Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Solve x + a = b and x − a = b, including decimals and fractions
Algebra
CCSS 6.EE.B.7England: KS3 Algebra
Objective and success criteria
Students will: Solve x + a = b and x − a = b, including decimals and fractions.
- 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: One-step equations
Leads to: Write and solve one-step equations from real situations
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 (One-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x/3 = 6 → x = 18Prompt: x is divided by 3. What undoes dividing?
- Solve: x/7 = 9 → x = 63Prompt: x is divided by 7. What undoes dividing?
- Solve: x/4 = 10 → x = 40Prompt: x is divided by 4. What undoes dividing?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve x + a = b and x − a = b, including decimals and fractions. 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: y + 4.9 = 9.7
- Step 1: y = 9.7 − 4.9
- Step 2: y = 4.8
- Answer: y = 4.8
- 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: y + 3.7 = 23.4 → y = 19.7Prompt: Subtract 3.7 from both sides.
- Solve: x + 1/6 = 1 1/3. Give x as a fraction or mixed number in simplest form. → 7/6 (1 1/6)Prompt: Subtract 1/6 from both sides.
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.
- Solve: x + 1/2 = 1. Give x as a fraction or mixed number in simplest form. → 1/2Prompt: Subtract 1/2 from both sides.
- Solve: y + 3.6 = 12.9 → y = 9.3Prompt: Subtract 3.6 from both sides.
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: One-step equations.
- 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: Write and solve one-step equations from real situations.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder