Math lesson plan · 5th grade (Year 6 in England) · 45 minutes
Puzzles with two unknowns
Algebra
CCSS 5.OA.A.2England: Y6 Algebra
Objective and success criteria
Students will: Puzzles with two unknowns.
- 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 equations with a letter for the unknown
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 (Solve equations with a letter for the unknown). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find n: 220 + n = 594 → 374Prompt: Use the inverse operation.
- Lucia buys 5 identical T-shirts and pays $60. Write it as 5 × t = 60. What is t, the price of one T-shirt? → 12Prompt: What times 5 makes 60?
- Find n: 5 × n = 40 → 8Prompt: Use the inverse operation.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Puzzles with two unknowns. 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: a is 3 times b, and a + b = 16. What is b?
- Step 1: 16 ÷ 4 = 4
- Step 2: b = 4
- Answer: 4
- 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.
- a is 3 times b, and a + b = 40. What is b? → 10Prompt: Think of b as 1 part and a as 3 parts.
- Two numbers add to 12 and their difference is 6. What is the larger number? → 9Prompt: If you add the sum and the difference, you get twice the larger number.
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.
- a + b = 14, where a and b are whole numbers greater than 0. How many different pairs (a, b) are possible? → 13Prompt: List them in order: a = 1, 2, 3, …
- a is 3 times b, and a + b = 24. What is b? → 6Prompt: Think of b as 1 part and a as 3 parts.
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 equations with a letter for the unknown.
- 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-5.
Free lesson plan from eurekami.com/lesson-plan-builder