Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Model real situations with two equations and solve
Algebra
CCSS HSA.CED.A.3CCSS HSA.REI.C.6England: GCSE Higher Algebra
Objective and success criteria
Students will: Model real situations with two equations and solve.
- 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: Systems of equations: word problems
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 (Systems of equations: word problems). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Adult tickets cost 13 and child tickets cost 6. A school sold 43 tickets and took 412 in total. How many adult tickets were sold? → 22Prompt: Let a = adult tickets and c = child tickets. Write two equations.
- Liam buys 3 apples and 2 pears for 74 cents. Another day, 1 apple and 4 pears cost 38 cents. How much does one pear cost, in cents? → 4Prompt: Write: 3a + 2p = … and a + 4p = … .
- Adult tickets cost 10 and child tickets cost 6. A school sold 45 tickets and took 334 in total. How many adult tickets were sold? → 16Prompt: Let a = adult tickets and c = child tickets. Write two equations.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Model real situations with two equations and solve. 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: The sum of two numbers is 38 and their difference is 10. What is the larger number?
- Step 1: 2x = 48
- Step 2: x = 24
- Answer: 24
- 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.
- The sum of two numbers is 91 and their difference is 5. What is the larger number? → 48Prompt: Let the numbers be x and y: x + y = sum, x − y = difference.
- Bike hire A charges $4.50 plus $1.50 per hour. Bike hire B charges $10.50 plus $0.50 per hour. After how many hours do they cost the same? → 6Prompt: Write cost = fixed fee + rate × hours for each company.
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.
- Amara buys 3 notebooks and 2 pens for $2.85. A friend buys 2 notebooks and 5 pens for $3. How much is one pen? Give the amount as a number. → 0.3Prompt: Write 3n + 2p = … and 2n + 5p = … .
- Gym A costs 32 plus 4 per visit. Gym B costs 12 plus 9 per visit. After how many visits do they cost the same? → 4Prompt: Write a cost equation for each gym.
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: Systems of equations: word problems.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder