, 17, 21
40, 30, 20, 10
2, 5, 10, 17
20, 18, 16, 14
RULE AS AN EXPRESSION
DIRECTIONS:
Find the next 4 terms to create a pattern using the rules given below.
No. PATTERN RULE
by 5
by 2 4
DIRECTIONS: Write the rule of the pattern as an expression.
No. THE FIRST FOUR TERMS RULE AS AN EXPRESSION
9, 11, 13, 15
3, 5, 7, 9
20, 15, 10, 5
4, 7, 12, 19
12, 8, 4, 0
1
The numbers in the list follow a pattern. 28, 35, 42, 49, 56, 63, ...
Which expression best describes the pattern of the list?
28 − 7x, where x = 2, 3, 4, 5, 6, ...
28 + 14x, where x = 0, 1, 2, 3, 4, ...
2
14 + 7x, where x = 2, 3, 4, 5, 6, ...
14x, where x = 2, 3, 4, 5, 6, ...
The numbers in the list follow a pattern. 72, 68, 64, 60, 56, 52, ...
Which expression cannot describe the pattern of the list?
40 + 4x, where x = 8, 9, 10, 11, 12, …
72 − 4x, where x = 0, 1, 2, 3, 4, …
3
80 − 4x, where x = 2, 3, 4, 5, 6, …
100 − 4x, where x = 7, 8, 9, 10, 11, …
The numbers in the list follow a pattern. 36, 45, 54, 63, 72, 81, ...
Which expression best describes the pattern of the list?
6x, where x = 6, 7, 8, 9, 10, ...
27 + 9x, where x = 1, 2, 3, 4, 5, ...
4
33 + 3x, where x = 1, 2, 3, 4, 5, ...
5x + 6, where x = 6, 7, 8, 9, 10, ...
The numbers in the list follow a pattern. 98, 100, 102, 104, 106, 108, ...
Which expression best describes the pattern of the list?
100 − 2x, where x = 1, 2, 3, 4, 5, ...
50 + 2x, where x = 25, 26, 27, 28, 29, ...
5
90 + 4x, where x = 2, 3, 4, 5, 6, ...
2(49 + x), where x = 0, 1, 2, 3, 4, ...
The numbers in the list follow a pattern. 10, 13, 16, 19, 22, 25, ...
Which expression cannot describe the pattern of the list?
5x, where x = 2, 3, 4, 5, 6, …
7 + 3x, where x = 1, 2, 3, 4, 5,
3x + 1, where x = 3, 4, 5, 6, 7, …
3x + 4, where x = 2, 3, 4, 5, 6,
DIRECTIONS:
Find the next 4 terms to create a pattern using the rules given below.
PATTERN RULE
DIRECTIONS: Write the rule of the pattern as an expression.
No. THE FIRST FOUR TERMS RULE AS AN EXPRESSION 13, 16, 19, 22
7, 12, 17, 22
33, 30, 27, 24
9, 12, 17, 24
27, 20, 13, 6
1
The numbers in the list follow a pattern. 9, 14, 19, 24, 29, 34, ...
Which expression best describes the pattern of the list?
4x + 5, where x = 0, 1, 2, 3, 4, ...
8x + 1, where x = 1, 2, 3, 4, 5, ...
2
5x − 1, where x = 2, 3, 4, 5, 6, ...
6x + 3, where x = 1, 2, 3, 4, 5, ...
The numbers in the list follow a pattern. 31, 34, 37, 40, 43, 46, ...
Which expression cannot describe the pattern of the list?
20 + 3x, where x = 4, 5, 6, 7, 8, ...
3x + 1, where x = 10, 11, 12, 13, 14, ...
3
22 + 3x, where x = 3, 4, 5, 6, 6, ...
25 + 3x, where x = 2, 3, 4, 5, 6, ...
The numbers in the list follow a pattern. 15, 18, 21, 24, 27, 30, ...
Which expression cannot describe the pattern of the list?
3x, where x = 5, 6, 7, 8, 9, …
9 + 6x, where x = 1, 2, 3, 4, 5, …
6 + 3x, where x = 3, 4, 5, 6, 7, …
3(1 + x), where x = 4, 5, 6, 7, 8, …
4
The numbers in the list follow a pattern. 60, 56, 52, 48, 44, 40, ...
Which expression best describes the pattern of the list?
5x, where x = 6, 7, 8, 9, 10, ...
30 + 6x, where x = 5, 6, 7, 8, 9, ...
5
60 − 4x, where x = 0, 1, 2, 3, 4, ...
60 − 3x, where x = 0, 1, 2, 3, 4, ...
