Unit 1, Lesson 1
Seth had some marbles that he shared equally with Josh. Then Josh gave half of his marbles to his sister, Elaine. If Elaine received 4 marbles, how many marbles did Seth start with?
16 marbles
Unit 1, Lesson 2
Jorge needs to be at soccer practice at 12:20 p.m. It takes him 20 minutes to walk there. Along the way, he plans to stop for 10 minutes at his friend’s house. At what time should Jorge leave for practice?
11:50 a.m.
Unit 1, Lesson 3
Yara created a three-digit number using the digits 2, 6, and 8. The difference of the hundreds digit and the ones digit is the tens digit. What is the three- digit number?
862 or 826
Unit 1, Lesson 4
Luanda and James received $600 altogether. James received $100 less than Luanda. How much did each person receive?
James: $250; Luanda: $350
Unit 1, Lesson 5
The numbers in a pattern are each multiplied by 2 if the first three numbers are 3,6, and 12. What’s the sixth number?
96
Unit 1, Lesson 6
Mr. Perez and his son hiked for 40 minutes. They stopped for a snack at 4:20 p.m. When did they start hiking?
3:40 p.m.
Unit 1, Lesson 7
This morning, Mrs. Chang had $2,354 in her bank account. This afternoon, she will deposit $725 into her account. At midnight, there will be an electronic deduction of $689. How much money will Mrs. Chang have in her account tomorrow morning?
$2,390
Unit 1, Lesson 8
Baseball games were played on Friday, Saturday, and Sunday. The number of people who attended were 32,431; 44,462; and 44,064. The greatest number of people attended Saturday’s game. Fewer than 40,000 people attended Sunday’s game. How many people attended each day?
Friday: 44,064 people; Saturday: 44,462 people; Sunday: 32,431 people
Unit 1, Lesson 9
Use some, all, or none to complete this sentence:
If all squares have four equal sides and four equal angles, then ______rhombuses are squares.
Some
Unit 1, Lesson 10
Darren wrote a 4 digit-number. Each digit is different. The digit in the thousands place is the least digit. The sum of the digit in the hundreds place and the digit in the ones place equals the digit in the tens place. The sum of the digit in in the hundreds place and the digit in the tens place is 12. The digit in the ones place is 2. What number did Darren write?
1,572
Unit 1, Lesson 11
In a game, four players scored 30, 40, 60, and 80 points. Raj had the highest score. Theo scored 10 points less than Kate. Jenny also played. Which player had each score?
Raj 80, Jenny 60, Kate 40, Theo 30
Unit 1, Lesson 12
Together, two DVD’s cost $32. One DVD costs $4 more than the other. How much did each DVD cost?
$18 and $14; algebraic solution: Let x = the price of one DVD.
x + (x + 4) = $32; 2x + 4 = $32; 2x = 28; x = $14; x + 4 = $18
Unit 1, Lesson 13
Gwen has 7 more tropical fish than Ramon has. Together they have 35 tropical fish. How many fish does each child have?
Ramon 14 fish, Gwen 21 fish;
r + (r + 7) = 35; 2r +7 =35; 2r = 28; r = 14; so r + 7 = 21
Unit 1, Lesson 14
Jose made a purchase for $7.81 and received 2 dollar bills and 1 quarter as change. What bills and coins did he give the cashier? Why?
Possible answer: Jose gave the cashier a $10 bill, a nickel, and a penny, so that his change would include 1 quarter rather than 4 pennies, 1 nickel, and 1 dime.
Unit 2, Lesson 1
A museum holds two crafts days for children. They have enough supplies for 138 projects. On Saturday, 72 children make projects. On Sunday, 57 children make projects. If each child makes one project, does the museum have enough supplies for all the children? Explain how you can use estimation to answer the question.
Yes, there are enough supplies, possible explanation: round 72 to 70 and round 57 to 60; then use mental math to add 70 + 60 = 130
Unit 2, Lesson 2
Maya read for 8 more minutes than Jonah read. Together, they read for 50 minutes. How many minutes did each student read?
Maya, 29 minutes; Jonah 21 minutes; r + (r + 8) = 50; 2r + 8 = 50; 2r + 42; r = 21, so r + 8 = 29
Unit 2, Lesson 3
Natasha drew two rectangles with different perimeters that each has an area of 1,600 square units. What could be the dimensions of her rectangles?
