Unit 1, Lesson 1
Find the pattern in these numbers: 0, 9, 18, 27, 36, 45. Write the next three numbers.
Possible pattern: Add 9; 54, 63, 72 Unit 1, Lesson 2
Dulal, Lien, and Kate have either the bird, the cat, or the fish. Dulal does not have the bird. Lien does not have the cat. Kate does not have the fish or the cat. Which pet does each person have? Explain. Dulal: Cat; Lien: Fish; Kate: Bird; used a table. Bird Cat Fish Dulal no yes no Lien no no yes Kate yes no no Unit 1, Lesson 3 Can you name two whole one- digit numbers that have a sum of 16 and a difference of 1? Why or why not?
No. The only pairs of one-digit numbers that have a sum of 16 are 8 + 8 and 7 + 9. Neither of these pairs has a difference of 1. Unit 1, Lesson 4
Mark cut a ribbon in half. He kept one half and gave ½ of the other half to each of 2 people. Juan got 4 inches. How much ribbon did Mark have to begin with? Explain how you found your answer.
16 inches; I drew a rectangle and filled in what I know. Unit 1, Lesson 5
Tyler, Kyra, and Emily finished the race in first, second, and third places. Tyler finished 1 second behind Emily. How many different ways could they have finished the race?
3 ways; make an organized list and delete items based on the conditions; Tyler cannot be first and always has to be behind Emily. K, E, T; E, K, T; E, T, K Unit 1, Lesson 6
Felipe created a three-digit number. The hundreds digit is 3 greater than the ones digit. The product of the tens and the ones digits is 6. The sum of the hundreds and the ones digits is 9. What is the 3-digit number?
623; Hundreds and Ones: 6 – 3 = 3 and 6 + 3 = 9; Tens: 2 x 3 = 6 Unit 1, Lesson 7
How many possible products can you get using any combination of two of these factors? 2, 5, 10
3 products, 10, 20, 50 Unit 1, Lesson 8
Tom finished the race 4 seconds behind Jane. Lou finished 7 seconds ahead of Tom. Write the order in which they finished the race. Explain.
Lou, Jane, Tom; I made a drawing using the given data Unit 1, Lesson 9
Jan has 5 times the number of dimes as she has nickels. She has half the number of nickels as she has pennies. Jan has 20 pennies. How many nickels does Jan have? How many dimes does Jan have?
10 nickels; 50 dimes Unit 1, Lesson 10
Write the number 18 on the board. Have students write the multiplication expressions that equal this product.
Possible answer: 9 x 2; 3 x 6; 1 x 18 Unit 1, Lesson 11
At the park, there are birds and dogs. Altogether there are 6 animals and 16 legs. How many birds and dogs are at the park? Show your work.
4 birds, 2 dogs; Amount Legs Amount Legs Birds 3 6 4 8 Dogs 3 12 2 8 Total 6 18>16 6 16 Unit 1, Lesson 12
Jake ran around a two mile track 3 times. Luke ran around the 2 mile track 5 times. The boys said together they ran 16 miles. Are the boys right? Explain how you know.
Possible answer: Yes, 3 x 2 plus 5 x 2 is the same as 8 groups of 2 or 16. Unit 1, Lesson 13
Carl’s teacher asked him to arrange 12 chairs in rows. She gave him these directions: place an equal number of chairs in each row and place more than 2 chairs in each row. What are some ways that Carl could arrange the chairs?
Possible answers: 2 rows and 6 chairs, 3 rows of 4 chairs, or 4 rows of 3 chairs. Unit 1, Lesson 14
Bella, Tom, Juan, and Katie are different heights. Their heights are 6 feet, 5 feet, 4 feet, and 3 feet. Bella is not 6 feet or 5 feet tall. Tom is not 6 feet or 4 feet tall. Katie is 3 feet tall. How tall is Juan?
