6th Grade: Algebraic Expressions

Write & Evaluate

100

What expression can be used to determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound?

3.25g + 0.74f

200

For the expressions 5-5x to have a negative value, what must be true about the value of x?

x must be greater than 1

300

Evaluate -2+4x÷3 when x= -6, 0, 9

When x=-6: -10

When x=0: -2

When x=12: 14

400

Select all expressions equivalent to 3⁄5x + 3:

A.) 4⁄5x - 1⁄5x + 3  

B.) 2⁄5 +3 3⁄5x -1

C.) 1+ 1⁄5x + 2 - 2⁄5x

D.) 1+ 3⁄5x + 2 

E.) 1 + 2⁄5x + 3

A & D

500

Diego is building a boat dock. The length of the dock is (x+8) feet. The width of the dock is (x+3) feet. Create two equivalent expressions to represent the perimeter of the boat dock. 

2(x+3)+2(x+8)

4x+22

Generate & Simplify

100

Simplify: 4a - 5b - 6 + 2b - 3a

a-3b-6

200

Simplify: -3.7 + 5g + 4k + 11.1 - 10g

-5g + 4k + 7.4

300

Simplify: 12 + (-4) - 2⁄5j - 4⁄5j + 5

-1 1⁄5j +13

400

Explain whether 8t-3y-4t is equivalent to 7t+(-3t)-3y

They are equivalent because both expressions simplify to 4t-3y

500

Simplify: -4a² + 5b² - 7a + 9a² +13 - 11b² - 5a - 19

5a² - 6b² - 12a - 6

Expand & Factor

100

Write the expanded form of the expression: -2.5(-3 + 4n + 8)

-10n - 12.5

200

Write the expanded form of the expression: -0.4(-5+7y-13.8)

2.8y - 7.52

300

Your friend factors the expression 15x-20xy as 5x(3-4xy). Are they correct? Explain why or why not.

They are incorrect. If you expand their expression back out it would be 15x-20x²y

400

Factor the expression: 12x +27y - 73

3(4x+9y) - 73

500

The area of a rug is 18a²b - 6ab + 21a² + 15a. What are possible dimensions?

3a (6ab + 7a - 2b + 5)

Add & Subtract

100

Explain why expressions must be subtracted in a particular order. Justify your reasoning with an example.

Subtraction doesn't apply with the Commutative Property. For example: 7-9 = -2 but 9-7 = 2. The answers are the same value, but with opposite signs.

200

Combine like terms: (-2z - 3)+(4c +6y- z)+(7+3c)

7c + 6y - 3z +4

300

Find the sum: (3⁄7 - 3 + 4n)+( 5⁄14 - 2n - 4)

2n - 6 3⁄14

400

Combine like terms: 9r - (4t - 3r + 2) + 7 + 9t

12r + 5t +5 

500

Subtract the expressions: (7j + 1⁄8q +3) - (5⁄8q - 11 + 2j)

5j - 1⁄2q +14

Popp Trivia

100

Ms. Poppleton's favourite food

Brussels Sprouts 

200

The last country Ms. Poppleton visited

Portugal

300

Ms. Poppleton's birthday

May 13

400

Ms. Poppleton's favourite dessert

Cheesecake

500

The names of Ms. Poppleton & Mr. Brown's cats

Hazel & Maya