Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Systems of equations: word problems
Algebra
CCSS HSA.CED.A.3CCSS HSA.REI.C.6England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Systems of equations: word problems.
- 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 linear equations (simultaneous equations); Write and solve equations from words
Leads to: Systems of three equations; Model real situations with two equations and solve
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 linear equations (simultaneous equations); Write and solve equations from words). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve the system: y = x + 5 and x + y = −1. Find x. → x = -3Prompt: Substitute the first equation into the second.
- Mateo thinks of a number, multiplies it by 6 and adds 20. The answer is 32. Find the number. → x = 2Prompt: Call the number x and write an equation.
- Solve: 3x + 4y = 25 and 5x − 4y = 31. Find y. → 1Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Systems of equations: word problems. 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: Adult tickets cost 10 and child tickets cost 4. A school sold 35 tickets and took 206 in total. How many adult tickets were sold?
- Step 1: c = 35 − a
- Step 2: 10a + 4(35 − a) = 206
- Step 3: 6a = 66
- Step 4: a = 11
- Answer: 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.
- Adult tickets cost 9 and child tickets cost 4. A school sold 25 tickets and took 200 in total. How many adult tickets were sold? → 20Prompt: Let a = adult tickets and c = child tickets. Write two equations.
- Jamal buys 3 apples and 2 pears for 60 cents. Another day, 1 apple and 4 pears cost 100 cents. How much does one pear cost, in cents? → 24Prompt: Write: 3a + 2p = … and a + 4p = … .
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.
- Sofia buys 3 apples and 2 pears for 103 cents. Another day, 1 apple and 4 pears cost 81 cents. How much does one pear cost, in cents? → 14Prompt: Write: 3a + 2p = … and a + 4p = … .
- Adult tickets cost 13 and child tickets cost 5. A school sold 38 tickets and took 278 in total. How many adult tickets were sold? → 11Prompt: Let a = adult tickets and c = child tickets. Write two equations.
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 linear equations (simultaneous 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 three equations; Model real situations with two equations and solve.
- 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