The numbers in the list follow a pattern. 26, 31, 36, 41, 46, 51, ...
Which expression best describes the pattern of the list?
5x + 1, where x = 5, 6, 7, 8, 9, ...
4x + 6, where x = 5, 6, 7, 8, 9, ...
3x + 5, where x = 7, 8, 9, 10, 11, ...
8x + 2, where x = 3, 4, 5, 6, 7, ...
1
The numbers in the list below follow a pattern.
66, 74, 82, 90, 98, 106, ...
Which expression describes the pattern of the list?
8x + 2, where x = 8, 9, 10, 11, 12, …
8x − 6, where x = 9, 10, 11, 12, 13, …
2
The numbers in the list below follow a pattern.
37, 42, 47, 52, 57, 62, ...
Which expression best describes the pattern of the list?
6 + 5x, where x = 6, 7, 8, 9, 10, ...
5x + 8, where x = 4, 5, 6, 7, 8, ...
3
The numbers in the list below follow a pattern.
87, 95, 104, 111, 119, 127, ...
10 + 8x, where x = 7, 8, 9, 10, 11, …
8x + 18, where x = 6, 7, 8, 9, 10, …
5x − 2, where x = 8, 9, 10, 11, 12, ...
5x + 2, where x = 7, 8, 9, 10, 11, ...
Which expression cannot describe the pattern of the list?
8x − 1, where x = 11, 12, 13, 14, 15, ...
8x − 12, where x = 14, 15, 16, 17, 18, ...
4
The numbers in the list below follow a pattern. 23, 25, 27, 29, 31, 33,...
8x − 9, where x = 12, 13, 14, 15, 16, ...
8x − 17, where x = 13, 14, 15, 16, 17, ...
Which expression cannot describe the pattern of the list?
2x + 3, where x = 10, 11, 12, 13…
2x − 3, where x = 9, 10, 11, 12, 13, …
5
The numbers in the list below follow a pattern. 77, 86, 95, 104, 113, 122, ...
Which expression best describes the pattern of the list?
9x + 3, where x = 6, 7, 8, 9, 10, …
9x - 2, where x = 10, 11, 12, 13,, ...
2x + 4, where x = 7, 8, 9, 10, 11, …
4x - 12, where x = 6, 7, 8, 9, 10, …
9x + 5, where x = 8, 9, 10, 11, 12, ...
9x - 4, where x = 12, 13, 14, 15, ...
6
The numbers in the list below follow a pattern.
64, 68, 72, 76, 80, 84, ...
Which expression cannot describe the pattern of the list?
6x + 32, where x = 8, 9, 10, 11, 12, …
4x − 6, where x = 13, 14, 15, 16, 17…
7
The numbers in the list below follow a pattern.
55, 61, 67, 73, 79, 85...
Which expression best describes the pattern of the list?
6x + 5, where x = 10, 11, 12, 13, 14...
8
6x + 40, where x = 4, 5, 6, 7, 8, …
4x + 32, where x = 8, 9, 10, 11, 12…
6x + 8, where x = 8, 9, 10, 11, 12, ...
6x - 5, where x = 10, 11, 12, 13, 14... 10x - 7, where x = 5, 6, 7, 8, 9, 10 ...
The numbers in the list below follow a pattern.
61, 68, 75, 82, 89, 96...
Which expression cannot describe the pattern of the list?
7x + 2, where x = 8, 9, 10, 11, 12, 13...
7x + 9, where x = 7, 8, 9, 10, 11, 12...
7x - 2, where x = 9, 10, 11, 12, 13, 14 ...
7x - 9, where x = 13, 14, 15, 16, 17,.. 9
The numbers in the list below follow a pattern. 69, 84, 99, 114, 129, 144,...
Which expression describes the pattern of the list?
15x + 9, where x = 10, 11, 12, 13, 14,… 15x + 12, where x = 3, 4, 5, 6, 7, 8, …
15x - 12, where x = 11, 12, 13, 14, 15… 15x + 9, where x = 4, 5, 6, 7, 8, 9, 10
The numbers in the list below follow a pattern.
90, 101, 112, 123, 134, 145, ...
Which expression best describes the pattern of the list?
11x + 2, where x = 8, 9, 10, 11, 12, 13…
11x - 2, where x = 12, 13, 14, 15, 16...
10x + 5, where x = 7, 8, 9, 10, 11, 12, ...
10x - 5, where x = 13, 14, 15, 16, 17…
MA.5.M.1.1
CONVERTING METRIC UNITS
Solve multi-step real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement.
