9 Algebra Questions And Practice Problems To Do With Your Middle Schoolers

April 21, 2024 | 2 min read

Beki Christian

Algebra questions involve using letters or symbols to represent unknown values or values that can change. Here you will find $\bf{9}$ algebra questions to test your knowledge and show you the different ways that algebra can be used to solve a problem to find an unknown value or to make generalizations.

Algebra in elementary school

Students as early as kindergarten begin to solve problems with algebraic thinking. Algebraic thinking starts with students understanding the properties of the operations, the relationships between them, and the composition of numbers.

They begin to relate concrete models to abstract expressions and equations, and continue this work throughout elementary school. They also look at patterns and the order of operations that will contribute to their understanding of algebra in later years.

This flexible understanding with the composition and representation of numbers, as well as the operations sets them up for more complex and abstract equations once they get to middle school.

9 Algebra Questions for Middle School

Use these 9 algebra questions to help your middle school students understand algebra. Answer key included!

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Algebra in middle school

Algebra encompasses many skills and concepts to help us make sense of the world and solve problems. In middle school, we learn to write basic algebraic expressions, write and solve linear equations, write and solve a system of linear equations, and graph linear equations on the coordinate plane. Later, we further develop these skills which allow us to work with more complex equations such as quadratic equations, polynomial equations, and exponential equations.

How to solve algebraic equations

When you are presented with an algebraic problem, it is important to make sense of the problem. Here are some of the key terms along with what they mean:

Solve the equation – find out the value of the unknown.
Substitute – put the values you have been given into the algebraic expression.
Coefficients – the amount a term has been multiplied by. For example, in the expression $4c+2, \; 4$ is the coefficient.
Constants – values which are not variable and stay the same. For example, for $4c+2, \; 2$ is the constant.
Binomial – a binomial or binomial expression is one which has two parts, like our example $4c+2.$
Simplify – collect together like terms to make the expression or equation look simpler.
Expand – multiply out the expressions inside parentheses.
Factorize – put into parentheses.
In terms of $x$ – rewrite the equation in the form $x = \dots$

Remember, when working with algebra, we must still apply the order of operations, PEMDAS. i.e. Parenthesis, Exponents (powers, square roots), Multiplication, Division, Addition, Subtraction.

When working with algebraic expressions and equations we must consider carefully which operations to deal with first.

Algebra practice questions for middle school

c+d

2c+d

2c+2d

2c-2d

$2$ chocolate bars would cost $2$ lots of $c,$ or $2c,$ and $2$ drinks would cost $2$ lots of $d,$ or $2d.$

10m

6m+4

6m+6

6m-4

We need to collect together like terms here so $4m + 2m = 6m$ and $5-1 = 4$ (watch out for the negative).

In middle school, we learn a variety of different algebra techniques to answer algebra questions and to practice problem solving with algebra. These include:

Simplifying algebraic expressions
Expanding brackets and factoring
Forming algebraic equations from word problems
Solving algebraic equations and inequalities
Substituting into expressions
Changing the subject of an equation
Working with real life graphs and straight line graphs
Sequences

gcse line graph equation — A slide guiding pupils through the equation of a straight line from Third Space Learning’s online intervention.

Algebra questions for middle school: basic algebra

8a-2b

12a-b

12a+5b

10a+b

basic algebra question 1b

\$24

\$67

\$48

\$27

In this question, $n$ is $7$ so we can substitute $7$ into the formula.

$Charge = \$20 + 4 × 7$

$Charge = \$48$

$4x$ and $6x$

$4$ and $x-6$

$2$ and $2x-3$

$2x$ and $2x-3$

There are two ways of attempting this question. We know that $\text{area of a rectangle } = \text{ length} \times \text{width}$ so we could multiply each pair together to see which pair makes $4x-6.$

\begin{aligned} &4x × 6x \quad \quad\quad\; \;24x^2 \\ &4 × (x − 6) \quad \quad \quad4x − 24\\ &2 × (2x − 3) \quad \quad \;\;4x − 6\\ &2x × (2x − 3) \quad \quad 4x^2 − 6x\\ \end{aligned}

Alternatively, if we factorise $4x-6$ we get $2(2x-3)$ meaning the sides could be $2$ and $2x-3.$

C=\cfrac{5(F-32)}{9}

C=\cfrac{5F-32}{9}

C=\cfrac{5F}{9}-32

C=5F-\cfrac{32}{9}

\begin{aligned} F&=\frac{9C}{5}+32 \hspace{3cm} &\text{subtract 32}\\\\ F-32&=\frac{9C}{5} &\text{multiply by 5}\\\\ 5(F-32)&=9C &\text{divide by 9}\\\\ \frac{5(F-32)}{9}&=C \end{aligned}

Algebra questions for middle school: forming and solving equations

20^{\circ}

26^{\circ}

8^{\circ}

34^{\circ}

The angles in a triangle add up to $180^{\circ}$ therefore we can write

4x+2x-10+3x-8=180

Now we have an equation we can solve.

\begin{aligned} 9x-18&=180 \hspace{3cm} &\text{add } 18\\ 9x&=198 &\text{divide by } 9\\ x&=22^{\circ} \end{aligned}

The angles are :

\begin{aligned} 4\times22&=88^{\circ}\\ 2\times22 -10&=34^{\circ}\\ 3\times22 -8&=58^{\circ} \end{aligned}

The smallest angle is $34^{\circ}$ .

70

42

22

35

To solve this we need to write an equation.

Let Jamie’s age now be $x$ . Then Jamie’s dad’s age is $4x$ .

In $14$ years time Jamie’s age will be $x + 14$ and Jamie’s dad’s age will be $4x + 14$ .

Since we know Jamie’s dad’s age will be two times Jamie’s age, we can write

$4x+14=2(x+14)$

Now we have an equation we can solve.

\begin{aligned} 4x+14&=2(x+14) \hspace{3cm} &\text{expand the brackets}\\ 4x+14&=2x+28 \hspace{3cm} &\text{subtract 2x}\\ 2x+14&=28 \hspace{3cm} &\text{subtract 14}\\ 2x&=14 \hspace{3cm} &\text{expand the brackets}\\ x&=7 \hspace{3cm} \end{aligned}

Jamie is currently $7$ years old meaning his dad is $28$ years old. The sum of their ages is $35$ .

Note: when algebraic equations contain denominators on either side, we can use the cross multiplication method to help us work out the answer. For example with the following expressions:

\cfrac{a}{b} = \cfrac{c}{d}

This can then become, $ad = bc$ and so on.

Algebra questions for middle school: graphs

y=2x-1

y=2x+1

y=4x-2

y=2x+5

At the point $(2, 5), \; x$ is $2$ and $y$ is $5.$ We can check which equation works when we substitute in these values:

\begin{aligned} y&=2x−1 \quad \quad \quad 5=2×2−1 \quad \quad \text{False}\\ y&=2x+1 \quad \quad 5=2×2+1 \quad \quad \text{True}\\ y&=4x−2 \quad \quad \quad 5=4×2−2 \quad \quad \text{False}\\ y&=2x+5 \quad \quad 5=2×2+5 \quad \quad \text{False} \end{aligned}

Looking for more algebra math questions?

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The content in this article was originally written by secondary teacher Beki Christian and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.