Year 6 - Maths
Explain why there is sometimes only one solution to a problem
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 why there is sometimes only one solution to a problem.
Key Notes
- Some problems with two unknowns have only one solution.
- If both the sum of and difference between the two unknowns are known then there will only be one solution.
- Some problems with two unknowns have many solutions.
- Some problems with two unknowns have an infinite number of solutions.
Vocabulary To Learn
- Sum: The sum is the total when numbers are added together.
- Difference: The difference is the result of subtracting one number from another. How much one number differs from another.
Common Mistakes To Avoid
- Pupils may draw bar models which are inaccurate and do not represent the problem effectively.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Some problems with two unknowns have only one solution. If both the sum of and difference between the two unknowns are known then there will only be one solution.
2. Use this key word in a maths sentence and explain it clearly. 'Sum'
The sum is the total when numbers are added together. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may draw bar models which are inaccurate and do not represent the problem effectively. Correction: These types of problems lend themselves to be drawn using bar models that are lined up one on top of the other. Model creating these bar models with the pupils and explaining how you know where the numbers sit within them.
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
- 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.