Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Write and solve two-step equations from real situations
Algebra
CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Write and solve two-step equations from real situations.
- 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: Solve two-step equations with negative numbers
Leads to: the next skill in this area.
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 (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: −7x − 3 = −10 → x = 1Prompt: First undo the subtraction: add 3 on both sides.
- Solve: 7 − 2x = 23 → x = -8Prompt: Subtract 7 from both sides.
- Solve and check by substituting: 4x + 5 = −3 → x = -2Prompt: To undo + 5, do the opposite.
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 two-step equations from real situations. 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: A phone plan costs $19 per month plus $8 per GB of data. One month's bill was $51. How many GB were used?
- Step 1: 8g = 51 − 19 = 32
- Step 2: g = 32 ÷ 8 = 4
- Answer: 4
- 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.
- A phone plan costs $18 per month plus $3 per GB of data. One month's bill was $36. How many GB were used? → 6Prompt: Write the equation: 18 + 3g = 36.
- A rectangular dog run is 8 m wide. Its perimeter is 72 m. Use 2L + 16 = 72 to find its length L, in m. → 28Prompt: Subtract 16 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.
- Tariq has $317 saved and adds $12 each week. After how many weeks will Tariq have $473? → 13Prompt: Equation: 317 + 12w = 473.
- A phone plan costs $11 per month plus $7 per GB of data. One month's bill was $46. How many GB were used? → 5Prompt: Write the equation: 11 + 7g = 46.
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: Solve two-step equations with negative numbers.
- 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
- 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