Math lesson plan · 8th grade (Year 9 in England) · 45 minutes

Solve equations with x on both sides

Algebra

CCSS 8.EE.C.7.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Objective and success criteria

Students will: Solve equations with x on both sides.

I can answer questions on today's skill on my own, without help.
I can explain each step and say why it works.
I can check my answer and spot a mistake.

Before and after

Needs first: Equations with the unknown on both sides; Solve two-step equations with negative numbers

Leads to: Solve equations with brackets and x on both sides; Solve equations with fractions or decimals on both sides; When are two plans equal? Equations from real comparisons

Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

Quick retrieval from earlier learning (Equations with the unknown on both sides; Solve two-step equations with negative numbers). Students answer on mini whiteboards.
Show answers together and note who needs support in the main task.

Solve: 3x − 11 = 8x − 71 → x = 12Prompt: Collect the x terms on one side.
Solve: −8x − 19 = −115 → x = 12Prompt: First undo the subtraction: add 19 on both sides.
Solve: 4(x + 2) = 3(x − 2) + 20 → x = 6Prompt: Expand the brackets on both sides first.

Hook · 5 min

Show a "think of a number" puzzle and ask the class to work out the starting number.
Share the objective: Solve equations with x on both sides. Read the success criteria together.

I do: model it · 10 min

Work through the example out loud, saying why you do each step, not just what you do.
Example: Solve: −6x − 1 = 2x − 17
Step 1: −1 = 8x − 17
Step 2: 16 = 8x
Step 3: x = 2
Answer: x = 2
Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

Do these together. Students try each step on whiteboards before you reveal it.
Use the hints as prompts rather than giving the answer.

Solve: −2x − 6 = 2x − 34 → x = 7Prompt: Add 2x to both sides so the x-term stays positive.
Priya solved 7x + 9 = 3x + 45 by adding 3x to both sides. Explain the mistake by finding the correct value of x. → x = 9Prompt: To remove 3x from the right, you must SUBTRACT 3x.

You do: independent practice · 10 min

Students work on the student sheet. Circulate and check the first two answers of every student early.
Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

Isla solved 6x + 8 = 5x + 15 by adding 5x to both sides. Explain the mistake by finding the correct value of x. → x = 7Prompt: To remove 5x from the right, you must SUBTRACT 5x.
Solve: −3x + 12 = 3x − 12 → x = 4Prompt: Add 3x to both sides so the x-term stays positive.

Watch out for

Doing an operation to one side of an equation but not the other.
Reading 3x as 3 + x, or thinking x always stands for one particular number.

Support and stretch

Support

Review first: Equations with the unknown on both sides.
Use concrete materials: balance scales or a balance drawing.
Give the first step of each question, or a partly worked example to finish.
Pair with a confident partner for the guided practice.

Stretch

Move on to: Solve equations with brackets and x on both sides; Solve equations with fractions or decimals on both sides; When are two plans equal? Equations from real comparisons.
Explain a common mistake in writing and how to fix it.
Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.

Free lesson plan from eurekami.com/lesson-plan-builder