Writing and Evaluating Expressions

Expressions with Parentheses

100

17 − (36 ÷ 4)

17 − (36 ÷ 4)

17 − 9

8

200

(14 + 7) ÷ (1 × 3)

(14 + 7) ÷ (1 × 3)

21 ÷ (1 × 3)

21 ÷ 3

7

300

(9 − 1) + 6 × 7

(9 − 1) + 6 × 7

8 + 6 × 7

8 + 42

50

400

12 ÷ 4 + (3 − 2) × 7

12 ÷ 4 + (3 − 2) × 7

12 ÷ 4 + 1 × 7

3 + 1 × 7

3 +7

10

500

(81 ÷ 9) + 25 − 17 × 2

(81 ÷ 9) + 25 − 17 × 2

9 + 25 − 17 × 2

9 + 25 −34

34 −34

0

Order of Operations

100

3 x (8 + 9) × 4

3 (8 + 9) × 4

3×( 1 7 )×4

5 1 × 4

204

200

(10 − 6 + 8 ÷ 2) × 3

(10 − 6 + 8 ÷ 2) × 3

(10 − 6 + 4) × 3

(4 + 4) × 3

 8 × 3

 24

300

20,000 ÷ (200 ÷ 20)

20,000 ÷ (200 ÷ 20)

20,000 ÷ 10

2,000

400

(4 + 20 ÷ 4)+ 60 ÷ 10 + 10

(4 + 20 ÷ 4)+ 60 ÷ 10 + 10

( 4+5 ) + 60 ÷ 10 + 10

 9 + 60 ÷ 10 + 10

9 + 6 +10

1 5 + 10

2 5

500

4 + 16 ÷ 4 x (72 ÷ 9 + 10)

4 + 16 ÷ 4 x (72 ÷ 9 + 10)

4 + 16 ÷ 4×( 8+10 )

4+16÷4×( 1 8 )

4 + 4 ×18

4 +72

7 6

More P.E.M.D.A.S

100

10 − 6 × 5 ÷ (2 + 4)

10 − 6 × 5 ÷ (2 + 4)

10 − 6 × 5 ÷ 6

 10 − 30 ÷ 6

10 − 5

 5

200

What are the steps we need to take when using the acronym P.E.M.D.A.S?

First, solve everything in parenthesis; then exponents. Next, multiplication or division whichever comes first! Next addition or subtraction; whichever comes first left to right. 

300

(9 × 9) + 7 + 54 ÷ 9

(9 × 9) + 7 + 54 ÷ 9

( 8 1 )+7+54÷9

 81+7 + 6

 8 8 + 6 

9 4

400

Why do mathematicians use order of operations (PEMDAS) to solve expressions? 

Order of operations is a set of rules for solving math equations and expressions with multiple operations. This set of rules ensures that ALL math equations are solved in the same way.

500

(9 × 6) + 56 ÷ 8 + 40 ÷ 10

(9 × 6) + 56 ÷ 8 + 40 ÷ 10

5 4 +56÷8+40÷10

 5 4 + 7 +40÷10

 54+7 + 4

 6 1 + 4

 6 5

Word Problems

100

At first, liam had 20 more polished rocks than Carlos. Then, Carlos gave 30 polished rocks to Liam. Now, Liam has twice as many polished rocks as Carlos. How many polished rocks did Liam have at first? 

1 unit ------> 30 + 20 + 30 = 80 

2 units -----> 80 x 2 = 160 

160 - 30 = 130 polished rocks 

200

A 1,500 cm long rope was cut into 3 smaller ropes, A,B, and C. Rope B is 300 cm longer than Rope A. Rope C is 300 cm longer than Rope B. How long is Rope C?

3 units -----> 1,500 + 300 x 3 = 2,400

1 unit  -----> 2,400 ÷ 3 = 800 cm

 

300

Which expression does NOT have the same value as 

(5 x 4) + 6 - (9 ÷ 3) ?

a. 5 x 4 + 6 - (9 ÷ 3)

b. 5 x (4 + 6 - 9 ÷ 3)

B. 5 x (4 + 6 - 9 ÷ 3)

400

A party center charged $215 per party for up to 15 children, and $4 per additional child. Which expression shows the total cost of a party for 25 children? 

A. 215 + 4 x 25 

B. 215 + 4 x (25 - 15)

B. 215 + 4 x (25 - 15)

500

Jasmine had twice as much money as her sister. After giving her sister $45, they each had the same amount of money. How much money did Jasmine have at first? 

1 unit -----> 2 x 45 = 90

2 units ----> 90 x 2 = 180

$180

Challenge!

100

2 x (6 x 7 - 2²) + 17

2 x (6 x 7 - 2²) + 17

2 x (42 - 4) + 17

2 x (38) + 17

76 + 17

93

200

6 x (1 x 6 + 7²) - 97

6 x (1 x 6 + 7²) - 97

6 x (6 + 49) - 97

6 x 55 - 97

330 - 97

233

300

An expression is a mathematical statement that uses numbers and operations to show value. 

True or False. 

True!

400

(10 + 2 − 5) × (6 ² ÷ (8 − 4))

(10 + 2 − 5) × (6 ² ÷ (8 − 4))

(12 − 5) × (6 ² ÷ (8 − 4))

7 × (6 ² ÷ (8 − 4))

7 × (6 ² ÷ 4)

7 × (36 ÷ 4)

7 × 9 = 63

500

What is your favorite part about math time and why? 

whole group?

independent time?

small group? 

sprint?

Answers may vary!