Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Ratio problems with algebra
Ratio and proportion
CCSS HSA.CED.A.1England: GCSE Higher Ratio
Objective and success criteria
Students will: Ratio problems with algebra.
- 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: Share in a given ratio; Two-step equations
Leads to: the next skill in this area.
Materials: Bar models, Double number lines, Ratio tables, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Share in a given ratio; Two-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Isla and Tariq share $77 in the ratio 3:4. How much does Isla get? (Type the number only.) → 33Prompt: How many parts are there altogether?
- The ratio of adults to children at a show is 5:4. There are 6 more adults than children. How many people are there in total? → 54Prompt: The difference in parts is 1.
- Luis and Diego share $63 in the ratio 5:2. How much does Diego get? (Type the number only.) → 18Prompt: How many parts are there altogether?
Hook · 3 min
- Share a recipe for 4 people and ask how much is needed for 6.
- Share the objective: Ratio problems with algebra. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: The ratio x : y is 3 : 4, and y is 2 more than x. Find x.
- Step 1: 4x = 3(x + 2)
- Step 2: 4x = 3x + 6
- Step 3: x = 6
- Step 4: x = 6
- Answer: x = 6
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 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 ratio x : y is 3 : 5, and y is 18 more than x. Find x. → x = 27Prompt: Write y as x + 18. Then x/(x + 18) = 3/5.
- (x + 5) : (3x − 9) = 2 : 3. Find x. → x = 11Prompt: Write the ratios as fractions and cross-multiply.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- The ratio x : y is 5 : 7, and y is 14 more than x. Find x. → x = 35Prompt: Write y as x + 14. Then x/(x + 14) = 5/7.
- (x + 6) : (3x + 14) = 2 : 5. Find x. → x = 2Prompt: Write the ratios as fractions and cross-multiply.
Watch out for
- Adding the same amount to both parts instead of multiplying.
- Mixing up part-to-part and part-to-whole ratios.
Support and stretch
Support
- Review first: Share in a given ratio.
- Use concrete materials: bar models.
- 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