Convert the following mass measurements. Use the mass section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
4 pounds = _______ ounces
5 tons = _______ pounds
2.5 kilograms = _______ grams
48 ounces = _______ pounds
4,000 pounds = _______ tons
DIRECTIONS: Convert the following length measurements. Use the length section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
6 feet = _______ inches
8 yards = _______ feet
3 meters = _______ centimeters
21 feet = _______ yards
DIRECTIONS: Convert the following time measurements. Use the time section of the Conversion Table as needed.
48 inches = _______ feet NO.
CONVERSION PROBLEM
3 minutes = _______ seconds
360 seconds = _______ minutes
240 minutes = _______ hours
5 hours = _______ minutes
9 days = ______ hours
DIRECTIONS:
Convert the following mass measurements. Use the mass section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
6 pounds = _______ ounces
3 tons = _______ pounds
5.1 kilograms = _______ grams
80 ounces = _______ pounds
8,000 pounds = _______ tons
DIRECTIONS: Convert the following length measurements. Use the length section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
3 feet = _______ inches
11 yards = _______ feet
5 meters = _______ centimeters
27 feet = _______ yards
60 inches = _______ feet
DIRECTIONS: Convert the following time measurements. Use the time section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
7 minutes = _______ seconds
300 seconds = _______ minutes
360 minutes = _______ hours
3 hours = _______ minutes
7 days = ______ hours
1
There are 12 inches in 1 foot. Kim has a piece of string 4 feet and 8 inches long. She cuts the string into 2 pieces of equal length. How many inches long is 1 piece?
2
There are 3 feet in 1 yard. Noel wants to put a fence around his vegetable garden. One side of his vegetable garden is 3 yards, 6 feet long and the other side is 2 yards, 3 feet wide. How many feet of fencing materials does Noel need?
3
There are 2 cups in 1 pint. A recipe calls for 4.5 pints of milk. Myrna only has 2 cartons of milk, each containing 3 cups. How much more milk does Myrna need?
4
There are 12 inches in 1 foot. A rectangular sandbox has a perimeter of 8 feet. If 1 side of the sandbox is 4 inches longer than the other side, what is the length of the longer side of the sandbox?
5
There are sixteen ounces in one pound. A box contains seven and a half pounds of nails. How many nails are there in the box if each nail weighs three ounces?
DIRECTIONS:
Convert the following length measurements. Use the mass section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
10 pounds = _______ ounces
9 tons = _______ pounds
8.8 kilograms = _______ grams
128 ounces = _______ pounds
10,000 pounds = _______ tons
DIRECTIONS: Convert the following length measurements. Use the length section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
12 feet = _______ inches 4 yards = _______ feet
9 meters = _______ centimeters
18 feet = _______ yards
36 inches = _______ feet
DIRECTIONS: Convert the following time measurements. Use the time section of the Conversion Table as needed.
NO. ANSWER CONVERSION PROBLEM
13 minutes = _______ seconds
180 seconds = _______ minutes
660 minutes = _______ hours
8 hours = _______ minutes
15 days = ______ hours
1
There are 12 inches in 1 foot and 3 feet in 1 yard. Debbie had a piece of fabric 3 yards and 9 feet long. She used 1.5 yards of the fabric to make a tablecloth and used the remaining fabric to make pillowcases. If Debbie used 18 inches of fabric to make 1 pillowcase, how many pillowcases did she make in total?
9 pillowcases
2
pillowcases 12 pillowcases
pillowcases
There are 12 inches in 1 foot. If the perimeter of a square is 1 feet, which of the following gives the length of the side of the square in inches?
There are 12 inches in 1 foot. Rowena used 11.25 feet of yarn to tie 15 bows. If she used the same amount of yarn to make each bow, how many inches of yarn did Rowena use to make 1 bow?
There are 2 pints in 1 quart, 4 quarts in 1 gallon, and 60 minutes in 1 hour. An orange squeezer machine can produce 8 pints of orange juice every 5 minutes. How many gallons of orange juice can the machine produce in 2 hours?
There are 60 minutes in 1 hour. A machine can make 55 widgets per minute. At this rate, how many hours will it take the machine to make 4,400 widgets?
1
There are 60 minutes in 1 hour. A printer can print 1 picture every of a minute. How many pictures can the printer print if it runs continuously for 2 hours?
80 pictures
2
3
pictures 180 pictures
pictures
There are 60 minutes in 1 hour. If Jerry can complete of his task in one hour, how many minutes will it take him to fully complete the task?
45 minutes
minutes 80 minutes
minutes
There are 12 inches in 1 foot. George wants to use a piece of wire 8 feet long to make several frames. Each frame requires 15 inches of wire. What is the greatest possible number of frames that George can make?
5 frames 6 frames
7 frames 8 frames 4
There are 3 feet in 1 yard. A rectangular courtyard has a perimeter of 12 yards. If one side of the courtyard is 2 feet longer than the other side, what is the length of the longer side of the sandbox?
There are 12 inches in 1 foot and 3 feet in 1 yard. Margret had a piece of fabric 5 yards and 6 feet long. She used 2 yards of the fabric to make a table runner and used the remaining fabric to make dinner napkins. If Debbie used 15 inches of fabric to make 1 table runner, how many dinner napkins did she make in total?
There are 2 cups in 1 pint. A recipe calls for 6.5 pints of cream. Emma only has 2 cartons of cream, each containing 4 cups. How much more cream does Emma need? 2 cups
cups
There are 12 inches in 1 foot. If the perimeter of a square is 2 feet, which of the following gives the length of the side of the square in inches?
There are 12 inches in 1 foot. Stephen used 13.75 feet of ribbon to wrap 33 gifts. If he used the same amount of ribbon to wrap each gift, how many inches of ribbon did Stephen use to wrap 1 gift?
There are 2 pints in 1 quart, 4 quarts in 1 gallon, and 60 minutes in 1 hour. A lemon squeezer machine can produce 12 pints of lemon juice every 5 minutes. How many gallons of lemon juice can the machine produce in 3 hours?
There are 60 minutes in 1 hour. A secretary can type 120 words per minute. At this rate, how many hours will it take the secretary to type 2,400 words?
MA.5.M.2.1
REAL-WORLD PROBLEMS INVOLVING MONEY
Solve multi-step real-world problems involving money using decimal notation.
Use decimal notation to solve multi-step real-world problems involving money.
STEP 1: Identify the prices, quantities, discounts, or any other monetary values mentioned in the problem. Record the decimal notation for each value.
STEP 2: Determine the unknown values that need to be solved, along with any comparisons that must be made.
STEP 3: Perform the necessary operations to find the answer.
Example 1
John is at the supermarket and wants to buy orange juice. The first option offers a 32-ounce bottle for $2.99, while the second offer is a 16-ounce bottle for $1.50. Which option is cheaper per ounce?
$2.99 ÷ 32 ounces = $0.09 per ounce and $1.65 ÷ 16 ounces = $0.10 per ounce
$0.09 per ounce < $0.10 per ounce
Therefore, $2.99 for 32 ounces of orange juice is a better buy.
Example 2
Alice, Bob, and Carol decided to contribute money to buy a gift for their friend. Bob contributed $5 more than twice the amount contributed by Alice, and Carol contributed $4 less than the amount contributed by Bob. If the price of the gift was $41, how much did Carol contribute?
B = Bob, A = Alice, and C = Carol
B = $5 + 2A (Bob contributed $5 more than twice the amount contributed by Alice)
C = B - $4 (Carol contributed $4 less than the amount contributed by Bob)
If the price of the gift was $41, how much did Carol contribute?
$41 = A + B + C $35 = 5A
$41 = 1A + $5 + 2A + $5 + 2A - $4 $35 = 5A
$41 = 5A + $6
$41 - $6 = 5A + $6 - $6 $7 = A
= $5 + 2A
= $5 + 2 × $7
= $5 + $14
= $19
=
- $4
= $19 - $4
= $15
DIRECTIONS:
DIRECTIONS:
DIRECTIONS: Compare the
Compare the price points below. Use the symbols >, <, or =.
DIRECTIONS:
Compare the price points below. Use the symbols >, <, or =.
DIRECTIONS:
Compare the price points below. Use the symbols >, <, or =.
1
Sarah is at the store and wants to buy juice. Which option would be cheaper: buying one 32-ounce bottle for $2.56 or buying two 16-ounce bottles for $1.44 each?
16-ounce bottle is $0.09 per ounce
16-ounce bottle is $0.08 per ounce
2
32-ounce bottle is $0.09 per ounce
32-ounce bottle is $0.08 per ounce
Robert, Doug, and Kevin agreed to put their money together buy a new gaming table. Doug gave $4 more than twice the amount that Kevin gave, and Kevin gave $3 less than the amount that Robert gave. If the price of the new gaming table was $27, how much did Kevin give for the new gaming table?
$5
$10
3
$8
$12
Mr. Romero left half of the money in his estate to his wife, to his eldest daughter, to his youngest daughter, and the remaining $100,000 to charity. How much was the total amount of money in Mr. Romero’s estate?
$1,000,000
4
Gene has $15 more than Andrew, and together they have a total of $32. How much money does Andrew have?
