Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Write and solve equations from words
Algebra
CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Write and solve equations from words.
- 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: Two-step equations; Write algebraic expressions
Leads to: Systems of equations: word problems
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Two-step equations; Write algebraic expressions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Which expression means "n divided by 8"? (n + 8 / n/8 / n − 8 / 8n) → n/8Prompt: Translate the words in order, carefully.
- Solve: 3x + 3 = −27 → x = -10Prompt: Subtract 3 from both sides.
- Which expression means "5 less than n"? (5n / n/5 / n − 5 / 5 − n) → n − 5Prompt: Translate the words in order, carefully.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Write and solve equations from words. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Mei thinks of a number, multiplies it by 7 and adds 17. The answer is 94. Find the number.
- Step 1: 7x + 17 = 94
- Step 2: 7x = 77
- Step 3: x = 11
- Answer: x = 11
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Elena thinks of a number, multiplies it by 4 and adds 28. The answer is 36. Find the number. → x = 2Prompt: Call the number x and write an equation.
- A rectangle is 7 cm longer than it is wide. Its perimeter is 34 cm. Find the width x in cm. → x = 5Prompt: If the width is x, the length is x + 7.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- The sum of 5 consecutive integers is 170. Let the smallest be x. Find x. → x = 32Prompt: The numbers are x, x + 1, … , x + 4.
- A rectangle is 3 cm longer than it is wide. Its perimeter is 50 cm. Find the width x in cm. → x = 11Prompt: If the width is x, the length is x + 3.
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: Two-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: Systems of equations: word problems.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder