EdPlace's Key Stage 3 Home Learning Maths Lesson: Solve Two-Step Equations Using Algebra

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Get them started on the lesson below and then jump into our teacher-created activities to practice what they've learnt. We've recommended five to ensure they feel secure in their knowledge - 5-a-day helps keeps the learning loss at bay (or so we think!).

Are they keen to start practising straight away? Head to the bottom of the page to find the activities.

Now...onto the lesson!

Key Stage 3 Statutory Requirements for Maths

Year 8 students should be able to use algebraic methods to solve linear equations in one variable.

Struggling with Two-Step Equations?

Number puzzles pop up frequently in everyday life so we’re used to solving them. For example, if bread rolls come in packets of 6, how many packets do you need to buy to have 24 buns? Or, if a special offer means you can buy 3 chocolate bars for £3.60, is this cheaper than buying them singularly at £1.30 each? However, can your child solve the following equation and demonstrate each step of their working?

6y - 21 = 63

Every good lesson has a purpose or an objective. We're confident that if you follow the step-by-step approach below your child will be able to:

1) Understand how to solve two-step equations

2) Apply this understanding to practice questions

3) Explain the inverse operations used

Step 1 - Key Terminology

Before we jump into solving equations it’s important to check that your child understands some key terminology.

An equation is simply a statement that tells us what an expression equals for one (or more values) of the variable in the equation.

You could consider an expression to be the equivalent of a phrase made up of words – it consists of terms and their operators. For example, 6x + 7y - 3.

A term is an individual number or a value (much like a word in a sentence). For example, 6p or 8q or, just 6. Your child will understand that a variable, in its simplest form here, is just the letter that they need to find the value of, in order to solve the equation.

Step 2 - Reverse Operations

As we need to undo or reverse the operations that have been applied to our variable to give the value stated in the equation, your child needs to understand the inverse of multiplying, dividing, adding and subtracting.

Ask your child to think about how they would fill in the number missing from the box in the puzzle below:

X 5 = 30

They probably know that the answer is 6. But how did they work this out?

You both may have counted through your 5 times table until you got to 30 and realised that the number in the box was 6. In formal mathematical terms, you applied the inverse operation to multiplying by 5 to both sides of the equation to find the answer: 6.

Below is a table that shows the inverse operation for each operation. For example, if you want to reverse the effect of adding 5 to both sides of an equation, you should subtract 5 from each side.

Operation	Inverse
Multiplying	Dividing
Dividing	Multiplying
Adding	Subtracting
Subtracting	Adding

It’s helpful to think of the equation as sitting on a balance scale. For an equation to retain the property of being equal on each side, you must do the same thing to each side. The left-hand side of the equation won’t equal the right-hand side if you only divide one side by 5.

So, after dividing both sides by 5, we have that p = 6, and as we know what value of p makes the equation equal, we have solved the equation.

Step 3 - Decide on the Order of Operations

More than one operation may have been applied to form the equation. So, we have to be able to work out the order in which the operations were applied to the variable (or letter). For example, the expression 5p + 7, means that p has been multiplied by 5 and then 7 has been added. The correct inverse operations will be to subtract 7 and then divide by 5.

Subtracting 7 from each side will give 5p = 30, and then dividing both sides by 7 will give p = 6. Here’s another example: Solve 16 – 5a = 13. We can think of this as 16 has been added to a, after it has been multiplied by -5 (negative 5).

Subtracting 16 from each side gives -5a (negative 5 times a) = -3 (negative 3). When we divide negative 3 by negative 5 we have -3/5 = 3/5. It’s worth noting that solutions to equations don’t have to be whole or positive numbers, but we can check that we are right by substituting our value of a back into the equation. So, let’s see if 16 - 5 × 3/5 = 13. As 16 – 3 = 13, we know that we have found the right solution for a.

Step 4 - Practice Solving Two-Step Equations

Now we can practice solving 2-step equations. Have your child attempt the following practice questions as a warm-up to the EdPlace activities.

1) 5p + 4 = 34

2) 10p + 8 = 68

3) 136 - 20p = 16

4) r/3 + 1 = 12 (Hint: we need to subtract 1, and then multiply by 3).

5) r/6 + 1 = 12

6) r/12 + 1 = 12

For each of questions 1-3 and 4-6. What do you notice about the solutions to these equations? Can you explain why this happens?

Step 5 - Consolidate Your Knowledge with Activities

Now that you’ve learnt to solve two-step equations, see if your child can apply their knowledge to the following 5 activities. Have them complete them in the order listed below. All activities are created by teachers and automatically marked.

All activities are created by teachers and automatically marked. Plus, with an EdPlace subscription, we can automatically progress your child at a level that's right for them. Sending you progress reports along the way so you can track and measure progress, together - brilliant!

Activity 1 - Solve One-Step Equations

Activity 2 - Simplify and Solve Equations

Activity 3 - Solve Two-Step Equations

Activity 4 - Solve Equations with Brackets

Activity 5 - Equations with the Variable on Both Sides

Answers

1) p = 6

2) p = 6

3) p = 6

4) r = 33

5) r = 66

6) r = 132