$8.50 $23.50
$24.50
5
$25.50
Together, Frank and Alice initially had $100 when they went to the fair. Frank spent $10 on a bag of chips at the fair. Tt this point, he has twice as much money as Alice, who has not yet spent any of her money. How much money did Frank have initially?
Compare the price points below. Use the symbols >, <, or =.
DIRECTIONS:
Compare the price points below. Use the symbols >, <, or =.
DIRECTIONS:
Compare the price points below. Use the symbols >, <, or =.
1
A mechanic normally works 8 hours per day and earns $13.50 per hour. For each hour the mechanic works in excess of 8 hours on a given day, he is paid 1.5 times his normal rate. If the mechanic works 10 hours on a given day, how much does he earn on that particular day?
2
Evelyn is paid $15 per hour for the first 40 hours she works per week and $20 per hour for each hour she works in excess of the first 40 hours per week. If Evelyn earned $740 last week, how many hours did she work last week?
3
If Albert gives Bernard $17 and Bernard gives David $13, the three of them will have the same amount of money. How much more money does Albert have than Bernard at the beginning?
4
Vicky has $6 more than Hank has. If Hank gives Leo $2 and Noel gives Hank $5, how much more money does Vicky have than Hank now?
5
John worked 40 hours last week, including 6 hours during the weekend. John earns $18 per hour during weekdays (Monday to Friday) and 1.5 times that amount during weekends. How much did John earn last week?
1
Emily has $3 more than Cynthia has, but $5 less than Kim has. If Emily has $17, how much money do Cynthia and Kim have altogether?
$32
$36
$34
$40 2
George went to the hardware store and spent of his money to buy a new power drill, to buy some bolt locks, and to buy some nails. If George spent the remaining $30 to buy a new hammer, how much did George spend at the hardware store?
$1,200 $1,500
$1,800
If Gene has four times the amount of money that he has now, he will have the exact amount of money to buy four video games and two CDs. If each video game costs $12.95 and each CD costs $8.50, how much money does Gene have now?
$14.60
Mr. Richie left half of the money in his estate to his wife, to his eldest daughter, to his youngest daughter, and the remaining $300,000 to charity. How much was the total amount of money in Mr. Richie’s estate?
$2,900,000
$3,000,000
$5,400,000
$4,600,000 5
Together, Billy and Laura initially had $150 when they went to the concert. Billy spent $15 on a snack at the concession stand. At this point, he has twice as much money as Laura, who has not yet spent any of her money. How much money did Billy have initially?
A carpenter normally works 9 hours per day and earns $11.50 per hour. For each hour the carpenter works in excess of 9 hours on a given day, he is paid 1.7 times his normal rate. If the carpenter works 11 hours on a given day, how much does he earn on that particular day?
$142.60 $149.60
Cate is paid $17 per hour for the first 30 hours she works per week and $25 per hour for each hour she works in excess of the first 30 hours per week. If Cate earned $660 last week, how many hours did she work last week? 30 hours
hours 35 hours
hours
If Zack gives Gary $19 and Gary gives Will $11, the three of them will have the same amount of money. How much more money does Zack have than Gary at the beginning?
Bob has $7 more than Henry has. If Henry gives Logan $4 and Nagel gives Henry $6, how much more money does Bob have than Henry now?
Jeremy worked 36 hours last week, including 4 hours during the weekend. Jeremy earns $15 per hour during weekdays (Monday to Friday) and 2.5 times that amount during weekends. How much did Jeremy earn last week?
USING VOLUME AS AN ATTRIBUTE OF THREE-DIMENSIONAL FIGURES
MA.5.GR.3.1
Explore volume as an attribute of three-dimensional figures by packing them with unit cubes without gaps. Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes.
Count the number of unit cubes to determine the volume. = 15 units = 1 unit3
Key:
Count the unit cubes for the length, width, and height of a rectangular prism to find its volume.
Step 1: Determine the length, width, and height of the right rectangular prism. These dimensions should be whole numbers.
Step 2: Multiply the number of unit cubes in the base layer (length × width) by the number of layers (height) to find the total number of unit cubes inside the prism. This total count represents the volume of the right rectangular prism in terms of unit cubes.
Step 3: Volume = Length × Width × Height
Example:
DIRECTIONS:
Find the volume of the right rectangular prisms below.
DIRECTIONS: Use the cubes to find the volume.
DIRECTIONS:
Use the unit cubes to measure the volume.
1
What is the volume of the rectangular prism?
256 cubic units
256 units
2
square units
boxes
Paris is filling a box with sugar cubes. She fills the bottom of the box with exactly 15 cubes. If she can fit 7 total layers in the box, what must the volume of the box be?