Possible answers: 40 x 40;
20 x 80
Unit 2, Lesson 4
Fiona researched the populations of several cities. What would be the population of each city rounded to the nearest ten thousand?
14,700 10,000 19,048 20,000
156,234 160,000 281,005 280,000
323,000 320,000 654,169650,000
Unit 2, Lesson 5
Mr. Peña is buying some clothes to wear on a camping trip. He needs two shirts that each cost $25, one jacket that costs $75, and boots that cost $55. How can you use mental math to find out how much Mr. Peña’s clothes will be?
Possible answer: Add $25 + $75 = $ 100; add $25 + $50 + $5 = $75 + $5 = $80, $100 + $80 = $180.
Unit 2, Lesson 6
Lamar bought 210 square feet of shingles for his porch roof. The roof is 8 feet by 27 feet. Does Lamar have enough shingles to cover the roof? How any square feet of shingles does Lamar actually need?
No. Lamar needs 216 square feet of shingles.
Unit 2, Lesson 7
Mr. Wen is ordering student planners for his class. He has 23 students in his class. Each student planner costs $4. How can you decompose 23 to make the multiplication easier to find the total cost? What will Mr. Wen pay for the student planners?
Possible answer: I can rewrite 23 as 20 + 3 then find the product for the tens and the product of the ones and add them together to find the total cost: $92.
Unit 2 Lesson 8
A large box of cereal holds about 19 servings. A community center orders 5 large boxes of the cereal. About how many servings will that provide?
About 100 servings
Unit 2 Lesson 9
Ms. Miller measured the length of a room as 12 feet and the width of the room as 9 feet. She told a carpet salesperson that she needed 42 square feet of carpeting. What did Ms. Miller do wrong? How can she correct her measurement?
She used the perimeter instead of the area (12 + 9 + 12 + 9 = 42). She should multiply 12 x 9 to find the area; 108 square feet.
Unit 2, Lesson 10
A store has 40 kites to give away. If each person gets the same number of kites, how many different ways are there to distribute the kites?
8 ways: 1 kite each to 40 people, 2 kites each to 20 people, 4 kites each to 10 people, 5 kites each to 8 people, 8 kites each to 5 people, 10 kites each to 4 people, 20 kites each to 2 people, 40 kites each to 1 person.
Unit 2, Lesson 11
Suppose 20 students play soccer and 15 students play baseball. Four students play both soccer and baseball. How many students play one sport or both sports?
31 students: 16 play only soccer (20 – 4 = 16), 11 play only baseball (15 – 4 = 11), and 4 play both soccer and baseball, 16 + 11 + 4 = 31
Unit 2, Lesson 12
If this pattern continues, what are the next three numbers? 7, 11, 15, 19, 23, . . .
27, 31, 35
Unit 2, Lesson 13
Thomas Jefferson, the third President of the United States, was born on April 13, 1743. The country made the Louisiana Purchase in 1803 during Jefferson’s presidency. How old was Jefferson when the Louisiana Purchase was made?
60 years old
Unit 2, Lesson 14
At a street fair, a fruit stand sells 105 pears. It sells four times as many oranges as pears, and two times as many apples as oranges. To the nearest hundred, how many of each fruit is sold?
100 pears, 400 oranges, and 800 apples
Unit 2, Lesson 15
If this pattern continues, what are the next three numbers in the pattern? 3, 9, 27, 81, . . .
243, 729, 2187
Unit 2 Lesson 16
Only 1,500 people are allowed in an auditorium at one time. Exactly 1,436 people attend a band concert in the auditorium on Friday. The attendance at a band concert in the auditorium on Saturday is 1,475. How many people in all attend the concert on Friday and Saturday? Was any information not needed?
2,911 people; 1,500 people allowed in the auditorium was not needed.
Unit 2, Lesson 17
Victoria is buying helium balloons for her gymnastics group to carry in a parade. There are 4 people in her group, and each person will carry 2 balloons. If the balloons cost $3 each, how much will Victoria spend on balloons?
$24
Unit 2, Lesson 18
The jogging path in a city park is in the shape of a rectangle. The rectangle measures 4,167 feet long and 1,988 feet wide. How many feet would Henry run, if he ran around the rectangular path once?
