Algebraic Expressions and Equations

Expression vs Equation

100

What is the difference between an expression and an equation? 

An expression does not have an equal sign whereas an equation does have an equal sign. 

200

Is this an expression or equation?

y+3

Expression

300

Is this an expression or equation?

3+x =6

Equation

400

Is this an expression or equation? 

3x²+5x=7

Equation

500

Is this an expression or equation? Explain why

7x+6x⁴+8y

Expression because there is no equal sign 

Writing expressions

100

6 less than a number

x-6

200

the sum of 8 and a number 

8+x 

300

2 times the sum of a number and 3

2(x+3)

400

5 times a number subtracted from 10

10-5x

500

4 times the product of 4 and a number plus 2 times the product of 6 and a number

4(4x)+2(6x)

Evaluating expressions

100

Solve the following when x=3

4+x

7

200

Solve the following when x=11

5x

55

300

Solve the following when x= 3 and y=5

2x-y

6-5= 1

400

Solve the following:

x=2

y=3

z=4

y(2^x +y +z)

3 (2²+3+4)

3 (4+3+4)

3 (11) = 33

500

Solve the following:

x=5

y=3

x²+2(xy)

5²+2(3)(5)

25+ 2(15)

25+30= 55

Vocab

100

A term that is a number by itself

Constant 

200

The numerical part of a variable term

Coefficient

300

A group of terms, separated by operations symbols (+,-), without an equals sign 

Algebraic Expression (an expression)

400

These are used to make up algebraic expressions. They can be constant, a variable alone, or a number multiplied by a variable.

term(s)

500

What are the term(s) in the following algebraic expression?

9t²+12t+30

9t², 12t, 30

Real World Examples

100

I had 3 apples but ate one. How many are left? 

Write an expression for the scenario and solve it. 

3-1

2 apples

200

My 6 friends and I wanted to go to the movies. Our parents helped us buy 3 tickets. How many do we still need to buy? Write the expression and solve for it. 

7-3

4 tickets 

300

Maria brought donut holes home for the store for breakfast. She brought home 50 donut holes. John ate 7, Collin ate 12, and Maria ate 8. How many donut holes are left? Write an expression that represents this scenario and then solve it.

50-7-12-8

23 donut holes left

400

A carton of eggs has 12 eggs. I need to buy 3 cartons of eggs. How many eggs will I have in total?

Write an expression and solve it

12 x 3

36 eggs 

500

There is a 100 students in the 6th grade. 20 students are in PE, 16 are in Reading, 28 are in Math, and 21 are in Science. How many students are in History? Write an expression and solve

100-20-16-28-21

15 students