Year 10 - Maths
Upper and lower bounds in multiplicative calculations
Rounding, estimation and bounds
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
This unit explores the impact of upper and lower bounds on additive and multiplicative calculations.
Lesson Summary
You will learn to calculate upper and lower bounds for calculations involving rounded numbers.
Key Notes
- The biggest possible product comes from multiplying the upper bounds together.
- The smallest possible product comes from multiplying the lower bounds.
- The biggest possible quotient comes from dividing an upper bound by a lower bound.
- The smallest possible quotient comes from dividing a lower bound by an upper bound.
Vocabulary To Learn
- Upper bound: The upper bound for a rounded number is the smallest value that would round up to the next rounded value.
- Lower bound: The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded.
- Error interval: An error interval for a number x shows the range of possible values of x. It is written as an inequality a ≤ x < b
Common Mistakes To Avoid
- Assuming that when dividing the UB will be the result of the UB ÷ UB.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The biggest possible product comes from multiplying the upper bounds together. The smallest possible product comes from multiplying the lower bounds.
2. Use this key word in a maths sentence and explain it clearly. 'Upper bound'
The upper bound for a rounded number is the smallest value that would round up to the next rounded value. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Assuming that when dividing the UB will be the result of the UB ÷ UB. Correction: Get the pupils to investigate dividing numbers. Keep the divisor the same and change the dividend. Ask the question, "What happens as the dividend increases?".
More Lessons In This Unit
- Advanced problem solving with rounding, estimation and bounds Study Guide
- Checking and securing understanding of estimating through rounding Study Guide
- Checking and securing understanding of rounding and truncating Study Guide
- Problem solving with rounding, estimation and bounds Study Guide
- Upper and lower bounds Study Guide
- Upper and lower bounds in additive calculations Study Guide
- Using upper and lower bounds practically Study Guide
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