12,310 feet
Unit 2, Lesson 19
Collin bakes cookies for a school bake sale. He bakes 4 batches of cookies on a large cookie sheet, which holds 24 cookies at a time. Then he bakes 12 batches of cookies on a small cookie sheet, which holds 15 cookies at a time. How many cookies did Collin bake in all?
276 cookies
Unit 3, Lesson 1
Jenny has $155. She buys 4 framed pictures for $22 each. Then, she buys a book for $18. How much money does Jenny have left?
$49
Unit 3, Lesson 2
Jana buys a pack of stickers that she wants to share with her friends. She divides the stickers into 5 equal groups for herself and four friends, and gives herself any remaining stickers from the pack. If each friend gets 22 stickers and Jana ends up with 25 stickers, how many stickers were in the pack?
113 stickers
Unit 3, Lesson 3
A plane flew round trip from New York, New York to London, England once a day for 8 days. At the end of the 8th day, the plane had traveled 55, 376 miles. How many miles did the plane travel on each one way trip?
3,461 miles
Unit 3, Lesson 4
Reasoning A palindrome is a number, word, or sentence that reads the same way forward as backward. For example, mom, 303, and Was it a cat I saw? are palindromes. Write a number with 4 digits and a word with 4 letters that are both palindromes.
Possible answers: deed, noon, sees, peep, toot; 1221
Unit 3, Lesson 5
Nikki, Paulo, Ted, Maya, and Rodney are standing in line at the movies. Nikki is standing directly in front of Maya. Maya is not last in line. Rodney is first. Ted is standing behind Maya. Paulo is not last in line. In what order are the friends standing in line?
Rodney, Paolo, Nikki, Maya, and Ted
Unit 3, Lesson 6
Starting at midnight on a Monday, a clock chimes every 6 hours and a whistle blows every 8 hours. When will they both sound at the same time?
Midnight on Tuesday; if students have difficulty getting started, have them figure out the times when the clock chimes on Monday; then have them figure out the time when the whistle blows; then, they can compare the lists to find matching times.
Unit 3, Lesson 7
Explain how you would figure out the number of:
Weeks in 6 months.
Days in 8 weeks.
Days in the last 3 months of the year.
Weeks in 6 months: 26 weeks; 52 weeks per year ÷ 2
(6–month periods in a year)
Days in 8 weeks: 56 days; multiply 7 days in a week by 8 weeks.
Days in the last 3 months of the year: 92 days; add 31 days for October, 30 days for November, and 31 days for December.
Unit 3, Lesson 8
Josie needs $215 for a trip. She has $55 saved already. If she earns $8 each hour at her baby sitting job, how many hours does she have to baby sit to reach her goal?
20 hours; $215 - $55 = $160; $160 ÷ $8 = 20
Unit 3, Lesson 9
Xander’s school collected about 3,700 books to donate. To the nearest hundred, what is the least number of books that could have been collected? What is the greatest number of books that could have been collected?
3,650; 3,749
Unit 3, Lesson 10
Mrs. Leonard is at a farmer’s market. She sees that pistachios are on sale. Each package of pistachios costs $5.68. Mrs. Leonard only has $31.00 with her. How many packages can she buy? What is a quick way to decide how many packages she can afford to buy?
Possible answer: Mrs. Leonard can round $5.68 up to $6.00. Then she can divide $31.00 by 6 to find that she can afford 5 packages of pistachios.
Unit 3, Lesson 11
Nine teachers and 58 students go on a field trip. Each van holds 7 passengers. How many vans does the group need to go on the field trip?
10 vans
Unit 4, Lesson 1
A group of travelers is leaving town on Tuesday at 7:30 a.m. The group will return at 8:00 p.m. the following Monday. How long will the group be out of town?
6 days 12 hours 30 minutes
Unit 4, Lesson 2
Anwar sold tickets for a school fair. Adult tickets cost $8, and student tickets cost $5. Anwar sold 12 tickets for $87. How many student tickets did Anwar sell?
3 student tickets
Unit 4, Lesson 3
Jaclyn and Sachiko are playing a guessing game. Jaclyn has silently selected a number between 1 and 16. She gives Sachiko the clues below to help her guess the number.
- The number is an odd number
- The number is greater than 10
- The number is a multiple of 3
What number did Jaclyn select?
