Math lesson plan · 8th grade (Year 9 in England) · 60 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 · 6 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: 3x + 5y = 20 and 4x − 5y = −55. Type the solution like (2, −3). → (−5, 7)Prompt: The y-terms are opposites. Add the equations to eliminate y.
- Solve the system: y = −3x − 2 and 4x + 2y = 2. Type the solution like (2, −3). → (−3, 7)Prompt: Substitute −3x − 2 for y in the second equation.
- Solve: x + 3y = 8 and 2x − 4y = −14. Type the solution like (2, −3). → (−1, 3)Prompt: Multiply the first equation by 2 so the x-terms match.
Hook · 6 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 · 12 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 · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- At a museum, 6 adult and 5 child tickets cost $144. 4 adult and 5 child tickets cost $116. How much is one adult ticket? (Type the number only.) → 14Prompt: Let a = adult price and c = child price. Write one equation for each group of tickets.
- In a basketball game, Mateo made 31 baskets, all 2-pointers or 3-pointers, scoring 90 points. How many 3-pointers did Mateo make? → 28Prompt: t + h = 31 and 2t + 3h = 90 (t = twos, h = threes).
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Two numbers add to 43 and their difference is 35. What is the larger number? → 39Prompt: x + y = sum and x − y = difference.
- At a museum, 2 adult and 2 child tickets cost $34. 1 adult and 4 child tickets cost $32. How much is one adult ticket? (Type the number only.) → 12Prompt: 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