22 unit cubes
75 unit cubes
3
unit cubes
A board game company has 800 identical dice cubes that must be shipped to a toy store. An employee packs 120 into the base of a small box, leaving no gaps. If the employee can fit exactly 5 more layers on top before the box is full, will she be able to fit all 800 dice in the box?
Yes, because that means she can fit 820 dice in the box.
No, because that means she can only fit 700 in the box.
No, because that means she can only fit 720 in the box.
Yes, because that means she can fit exactly 800 dice in the box.
4
Which of the following is not a unit cube?
Figure A
Figure B
DIRECTIONS:
Use the unit cubes to measure the volume.
What is the volume of the rectangular prism below?
Nate and Katie are playing with blocks. Their prisms are represented below. Both claim that their prisms have volumes of 80 cubic units. Who is correct? Nate is correct.
correct.
correct.
What is the volume of the prism shown below?
For which of the following can the volume not be found by counting unit cubes?
Nate Katie
1
What is the volume of the rectangular prism below?
2
Freddy is arranging Rubik’s cubes (in the shape of a rectangular prism) in a box. The box holds 144 cubes in the bottom layer. He arranges 8 layers. What is the volume of the box? 1,152 unit cubes
3
What is the volume of the figure below?
4
Kim and Natalie are looking at the figures given below. Kim claims that both cubes have different volumes, but Natalie says they have the same volume. Who is correct?
Kim is correct.
Natalie is correct. Both are correct. Neither are correct.
5
What is the volume of the prism shown below?
6
Charlie arranges blocks of a game into 11 rows of 8 blocks each. If he arranges 6 layers, what is the volume of the structure he makes?
428 unit cubes
880 unit cubes
7
What is the volume of the prism shown below ?
unit cubes
unit cubes
8
35 unit cubes
unit cubes 45 unit cubes
unit cubes
Alex is stacking cubes to form a rectangular prism. He arranges 6 layers of cubes, with each layer having 7 cubes in each row and 4 cubes in each column. What is the volume of the rectangular prism?
9
A toy company wants to ship 450 identical toy blocks. The base of the crate has been filled without spaces with 50 blocks and can fit 9 more layers. Can all 450 toy blocks fit?
Yes, 500 blocks fit.
10
No, only 400 blocks fit.
No, only 450 blocks fit. Yes, exactly 450 blocks fit.
Ava is stacking cubes to form a tower. She arranges 10 layers of cubes, with each layer having 3 cubes in each row and 9 cubes in each column. What is the volume of the tower? 270
PLOTTING POINTS REPRESENTATIVE OF REAL-WORLD PROBLEMS
MA.5.GR.4.2
Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.
Interpreting the coordinate values can effectively represent mathematical and real-world problems.
STEP 1: Read the real-world problem, and identify the relevant variables and quantities involved.
STEP 2: Understand what each coordinate represents such as, a measurement of time, distance, height, length, etc.
STEP 3: Assign appropriate coordinates to the quantities, with the x-coordinate representing the first quantity (time, number of items, etc.) and the y-coordinate (distance, cost, etc.) representing the second value.
STEP 4: Plot the points in the first quadrant of the coordinate plane based on the assigned coordinates for each situation.
STEP 5: Read the coordinates (x, y) of each plotted point and interpret them in the context of the problem.
Example: Plot the hotel at (3, 5).
DIRECTIONS:
Determine the coordinates for the locations listed below.
PLACE
DIRECTIONS:
Determine the coordinates for the locations listed below.
1
Edgar planted a tree in his backyard. He used the graph given to record the tree’s height at the end of each week.
How tall was the tree when Edgar planted it in his backyard?
2
Using Edgar’s graph that records the tree’s height over a 9week period, how many inches did the tree grow between Week 5 and Week 7?
Camilo tracked the number of miles he walked while exercising at the end of each hour using the graph given.
At what time did Camilo start walking? 8:00 AM 7:00 AM 9:00 AM 10:00 AM 4
Using Camilo’s graph on the right, how far had he traveled two hours after he started walking?
DIRECTIONS:
Determine the coordinates for the locations listed below.
HOSPITAL
HOSPITAL
Lisa kept track of the number of emails she sent at the end of each day using the graph given.
On which day did she send the most number of emails?
6 Day 7 Day 8 Day 9 2
Lisa analyzed the graph she made tracking the number of emails she sent over 9 days.
On which day did she send no emails?
1
2
Using Lisa’s graph detailing the number of emails she sent over a 9-day period, how many days did she send more than 25 emails per day?
According to Lisa’s graph, how many more emails did she send on Day 6 than on Day 5?
1
Arnold kept track of the number of videos he watched online each week using the graph given.
