Year 6 - Maths
Explain how you know you have found all the possible solutions to a problem with two unknowns
Solving problems with two unknowns
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will compare and represent the structure of problems with two unknowns using a bar model. They will systematically solve problems with two unknowns using trial and improvement.
Lesson Summary
You will learn to explain how you know you have found all the possible solutions to a problem with two unknowns.
Key Notes
- A trial and improvement approach can be used if a model can't easily be drawn.
- A table can be used to record and check all possible solutions have been found.
- Some problems with two unknowns have an infinite number of solutions.
Vocabulary To Learn
- Systematically: To work systematically means to work in an organised way, often according to a fixed plan or system.
- Infinite: Infinite means without an end. If something is unlimited, you could say it has an infinite number of things.
Common Mistakes To Avoid
- Pupils attempt to represent the problems with bar models rather than take a systematic, trial and improvement approach.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A trial and improvement approach can be used if a model can't easily be drawn. A table can be used to record and check all possible solutions have been found.
2. Use this key word in a maths sentence and explain it clearly. 'Systematically'
To work systematically means to work in an organised way, often according to a fixed plan or system. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils attempt to represent the problems with bar models rather than take a systematic, trial and improvement approach. Correction: Encourage pupils to represent each problem how they would like. Pupils should take time to notice why it is that the bar model if not appropriate to help solve these problems and identify these clues within the questions.
More Lessons In This Unit
- Compare the structure of problems with one or two unknowns Study Guide
- Explain how to balance an equation with two unknowns Study Guide
- Explain how to represent an equation with a bar model Study Guide
- Explain why there is sometimes only one solution to a problem Study Guide
- Represent and solve problems with two unknowns efficiently Study Guide
- Represent the structure of a problem with two unknowns in context Study Guide
- Solve problems with two unknowns in a range of contexts Study Guide
- Solve problems with two unknowns with one, several and infinite solutions Study Guide
- Use a bar model to represent spatial problems with two unknowns Study Guide
Browse all guides in the Year 6 Maths guide library.