6 feet tall Unit 1, Lesson 15
Brian’s basketball team will use two-digit numbers on their uniforms. Each player can choose a 1 or a 2 for the first digit. The second digit must be a 0, 1, 2, or 3. What are the possible uniform numbers?
Possible answers: 10, 11, 12, 13, 20, 21, 22, 23 Unit 1, Lesson 16
Taylor is thinking of a number that is greater than 20 but less than 30. The product of the digits is 10. What is the number?
25 Unit 1, Lesson 17
The bookstore is advertising a special “buy 2 books and get 1 free” sale. The regular price for one book is $9. How much would it cost to buy 6 books while they are on sale?
$36 Unit 1, Lesson 18
Brad has 7 coins worth 32¢. What are the coins? Explain.
1 dime, 4 nickels, 2 pennies; Add coins to find the group of 7 coins and a total of 32¢. Unit 1, Lesson 19
The first two digits of a three digit number is the product of 7 and 9. The first and last digits of the three digit number are the same. What is the three digit number?
636 Unit 2, Lesson 1
Two pens cost 30¢ in all. One pen costs 10¢ more than the other pen. How much does each pen cost? Explain how you found your answer.
30¢ - 10¢ = 20¢ so 20¢ needs to be divided equally to find the other two parts. One pen cost 10¢ and the other pen costs 20¢ Unit 2, Lesson 2
Will made a sign by cutting a board into 2 equal sections. Then he cut 3 inches off the piece he wanted to use. This gave him a sign that was 11 inches long. How long was Will’s original board?
28 inches Unit 2, Lesson 3
Raphael has homework in Math, English, and Social Studies. How many different ways can he complete his assignments?
6 Unit 2, Lesson 4
An extra-large popcorn costs 89¢, a large popcorn costs 81¢, and a medium popcorn costs 73¢. If the pattern continues, how much will the small popcorn cost? Explain.
65¢; Small comes after medium. Unit 2, Lesson 5
Alex, Josh, and Julie have either a bike, skateboard, or rollerblades. Josh does not have the skateboard. Alex does not have the rollerblades or the skateboard. Which does each person have?
Alex: bike; Josh: rollerblades; Julie: skateboard Bike Skateboard Rollerblades Alex yes no no Josh no no yes Julie no yes no Unit 2, Lesson 6
Tom has 5 coins worth 66¢. What are the coins? Explain
2 quarters, 1 dime, 1 nickel, 1 penny; Add different values to find 5 coins worth 66¢. Unit 2, Lesson 7
A function machine divides each input by 8. What is the output when the input is 16? 80? 8? 64?
2; 10; 1; 8 Unit 2, Lesson 8
When Josh, his cat, and his dog all stand on the scale together, the scale reads 107 pounds. When Josh and his cat stand on the scale, it reads 82 pounds. When Josh and his dog stand on the scale, it reads 95 pounds. How much does Josh weigh?
70 pounds Unit 2, Lesson 9
There are 2 books on the first shelf, 4 books on the second shelf, 6 books on the third shelf, and 8 books on the fourth shelf. How many books are on the seventh shelf? Give the rule for the pattern and find the number of books on the 7th shelf.
Add 2; 14 books Unit 2, Lesson 10
Mr. Raj’s garage contains 3 bicycles and a tricycle. How many wheels are there altogether?
9 wheels Unit 2, Lesson 11
Jordan plans to eat a banana for three days in a row, then an apple for two days, and then an orange for two days. If he eats the first banana on Tuesday, which day of the week will he eat the first orange?
Sunday Unit 2, Lesson 12
Use the clues to find the three digit mystery number. The digit in the ones place is the largest one digit square number. The digit in the tens place is the product of 5 and 0. The digit in the hundreds place is the smallest odd whole number. What is the number? 109 Unit 2, Lesson 13
The sum of two numbers is 12 and their difference is 2. What is the product of the two numbers?
5 + 7 = 12; 7 – 5 = 2; 7 x 5 = 35 Unit 2, Lesson 14
Keisha bought a package of pencils. She can place the pencils into equal groups of 2, 3, or 4. How many pencils could be in the package? Explain.
Possible answer: 12; Two groups of 6 equal 12, 3 groups of 4 equal 12, and 4 groups of 3 equal 12. Unit 2, Lesson 15
Ashley had a long piece of ribbon. She cut an 8-inch length from one end of the ribbon. Then she cut the rest of the ribbon into four equal lengths of 10 inches each. How long was the original piece of ribbon?
48 inches Unit 3, Lesson 1
Tell whether each statement is true or false. If it is false, give an example that shows why it is false.
If you multiply two even numbers, the product will be even. True
If you multiply an odd and an even number, the product will be odd. False; Possible example: 5 x 4 = 20
If you multiply two odd numbers, the product will be odd. True Unit 3, Lesson 2
Rhonda cut one string into two equal pieces. Next she cut 11 inches off one piece. That gave her a piece of string that was 29 inches long. How long was the whole piece of string? Use paper strips to act out the problem.
80 inches Unit 3, Lesson 3
The store uses soup cans to make displays. The first display uses 45 cans. The second uses 51 cans. The third uses 57 cans. If the pattern continues, how many cans are in the fourth display?
63 cans Unit 3, Lesson 4
Pablo cut string into 4 equal pieces. Then, he cut each piece in half. Now, each piece has a 2-inch length. What was the length of the whole string?
16 inches Unit 3, Lesson 5
Nate, Pamela, Tom, and Robin are friends. Tom is taller than Robin. Nate is shorter than Tom but taller than Robin. Pamela is taller than Tom. List the friends in order from shortest to tallest.
Robin, Nate, Tom, Pamela Unit 3, Lesson 6
The tens digit of a two-digit number is two more than the ones digit. If you reverse the digits, you get a number that is a multiple of both 4 and 6. What is the original number?
42 Unit 3, Lesson 7
In Mr. Porter’s class, there are 15 students on the basketball team or the football team (or both). If 6 students are on the basketball team and 12 students are on the football team, how many students are on both the basketball and football team?
3 students Unit 3, Lesson 8
Di’s sister is 3 years older than Di. The sum of their ages is 19 years. How old is Di? How old is her sister? Explain how you found your answer.
8; 11; I guessed numbers for Di’s age and checked the sum. Di’s Age Sister’s Age Sum 6 9 15 < 19 7 10 17 < 19 8 11 19 Unit 3, Lesson 9
Madison wears a uniform to work. Her uniform has two different colored shirts, red and blue. The uniform has two pairs of pants in different colors, tan and black. She can mix the shirts and pants to make different outfits. How many different outfits can Madison make?
4 outfits Unit 3, Lesson 10
A flight monitor in an airport shows that a plane departed at 1:34 p.m. and arrived at its destination at 4:14 p.m. How long was the flight?
2 hours 40 minutes Unit 3, Lesson 11
Sarah spent $5 from her savings to buy a book. Then, she spent half of her remaining savings when she paid $9 for a shirt. How much money did Sarah have in savings before she bought the book and the shirt?
$23 Unit 3, Lesson 12
Zach bought a carton of 8 bottles of water. Each bottle holds 2 liters. How many liters of water did Zach buy altogether?
16 liters Unit 3, Lesson 13
Harper, Luke, and Jolie either drive a car, truck, or van. Luke does not drive the truck. Jolie does not drive the car or truck. Which does each person drive?
Harper: Truck; Luke: Car; Jolie: Van Unit 3, Lesson 14
Becky is placing pennies in rolls of 50. If a penny weighs about 3 grams, about how much will a roll of 50 pennies weigh?
About 150 grams Unit 3, Lesson 14
Gray finished her band practice at 4:40 p.m. She practiced for 1 hour and 10 minutes. What time did band practice start?
