Year 6 - Maths
Represent and solve problems with two unknowns efficiently
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 represent problems with two unknowns and solve using an efficient strategy.
Key Notes
- The model can represent a scaling structure with one part being __ times the size of the other.
- The model can represent an additive structure.
Vocabulary To Learn
- Coefficient: A coefficient is number used to multiply an unknown value.
- Efficient: To solve something efficiently means to solve a problem quickly whilst also maintaining accuracy.
Common Mistakes To Avoid
- Pupils think that the removal of the multiplication symbol can result in the number becoming a two-digit number rather than two, single digits being multiplied together.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The model can represent a scaling structure with one part being __ times the size of the other. The model can represent an additive structure.
2. Use this key word in a maths sentence and explain it clearly. 'Coefficient'
A coefficient is number used to multiply an unknown value. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils think that the removal of the multiplication symbol can result in the number becoming a two-digit number rather than two, single digits being multiplied together. Correction: Using the language of 'lots of' may support pupils to see that an algebraic equation with coefficients represents multiplication. For example: 40 can be read as 'four lots of 0'.
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 how you know you have found all the possible solutions to a problem with two unknowns Study Guide
- Explain why there is sometimes only one solution to a problem 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.