Make some worksheets for practicing in the Sumer for math grade 7

I'd love to help you build some custom math worksheets to keep your skills sharp over the summer! To make sure these are perfectly tailored for you, let's figure out where we should focus our practice.

Which 7th-grade math topics do you feel most challenging, or which ones would you like to practice the most this summer?

Equations and expressions

It is awesome that you want to target equations and expressions. Before we dive into solving them, we should make sure we can tell them apart because they look similar but do very different jobs.

Your path

Geometry: Area, Volume, and Angles

Statistics and Probability

The Matchup: Expressions vs. Equations

Think of an like a phrase in a sentence. It represents a single value or quantity, but it doesn't state a complete fact. On the other hand, an is like a complete sentence: it uses an equal sign to state that two expressions are perfectly equal to each other.

Feature	Expression	Equation
Has an Equal Sign?	No	Yes (equals sign)
Goal	Simplify or Evaluate	Solve for the variable
Example	$5x - 3$	$5x - 3 = 12$

To make sure this clicks, how would you classify this math statement: $4y + 8 = 20$ ?

It's an equation

Spot on. It is absolutely an equation because of that trusty equal sign holding both sides in balance.

Now that you have got the difference down, let us tackle our first major step for simplifying expressions: combining .

The Art of Combining Like Terms

Think of variables like different kinds of fruit. If you have three apples and pack two more apples, you have five apples. But if you have three apples and two bananas, you cannot just blend them into five "apple-bananas". They have to stay separate.

In algebra, we do the exact same thing. We group matching variable parts together, and we group plain numbers together. Let us walk through a quick example:

$3x + 5 + 2x + 4$

To simplify this, we group the parts that match:

First, look at the variable terms: $3x$ and $2x$ . Because they both have the variable $x$ , we can add them up. $3x + 2x = 5x$
Next, look at the constant numbers: $5$ and $4$ . Since they are both plain numbers with no variables, we can add them up too. $5 + 4 = 9$

Now we put our simplified parts together to get our final simplified expression:

$5x + 9$

Let us see how you feel with this. How would you simplify this expression?

$7b + 3 + b + 8$

Is the answer 8b + 11?

You nailed it! That is absolutely correct. Combining those $7b + 1b$ gives you $8b$ , and adding $3 + 8$ gets you $11$ . You are officially a pro at simplifying expressions!

Now that you have mastered expressions, we are ready to move on to equations. To solve an equation, we have to learn the concept of maintaining .

A balanced scale showing a box labeled x and three yellow unit circles on the left, and seven yellow unit circles on the right.

Think of an equation like a balanced scale. If you do something to one side, you have to do the exact same thing to the other side to keep it perfectly even.

Our ultimate goal when solving an equation is to get the variable completely by itself on one side. This process is called .

Let us look at a simple one-step equation:

$x + 3 = 7$

To get $x$ by itself, we need to undo the $+ 3$ . The opposite of adding $3$ is subtracting $3$ . If we subtract $3$ from the left side, we must also subtract $3$ from the right side to keep our scale balanced:

$x + 3 - 3 = 7 - 3$

$x = 4$