3:30 p.m. Unit 4, Lesson 1
Aretha is taller than Sean. Sean is shorter than Hamid. Aretha is the tallest student. Order the students from shortest to tallest.
Sean, Hamid, Aretha Unit 4, Lesson 2
Field hockey practice started at 10:30 a.m. and ended at 1:00 p.m. How long was field hockey practice?
2 hours 30 minutes Unit 4, Lesson 3
Cole created a three-digit number. The hundreds digit is 5 greater than the ones digit. The product of the tens and ones digits is 8. The sum of the hundreds and the one digits is 9. What is the three- digit number?
742; Hundreds and Ones: 7 – 2 = 5 and 7 + 2 = 9; Tens: 8 = 4 x 2 Unit 4, Lesson 4
A function machine adds 3 to each input. What is the output when the input is 3? 8? 12? 25?
6; 11; 15; 28 Unit 4, Lesson 5
A palindrome is a number that is the same whether is read from left to right or from right to left, such as 121. Use the digits 5 and 6 to make all possible three-digit palindromes. Explain how you found your answer.
666, 656, 555, 565; I put the same digit in the front, back, and middle. Then, I changed the digit in the middle. Unit 4, Lesson 6
Luis, Evan, Zoey, and Layla lined up to get their picture taken. Zoey did not have her picture taken first or second. Luis was last to have his picture taken. Layla had her picture taken before Evan, in what order did they line up?
Luis: Fourth; Evan: second; Zoey: Third; Layla: First Unit 4, Lesson 7
Three people ran in a race. Jo finished the race after Paul. Paul finished the race before Hanh. Hanh was not last. Who finished the race first? Who finished the race last?
Paul, Jo Unit 4, Lesson 8
A children’s museum had two crafts days. They had enough supplies for 125 projects. On the first day, 65 children make a project. On the second day, 51 children made a project. The museum had supplies for how many projects left?
9 projects Unit 4, Lesson 9
Akio has 4 dollars, 8 quarters, and 20 nickels. How much money does he have? He spends $5. How much money does he have left?
$7; $2 Unit 4, Lesson 10
Write the number 134 on the board. Have students write this number in as many different ways as possible, such as an addition or subtraction expression.
Possible answer: 100 + 30 + 4 Unit 4, Lesson 11
Hirva, Sammy, and Garrett have a red, a blue, and a yellow balloon. Garrett is not holding the yellow balloon. Hirva is not holding the blue or a yellow balloon. Which color balloon is each person holding?
Hirva: Red; Sammy: Yellow; Garrett: Blue Unit 4, Lesson 12
JiSun bought eight items. She paid with a $5 bill and got $1 in change. If the store sells pens for 50¢ each, pencils for 25¢ each, and a set of markers for $1 each, which 8 items did she buy?
2 sets of markers, 2 pens, and 4 pencils Unit 4, Lesson 13
Riley cut a piece of ribbon into 5 equal pieces. Then she cut each piece in half. Now each piece has a 6-inch length. What was the length of the whole piece of ribbon?
60 inches Unit 4, Lesson 14
Mia buys barrettes that cost a total of 67 cents. She gives the clerk three quarters. How much change should Mia receive?
8 cents Unit 4, Lesson 15
Three students can sit on each of the two long sides of the rectangular picnic table. One student can sit at each end of the table. How many students could be seated if three tables were connected end to end? Make a drawing to help you solve the problem.
20 students Unit 4, Lesson 16
Xavier weighed a bag of apples. Then he added 2 more pounds of apples to the bag. After taking 4 pounds of apples out, the bag weighed 5 pounds. How much did the bag of apples weigh in the beginning?
7 pounds Unit 4, Lesson 17
How many different ways can Avery, Isabella, Tanisha, and Sophia stand in a line if Avery is always first?
6 ways Unit 4, Lesson 18
Teresa scored 26 points in 10 volleyball games. In each game, she scored either 2 or 3 points. In how many games did she score 3 points? Explain how you found your answer.
