Grade 4 Patterns and Algebra

Grade 4 – Patterns and Algebra

1. Last summer, Max earned 5 stickers for every book he read. He earned 40 stickers in all for reading books.

Which number sentence could be used to find b, the number of books Max read?

A. b ÷ 5 = 40

B. 5 + b = 40

C. b – 5 = 40 D. 5 × b = 40

2. The table below shows the amounts of money needed to park for different numbers of minutes. Each 6 minutes costs the same amount of money.

Parking Amounts

Time Amount of (in Money minutes) 5 cents 6 10 cents 12 15 cents 18 20 cents 24 25 cents 30

How much money will it cost to park for 60 minutes?

A. 50 cents B. 55 cents C. 65 cents D. 72 cents

3. Angelina wrote the number pattern below. 101, 122, 143, 164, 185, ?

She adds the same number each time to find the next number in the pattern.

What is the next number in Angelina's pattern?

4. Ms. Lin made the models shown below.

Each has the same weight. Each has the same weight. a. What is the weight, in pounds, of 1 ? Show your work or explain how you got your answer. b. What is the weight, in pounds, of 1 ? Show your work or explain how you got your answer. c. What is the least number of and that have a total weight of 21 pounds? Show your work or explain how you got your answer.

5. Pedro wrote the number sentences below.

36 = × 4

× = 18

The value of is the same in both sentences. Both of Pedro’s number sentences are true. What is the value of ?

6. Shannon made the map below to show the towns on Pine Island.

She marked the distance, in inches, between Stanford and Hillcrest on the map. About how many miles is Stanford from Hillcrest?

A. 15 B. 30 C. 35 D. 45 7. The table below shows the different numbers of boxes that are needed to hold different numbers of jars. Each box holds the same number of jars.

Jars in Boxes

Numbe Number r of of Jars Boxes

How many jars does each box hold?

A. 6 B. 8 C. 10 D. 12

8. A number machine uses a rule to change each number that is put into it to a different number. The same rule is used every time. The picture below shows what happened when the numbers 6, 9, and 11 were put into the number machine.

Which of the following could be the rule used by the number machine?

A. multiply by 2 B. multiply by 6 C. add 3 D. add 6

9. The pictures below show how two different groups of shapes balance a scale.

If 1 block weighs 10 pounds, what is the weight, in pounds, of 1 ball? Show or explain how you got your answer.

a. What is the total number of blocks needed to balance 6 balls? Show or explain how you got your answer.

b. What is the total number of balls needed to balance 10 cans? Show or explain how you got your answer.

10. Both of the scales shown below are balanced.

How many cans are needed to balance 1 star?

11. One large box of cookies contains the same number of cookies as 6 small boxes. Each small box contains an equal number of cookies. The boxes of cookies are shown below. A large box of cookies contains 84 cookies. What is the total number of cookies that a small box contains?

A. 9 B. 11 C. 14 D. 20

11. Write a rule for the input/output table shown below.

Input 7 1 5 9 13 Output 13 7 11 15 19

12. Lillian used a rule to make the number pattern shown below.

3 7 12 16 21 25 30 ?

If the pattern continues in the same way, what will be the next number in the pattern? Show or explain how you got your answer. a. Jenna used the same rule as Lillian to make a number pattern. She began her pattern with the number 10. Should the number 25 be one of the numbers in Jenna’s pattern? Show or explain how you got your answer. 13. On a test, Hannah scored 8 points higher than Todd. On the same test, Hannah scored 7 points lower than Juanita.

 H represents Hannah's score on the test.  T represents Todd's score on the test.  J represents Juanita's score on the test.

Based on the information above, which of the following must be true?

A. J < T B. T < J C. H > J D. J < H

14. The 17 tokens shown below are used to play a game. Each kind of token is worth a different number of points.

The picture below shows two clues about the number of points each kind of token is worth.

a. If each is worth 20 points, how many points is each worth? Show your work or explain how you got your answer.

b. b. If 4 friends play the game, they will divide the 17 tokens into 4 groups so that each friend's group of tokens is worth the same number of points. What is the total number of points each friend's group of tokens is worth? Show your work or explain how you got your answer.