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Math lesson plan · 9th grade (Year 10 in England) · 60 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 · 6 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.
  1. Adult tickets cost 10 and child tickets cost 2. A school sold 38 tickets and took 196 in total. How many adult tickets were sold? → 15Prompt: Let a = adult tickets and c = child tickets. Write two equations.
  2. Sofia buys 3 apples and 2 pears for 52 cents. Another day, 1 apple and 4 pears cost 64 cents. How much does one pear cost, in cents? → 14Prompt: Write: 3a + 2p = … and a + 4p = … .
  3. Adult tickets cost 14 and child tickets cost 6. A school sold 50 tickets and took 412 in total. How many adult tickets were sold? → 14Prompt: Let a = adult tickets and c = child tickets. Write two equations.

Hook · 6 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 · 12 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 · 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.
  1. The sum of two numbers is 55 and their difference is 7. What is the larger number? → 31Prompt: Let the numbers be x and y: x + y = sum, x − y = difference.
  2. Bike hire A charges $3 plus $1.50 per hour. Bike hire B charges $7 plus $1 per hour. After how many hours do they cost the same? → 8Prompt: Write cost = fixed fee + rate × hours for each company.

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.
  1. Bike hire A charges $4 plus $3 per hour. Bike hire B charges $9 plus $2 per hour. After how many hours do they cost the same? → 5Prompt: Write cost = fixed fee + rate × hours for each company.
  2. Daniel buys 3 notebooks and 2 pens for $3.35. A friend buys 2 notebooks and 5 pens for $3.15. How much is one pen? Give the amount as a number. → 0.25Prompt: Write 3n + 2p = … and 2n + 5p = … .

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

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Model real situations with two equations and solve

Name

Date

Score/ 8

  1. Question 1

    Gym A costs 29 plus 6 per visit. Gym B costs 14 plus 9 per visit. After how many visits do they cost the same?

    Answer

  2. Question 2

    The sum of two numbers is 77 and their difference is 15. What is the larger number?

    Answer

  3. Question 3

    Sam buys 3 notebooks and 2 pens for $4.15. A friend buys 2 notebooks and 5 pens for $7.35. How much is one pen? Give the amount as a number.

    Answer

  4. Question 4

    Gym A costs 31 plus 2 per visit. Gym B costs 16 plus 7 per visit. After how many visits do they cost the same?

    Answer

  5. Question 5

    The sum of two numbers is 66 and their difference is 8. What is the larger number?

    Answer

  6. Question 6

    Daniel buys 3 notebooks and 2 pens for $2.30. A friend buys 2 notebooks and 5 pens for $3. How much is one pen? Give the amount as a number.

    Answer

  7. Question 7

    Bike hire A charges $4 plus $1 per hour. Bike hire B charges $10 plus $0.50 per hour. After how many hours do they cost the same?

    Answer

  8. Question 8

    The sum of two numbers is 80 and their difference is 4. What is the larger number?

    Answer

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Answer key: Model real situations with two equations and solve

  1. 1. 5

  2. 2. 46

  3. 3. 1.25

  4. 4. 3

  5. 5. 37

  6. 6. 0.4

  7. 7. 12

  8. 8. 42