6 games, possible explanation: Guessed 5 games at 3 points and 5 games at 2 points, totaling 25 points < 26 points. So, I increased the 3-point games to 6 and decreased the 2- point games to 4. Unit 5, Lesson 1
A palindrome is a number that is the same whether read from left to right or from right to left, such as 121. Use the digits 5 and 6 to make all possible three-digit palindromes. Digits can be repeated within a number. Explain how you found your answer.
666, 656, 555, 565; I put the same digit in the front and back. Then I changed the digit in the middle. Unit 5, Lesson 2
Luis, Evan, Zoey, and Layla lined up to get their picture taken. Zoey did not have her picture first or second. Luis was last to have his picture taken. Layla had her picture taken before Evan. In what order did they line up?
Layla: first; Evan: second; Zoey: third; Luis: fourth Unit 5, Lesson 3
A function machine subtracts 5 from each input. What is the output when the input is 8? 12? 20? 115?
3; 7; 15; 110 Unit 5, Lesson 4
Have students write the number for eight hundred forty and find the number that is 100 more.
840; 940 Unit 5, Lesson 5
On Saturday, Payat’s family arrived at a street fair at 1:15 in the afternoon. They left the fair at 5:35 the same afternoon. How much time did they spend at the fair?
4 hours 20 minutes Unit 5, Lesson 6
Seth had some marbles that he shared equally with Josh. Then Josh gave half his marbles to his sister Elaine. If Elaine received 4 marbles, how many marbles did Seth start with?
16 marbles Unit 5, Lesson 7 Mr. Kaku has a CD storage unit that holds 63 CDs. Each shelf of his CD storage unit holds 9 CDs. All but 3 of the shelves are full. How any shelves are full?
4 shelves
Unit 5, Lesson 8 A 36-inch board is cut into two pieces. One piece is 4 inches longer than the other. How long is the shorter piece? How long is the longer piece?
16 inches; 20 inches
Unit 5, Lesson 9 Carlie collected 17 box tops for a class project. That was 9 more box tops than Brooke collected. How many box tops did Brooke and Carlie collect altogether?
25 box tops
Unit 5, Lesson 10 A small drink is 72¢, a medium drink is 77¢, and a large drink is 82¢. If the pattern continues, how much is an extra-large drink likely to cost? Explain.
87¢; I wrote out the numbers to find the pattern, which is add 5¢. Extra-large is after large, so I add 5¢ to 82¢ and get 87¢. Unit 5, Lesson 11 Mr. Jackson watched his daughter play in a soccer tournament. He arrived at 9:30 in the morning. He and his daughter went home at noon. How long was Mr. Jackson at the soccer tournament?
2 hours and 30 minutes Unit 6, Lesson 1 Logan has a collection of trading cards. His friend gave him 6 more cards. Logan sold 12 cards at a trade fair. Then he bought 20 cards. Logan now has 50 cards. How many cards did he have to start with?
36 cards Unit 6, Lesson 2 There were 687 people at a school play. Round the number of people to the nearest ten and to the nearest hundred.
690; 700
Unit 6, Lesson 3 Jack created an art piece using marbles. The first row of the art piece has 1 marble. The second row has 3 marbles. The third row has 6 marbles. The fourth row has 10 marbles. If the pattern continues, how many marbles will be in the eighth row? Explain.
36 marbles; I used the pattern +2, +3, +4, and so on. The eighth row would have 36. Unit 6, Lesson 4 Kylie is 6 years younger than her brother. The sum of their ages is 22. How old is Kylie? How old is her brother?
8 years; 14 years
Unit 6, Lesson 5 Liam, Shay, Mason, and Noah have different numbers on their jerseys. The numbers are 23, 24, 25, and 26. Liam’s number is an even number. Shay’s number is a multiple of 5. Noah’s number is not an even number. Mason’s number is a multiple of 4. What number does each boy have on his jersey?
