Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Solve real problems with two equations
Algebra
CCSS 8.EE.C.8.CEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve real problems with two equations.
- 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 systems by elimination; Solve systems by substitution
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 systems by elimination; Solve systems by substitution). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 5x + 5y = −45 and 2x − 5y = 17. Type the solution like (2, −3). → (−4, −5)Prompt: The y-terms are opposites. Add the equations to eliminate y.
- Solve the system: y = 3x − 19 and 2x + 2y = 18. Type the solution like (2, −3). → (7, 2)Prompt: Substitute 3x − 19 for y in the second equation.
- Solve: 2x + 2y = −8 and 6x − 3y = 12. Type the solution like (2, −3). → (0, −4)Prompt: Multiply the first equation by 3 so the x-terms match.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve real problems with two equations. 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: At a museum, 5 adult and 5 child tickets cost $70. 4 adult and 2 child tickets cost $48. How much is one adult ticket? (Type the number only.)
- Step 1: c = 4
- Step 2: a = 10
- Answer: 10
- 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.
- 2 adult and 3 child tickets cost $36. 1 adult and 4 child tickets cost $33. How much is one adult ticket? (Type the number only.) → 9Prompt: Write two equations: 2a + 3c = 36 and a + 4c = 33.
- In a basketball game, Nia made 23 baskets, all 2-pointers or 3-pointers, scoring 62 points. How many 3-pointers did Nia make? → 16Prompt: t + h = 23 and 2t + 3h = 62 (t = twos, h = threes).
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.
- Two numbers add to 49 and their difference is 13. What is the larger number? → 31Prompt: x + y = sum and x − y = difference.
- At a museum, 5 adult and 6 child tickets cost $77. 1 adult and 4 child tickets cost $21. How much is one adult ticket? (Type the number only.) → 13Prompt: Let a = adult price and c = child price. Write one equation for each group of tickets.
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 systems by elimination.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder