Year 10 - Maths
Upper and lower bounds
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 the lower and upper bounds of values and express these as a ≤ x < b.
Key Notes
- When given a rounded number you can say what the biggest and smallest values of the unrounded number could have been .
- You can use a ≤ x < b notation to express the range of values the unrounded number could have taken.
- You can use those values in your estimate to see what your biggest and smallest answers could have been.
- The range of possible answers is the error interval.
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
- For example if a measurement of 12 cm has been given to the nearest centimetre assuming the upper bound is 12.4 cm.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When given a rounded number you can say what the biggest and smallest values of the unrounded number could have been . You can use a ≤ x < b notation to express the range of values the unrounded number could have taken.
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: For example if a measurement of 12 cm has been given to the nearest centimetre assuming the upper bound is 12.4 cm. Correction: Emphasise the infinite nature of a measurement.
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 in additive calculations Study Guide
- Upper and lower bounds in multiplicative calculations Study Guide
- Using upper and lower bounds practically Study Guide
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