Liam: 26; Shay: 25; Mason: 24; Noah: 23 Unit 6, Lesson 6 Fill in the blank with always, sometimes, or never. The opposite sides of a parallelogram are ______parallel. Parallelograms ______have 3 sides. A parallelogram ______has right angles. always; never; sometimes Unit 6, Lesson 7 Mrs. Yoshira wants to buy pens and pencils for her 24 students. Pencils are sold in packs of 8 pencils for $2. Pens are sold in packs of 6 pens for $2. How many packs of pens and pencils should she buy? How much will it cost? $14 Possible answer: 3 packs of 8 pencils each and 4 packs of 6 pens each Unit 6, Lesson 8 Alicia started the drive to her grandmother’s house at 11:30 a.m. She arrived at 2:45 p.m. How long was Alicia’s drive?
3 hours 15 minutes
Unit 6, Lesson 9 Decide if the second number is 10 more or 10 less than the first number. 1. 108 ─› 98 2. 914 ─› 924 3. 296 ─› 306
1. 10 less 2. 10 more 3. 10 more Unit 6, Lesson 10 Pat wants to make rectangular cards with a perimeter of 12 inches. How many different cards can Pat make that have a different length and width? Make drawings of each card and label the length and width.
2 cards 4 in. 5 in. 1 in. 2 in. Unit 6, Lesson 11 Ishwar plans to carpet a square section of his room. The length and width of this section are 5 feet. How much carpet does Ishwar need for this section of his room?
25 square feet
Unit 7, Lesson 1 Jay has a triangle, a square, and a circle. He wants to make a pattern using each figure. How many different patterns can he make without repeating a figure? Explain.
6 patterns; make an organized list: triangle, square, circle; triangle, circle, square; square, circle, triangle; square, triangle, circle; circle, triangle, square; circle, square, triangle Unit 7, Lesson 2 Tamara has a rectangular garden with an area of 20 square feet that she would like to put a fence around. What is the length and width of the rectangle that would have the greatest perimeter? Explain how you found your answer.
A rectangle with sides 20 feet by 1 foot; Possible explanation: I drew pictures of rectangles with areas of 20 square feet and added the lengths of the sides to find which had the greatest perimeter. Unit 7, Lesson 3 Kevin has a dog and a cat. The dog weighs 10 pounds more than the cat. Together they weigh 40 pounds. How much does the cat weigh? How much does the dog weigh?
15 pounds; 25 pounds
Unit 7, Lesson 4 Write true or false for each sentence.
1. All trapezoids are quadrilaterals. 2. Some quadrilaterals are squares, rectangles, parallelograms, and triangles.
1. True; 2. False Unit 7, Lesson 5 The students voted for their favorite color. Three students voted for blue, five students voted for red, two students voted for green, and six students voted for orange. Create a line plot using the data. Then, write a conclusion about the data. Possible answer: Green was the color chosen by the fewest students. Unit 7, Lesson 6 The students voted for their favorite sport, 4 students voted for baseball. 5 students voted for soccer. 3 students voted for tennis. 6 students voted for football. Create a line plot using the data. Then, write a conclusion about the data.
Possible answer: Football was liked the most of all the sports. Unit 7, Lesson 7 How many eights are in three fourths? Write an equation and use a fraction model to explain why the fractions are equivalent.
¾ = 6/8
Unit 7, Lesson 8 Kai, Todd, and Jun chose blue, red, or green as their favorite color. No one chose the same color. Jun does not like blue. Kai does not like green or blue. Which color did each choose?
Kai: red; Todd: blue; Jun: green Blue Red Green Kai no yes no Todd yes no no Jun no no yes Unit 7, Lesson 9 Eli and Oanh each ordered the same size pizza. Eli ate ¾ of his pizza and Oanh ate 3/5 of his pizza. Who ate more pizza? Explain.
Eli ¾
3/5