In which week did he watch the greatest number of videos?
Week 2
Week 6
2
Week 4
Week 8
Arnold’s graph shows the number of videos he watched online for the last 9 weeks.
How many videos did he watch during Week 2 and Week 3 combined?
30 videos 90 videos
50 videos 40 videos
3
Using Arnold’s graph which kept track of the number of videos he watched online, how many weeks did he watch less than 50 videos?
Seven
Eight Five Four
4
Frank tracked the number of miles he walked while exercising at the end of each hour using the graph given.
Between which two hours did Frank walked 4 miles?
10:00 AM and 11:00 AM 11:00 AM and 12:00 PM 1:00 PM and 2:00 PM 2:00 PM and 3:00 PM
5
Using Frank’s graph on the right, at what time did Frank appear to take a break from walking on his hike? 11:00 - 2:00 PM 12:00 - 2:00 PM 1:00 - 2:00 PM 2:00 - 4:00 PM
6
Sam is tracking the number of fruits he eats each week using the graph on the right. How many fruits did he eat during Week 3?
7
fruits
fruits
fruits
The graph represents the number of push-ups Ahmed did each day for a month. On which day did he do the least number of push-ups? Day 1
3
8
2
8
Mr. Perez is keeping track of the number of books his class reads each year using the graph on the right. How many books did his class read during Year 5 and Year 6 combined?
MA.5.DP.1.1
CREATING TABLES, GRAPHS, AND LINE PLOTS
Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
STEP 1: Determine the range of your data, which is the minimum and maximum values of your measurements. This will help you set up the axis appropriately.
STEP 2: Create a horizontal axis (x-axis) for your line plot. Label it with the fractions you are working with, such as 1/8, 1/4, 3/8, 1/2, and so on.
STEP 3: Divide the x-axis into equal segments based on the fractions you are dealing with. For example, if you are using 1/5, each segment would represent 1/5 of the unit.
STEP 4: Give your line plot a descriptive title that explains what the plot is displaying, such as "Measurements in Fractions of a Unit."
STEP 5: Title the x-axis with a clear label like "Fractions" or "Measurement Units." Add a label to the y-axis if your measurements have corresponding values on another scale.
Example:
Number of Slices Consumed (each)
Personal Pan Pizza Consumed by Students Personal Pan Pizza Cut in Fifths
DIRECTIONS:
Use the fractions below to create a tally table and line plot.
DIRECTIONS: Plot the set of data in the graph provided.
WEIGHT OF A NEWBORN
DIRECTIONS:
Use the fractions below to create a tally table and line plot.
DIRECTIONS: Plot the set of data in the graph provided.
1
Jeff measured the length, in inches, of 12 grasshopper specimens during a science experiment. The table below shows the data he gathered.
Which of these tables matches the data displayed above?
2
Alfred recorded the number of hours he spent playing video games each day for seven days. He played 1 hours on Day 1, 1 hours on Day 2, 1 hours on Day 3, 1 hours on Day 4, 1 hours on Day 5, 1 hours on Day 6, and 1 hours on Day 7. Which of these line graphs matches the data?
DIRECTIONS:
Use the fractions below to create a tally table and line plot.
DIRECTIONS: Plot the set of data in the graph provided.
1
The table below shows the length of some grasshopper specimens. Which of the line plots below matches the data?
2
A vendor recorded how many pounds of potatoes she sold each day for seven days. She sold 5 pounds on Day 1, 4 pounds on Day 2, 4 pounds on Day 3, 5 pounds on Day 4, 5 pounds on Day 5, 5 pounds on Day 6, and 5 pounds on Day 7. Which of these line graphs matches the data?
1
Kim found 12 cans of paint in her garage. The table below shows the amount of paint, in pints, in each of the cans she found.
Which of these tables matches the data displayed above?
2
Alfred recorded the amount of rainfall each day for seven days. He recorded 6 inches of rainfall on Day 1, 5 inches on Day 2, 6 inches on Day 3, 6 inches on Day 4, 5 inches on Day 5, 5 inches on Day 6, and 5 inches on Day 7. Which of these line graphs matches the data?
3
The table below shows the distances the students lived from the school. Which of the line plots below matches the data?
4
Ben filled six bottles with oil. He filled the first bottle with 3 quarts of oil, the second bottle with 2 quarts of oil, the third bottle with 3 quarts of oil, the fourth bottle with 3 quarts of oil, the fifth bottle with 2 quarts of oil, and the sixth bottle with 3 quarts of oil. Which of these line graphs matches the data?
MA.5.DP.1.2
MEAN, MEDIAN, MODE, AND RANGE
Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range.
Calculating the mean (average) of a set of whole-number values.
