Expressions and Patterns: math practice, Grade 5 – download the PDF

1 Operations in the right order ★★★

Evaluate each expression.

1. \( 14 + 6 \times 2 \)
2. \( 30 - 12 \div 4 \)
3. \( 5 \times 4 - 3 \)
4. \( 48 \div 6 + 9 \)

2 Parentheses first ★★★

Evaluate each expression.

1. \( (14 + 6) \times 2 \)
2. \( (30 - 12) \div 3 \)
3. \( 5 \times (9 - 4) \)
4. \( 60 \div (4 + 6) \)

3 Left to right ★★★

Evaluate, working from left to right when operations have the same rank.

1. \( 40 - 15 + 5 \)
2. \( 24 \div 4 \times 3 \)
3. \( 9 \times 2 \div 6 \)
4. \( 50 - 20 - 10 \)

4 From words to symbols ★★★

Write an expression for each sentence, then evaluate it.

1. Add 6 and 9, then multiply by 4.
2. Multiply 6 by 4, then add 9.
3. Subtract 7 from 25, then divide by 3.
4. Divide 36 by 4, then subtract 2.

5 Continue the pattern ★★★

A pattern starts at 5 and the rule is “add 4”. The first three terms are \( 5, 9, 13 \). Write the next four terms.

6 Ordered pairs from two patterns ★★★

Pattern A starts at 0 and adds 2. Pattern B starts at 0 and adds 10. Write the first five terms of each pattern, then the five ordered pairs (term of A, term of B).

7 Reading points ★★★

Write the ordered pair for each of the points A, B, C and D.

8 Two kinds of operations ★★★

Evaluate \( 3 \times (8 + 5) - 12 \div 4 \). Show each step.

9 Nested groups ★★★

Evaluate.

1. \( [\, 20 - (3 + 5) \,] \times 4 \)
2. \( 2 \times [\, 36 \div (2 + 4) \,] + 1 \)
3. \( \{ 5 \times [\, 2 + (9 - 3) \,] \} \div 4 \)

10 Find the mistake ★★★

Leo wrote \( 8 + 2 \times 5 = 50 \). What did he do wrong? What is the correct value? Where could you add parentheses so that the value is 50?

11 Expressions for stories ★★★

Write one expression for each story and evaluate it.

1. Ana has 3 packs of 8 stickers and gives away 5 stickers. How many are left?
2. A team buys 5 jerseys at 12 dollars each and receives an 8-dollar discount. What does the team pay?
3. Each of 4 friends pays for a 7-dollar ticket and a 3-dollar snack. What is the total?

12 Which is larger? ★★★

Without calculating, decide which is larger. Explain.

1. \( 6 \times (23 + 19) \) or \( 23 + 19 \)
2. \( 0.5 \times (62 - 18) \) or \( 62 - 18 \)
3. \( (45 + 30) \div 5 \) or \( 45 + 30 \)

13 Say it in words ★★★

Describe each expression in words, without evaluating it.

1. \( 2 \times (15 + 4) \)
2. \( (15 + 4) \div 2 \)
3. \( 3 \times 10 + 4 \)

14 Comparing two patterns ★★★

Pattern A starts at 0 and adds 4. Pattern B starts at 0 and adds 8. List the first six terms of each, write the ordered pairs, and describe how B compares with A. Why does this happen?

15 Graph two patterns ★★★

Pattern A starts at 0 and adds 5. Pattern B starts at 0 and adds 10. Write the first five terms of each, list the ordered pairs (A, B), plot them on a coordinate plane and describe what you notice.

16 Different starting numbers ★★★

Pattern A starts at 1 and adds 3. Pattern B starts at 2 and adds 6.

1. Write the first five terms of each and the ordered pairs (A, B).
2. If the next term of A is 16, what is the next term of B?
3. What are the 10th terms of A and B?

17 Four times as large ★★★

Pattern P starts at 0 and adds 3. Pattern Q starts at 0 and adds 12.

1. Write four ordered pairs (P, Q), starting with \( (0, 0) \).
2. What is the y-value of the pair whose x-value is 15?
3. Which of these points is on the graph: \( (21, 84) \), \( (12, 40) \), \( (30, 120) \)?

18 Use all four numbers ★★★

Use each of the numbers 8, 3, 2 and 5 exactly once, with the operations \( + \), \( - \), \( \times \), \( \div \) (and parentheses if you need them), to write an expression equal to 21.

19 Saving money ★★★

Sam saves 6 dollars each week and Ava saves 12 dollars each week. Both start with 0 dollars.

1. Write the amounts for weeks 0 to 5.
2. Write the ordered pairs (Sam’s amount, Ava’s amount).
3. When Sam has $42, how much does Ava have?

20 Is it true? ★★★

Marco says \( 4 \times (13 + 9) = 4 \times 13 + 9 \). Is he right? Find the value of each side. Then write the version that is correct.

21 Check the points ★★★

Mia plots the pairs \( (0, 0),\ (2, 6),\ (4, 12),\ (6, 18) \) and says that y is always 3 times x. Is she right? Which of these points are also on her graph: \( (5, 15) \), \( (8, 24) \), \( (10, 20) \)?