15
Unit 4, Lesson 4
Vicki wrote this riddle: I am a 5-digit number. My thousands digit is 2 less than my ten thousands digit. My hundreds digit is 6. My ones digit is 2. My tens digit is 3 more than my ones digit. My ten thousands digit is 2 less than my tens digit. What is the number in Vicki’s riddle?
31,652
Unit 4, Lesson 5
How many possible products can you get using any combination of two factors chosen from these five factors: 2, 4, 5, 6, and 8?
10 products; 8, 10, 12, 16, 20, 24, 30, 32, 40, 48
Unit 4, Lesson 6
All of the numbers in a red box are odd and greater than 400. All of the numbers in a blue box are even and less than 300. None of the numbers in a green box are less than 500. In which box should you place the number 708? In which box will you place the number 495?
708, 495
Unit 4, Lesson 7
Jack collects sports trading cards. He has 44 baseball cards, 92 basketball card, 76 hockey cards, and 152 soccer cards. How many more soccer cards than baseball and hockey cards does Jack have?
32 more soccer cards
Unit 4, Lesson 8
Tyler is thinking of a number. If 5 is added to his number and 8 is subtracted from the total, the result is 2. What is Tyler’s number?
n+ 5 – 8 = 2; n = 5
Unit 4, Lesson 9
A jar contains marbles. The number of marbles can be divided into 4, 5, or 8 equal groups. What is the least number of marbles in the jar?
40 marbles
Unit 4, Lesson 10
Paul is buying 3 pennants for each of his 4 friends. If each pennant costs $2, how much will Paul spend?
$24
Unit 4, Lesson 11
Jamie bought 3 books at the school book fair. Two of the books cost $6.00 each. Jamie paid with a twenty-dollar bill and received $3.00 in change. Assuming Jamie did not pay sales tax, how much did the third book cost?
$5.00
Unit 4, Lesson 12
I am a two-digit number. My tens digits is 3 more than my ones digit. If you divide me by 8, the remainder is 2. What number am I?
74
Unit 5, Lesson 1
John bought a computer game for $50. The game requires a monthly charge of $15 a month to play. How much money will John have spent to buy the game and play for a year?
$50 + (12 x $15) = $230
Unit 5, Lesson 2
Mike has 48 stamps in his collection. Jamal has 3 times as many stamps as Mike. Jill has 14 fewer stamps than Mike. Barry has half the number of stamps as Jill. Who has the most stamps? Who has the least stamps?
Jamal; Barry
Unit 5, Lesson 3
Margo has saved $455. She wants to buy a new television that costs $980. Margo saves $60 each month. How many months will it take Margo to save up the rest of the money for the television she wants to buy?
9 months
Unit 5, Lesson 4
The Kane family travels on a 1,238-mile trip from New York to Miami. The first day, the Kane’s travel 405 miles, and the second day they travel 390 miles. How many more miles must the Kane family travel to reach Miami?
443 miles
Unit 5, Lesson 5
The Smiths are driving to a friend’s house. They leave their house at 8:30 a.m. They drive until 11:30 a.m. before they take a half hour break. They arrive at their friend’s house at 2:45 p.m. How long did the Smiths drive?
5 hours 45 minutes
Unit 5, Lesson 6
Stefan has 15 stamps. Barbara has 3 times as many stamps as Stefan. Jacob has 43 stamps. Noah has 20 more stamps than Stefan. How many stamps do Stefan, Barbara, Jacob, and Noah have altogether?
138 stamps
Unit 5, Lesson 7
Martina picked 7 baskets of apples. Each basket had 16 apples. Maria then packed the apples in 8 bags for a fair. How many apples were in each bag?
14 apples
Unit 5, Lesson 8
Nathan wants to buy a computer for $595. He has saved $155. He works a job that pays him $8 an hour. If he saves all the money he gets from his job, how many hours will he have to work to get the rest of the money for the computer?
55 hours
Unit 6, Lesson 1
A school chorus director is putting fourth-graders into rows. She puts 1 student in the first row, 2 students in the second row, 3 students in the third row, and so on. There are 8 rows in all. How many students are in the chorus?
36
Unit 6, Lesson 2
Bella and Enrique are sharing a pizza. Bella is hungry, so she says she will eat ¼ of the pizza. Enrique says he is hungrier than Bella, so he will eat 1/8 of the pizza. Will Enrique eat more than Bella? Explain.