STEP 1: Add up all of the values provided in the table or line plot.
THIRD: Interpret the result as “the mean number of tickets sold over 10 hours is 16”.
Calculate the median (middle number of an ordered data set)
STEP 1: Arrange the data in ascending order.
STEP 2: If the data set has an odd number of values, the median is the middle value.
Example:
FIRST: 5, 7, 12, 12, 15, 16, 18, 20, 22, 23, 28
SECOND: 16 + 18 = 34 (two numbers in the middle)
Calculate the mode (the number that appears most frequently).
STEP 1: Identify the value that occurs with the highest frequency.
STEP 2: If multiple values share the highest frequency, the dataset is multimodal, and there is no mode.
SECOND: 12 appears twice whereas, all other numbers appear only once. Example:
FIRST: 5, 7, 12, 12, 15, 16, 18, 20, 22, 23, 28
THIRD: 34 ÷ 2 = 17
FOURTH: Interpret the result as the median is 17.
Calculate the range (the number that appears most frequently).
STEP 1: The range is the difference between the highest and lowest values in the data set.
STEP 2: Subtract the smallest value from the largest value to find the range.
Example:
FIRST: Identify the highest value: 28
SECOND: Identify the lowest value: 5
THIRD: Subtract 28 - 5 = 23
DIRECTIONS:
Calculate the mean, median, mode, and range of the data sets below.
DIRECTIONS:
Calculate the mean, median, mode, and range of the data sets below.
1
Michelle did a survey in her class. She asked the students in her class how many siblings they had and recorded the responses to her survey in the table below.
Based on the results of her survey, what was the mean number of siblings per student?
Michelle did a survey in her class. She asked the students in her class how many siblings they had and recorded the responses to her survey in the table below.
Based on the results of her survey, what was the mode of the number of siblings of the students in her class?
3
Michelle did a survey in her class. She asked the students in her class how many siblings they had and recorded the responses to her survey in the table below. Based on the results of her survey, what was the median number of siblings of the students in her class?
Michelle did a survey in her class. She asked the students in her class how many siblings they had and recorded the responses to her survey in the table below.
Based on the results of her survey, what was the range of the number of siblings of the students in her class?
The organizers used the table below to keep track of the number of medals won by the participants of the contest.
What is the range of the number of medals won by the participants of the contest?
DIRECTIONS:
Calculate
1
A bake shop kept track of the number of cupcakes it sold each day using the line plot given.
What was the mean number of cupcakes sold per day by the bake shop per day?
day
2
A bake shop kept track of the number of cupcakes it sold each day using the line plot given.
What was the median number of cupcakes the bake shop sold?
A bake shop kept track of the number of cupcakes it sold each day using the line plot given.
What was the mode of the number of cupcakes that the bake shop sold?
The organizers used the table given to keep track of the number of medals won by the participants of the contest.
What is the median number of medals won by the participants of the contest?
During the school’s recycling drive, the students in Ms. Anne’s class collected the following numbers of empty bottles per student: 12, 15, 10, 8, 16, 20, 14, 12, 7, 11, 9, and 10. What is the mean number of empty bottles per student that Ms. Anne’s class collected?
1
A bakeshop kept track of the number of cupcakes it sold each day using the line plot given.
What was the range of the number of cupcakes that the bakeshop sold?
2
The organizers used the table given to keep track of the number of medals won by the participants of the contest.
What is the mode of the number of medals won by the participants of the contest?
3
The organizers used the table given to keep track of the number of medals won by the participants of the contest.
What is the mean number of medals won per participant?
4
A convenience store kept track of the number of cold drinks it sold each day using the line plot given.
What was the range of the number of cold drinks that
A convenience store kept track of the number of cold drinks it sold each day using the line plot given.
What was the median number of cold drinks that the store sold?
During the school’s food drive, the students in Mr. Allen’s class collected the following numbers of soup cans: 23, 17, 11, 14, 21, 16, 10, 18, 12, 24, 6, and 20. What is the mean number of used soup cans per student that the students that Mr. Allen’s class collected?
10 pages per student 12 pages per student 14 pages per student 16 pages per student
The organizers used the table given to keep track of the number of trophies won by the participants of the contest.
What is the mode of the number of trophies won by the participants of the contest?
The organizers used the table given to keep track of the number of trophies won by the participants of the contest.
What is the mean number of trophies won by the
of the contest?
The organizers used the table given to keep track of the
of trophies
by the participants of the contest.
What is the range number of trophies won by the participants of the contest?
The organizers used the table given to keep track of the number of trophies won by the participants of the contest.
What is the median number of trophies won by the participants of the contest?
