Math lesson plan · 7th grade (Year 8 in England) · 45 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 · 5 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 "10 more than n"? (n + 10 / 10n / n − 10 / 10 − n) → n + 10Prompt: Translate the words in order, carefully.
- Solve: −3x − 9 = 3 → x = -4Prompt: Add 9 to both sides.
- Which expression means "11 less than n"? (n + 11 / n/11 / 11 − n / n − 11) → n − 11Prompt: Translate the words in order, carefully.
Hook · 5 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 · 10 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 · 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.
- Sam thinks of a number, multiplies it by 3 and adds 9. The answer is 39. Find the number. → x = 10Prompt: Call the number x and write an equation.
- A rectangle is 10 cm longer than it is wide. Its perimeter is 48 cm. Find the width x in cm. → x = 7Prompt: If the width is x, the length is x + 10.
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.
- A rectangle is 3 cm longer than it is wide. Its perimeter is 30 cm. Find the width x in cm. → x = 6Prompt: If the width is x, the length is x + 3.
- The sum of 3 consecutive integers is −27. Let the smallest be x. Find x. → x = -10Prompt: The numbers are x, x + 1, … , x + 2.
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