Year 8 - Maths
Inequality notation to express error
Estimation and rounding
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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 helps pupils understand rounding to different decimal places, and significant figures. Pupils will also learn how to truncate numbers and understand the contexts in which these skills are useful. The unit ends will an exploration of rounding and inequality errors.
Lesson Summary
You will learn to calculate possible errors expressed using inequality notation 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.
Vocabulary To Learn
- Range: A range of values where every value in the range estimates to the given value.
- 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
- Incorrect use of the error interval i.e $$a ≤ x ≤ b$$ or writing the error interval as $$a ≤ x > b$$
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. 'Range'
A range of values where every value in the range estimates to the given value. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Incorrect use of the error interval i.e $$a ≤ x ≤ b$$ or writing the error interval as $$a ≤ x > b$$. Correction: As a check, encourage students to round the upper limit interval by the degree of accuracy to see if it evaluates to the rounded number. Also, draw a number line to show the meaning of $$a ≤ x > b$$ and allow students to see the error.
More Lessons In This Unit
- Checking by estimating Study Guide
- Checking understanding of rounding Study Guide
- Degrees of accuracy Study Guide
- Estimating numerical calculations Study Guide
- Overestimating vs underestimating Study Guide
- Problem solving with estimation and rounding Study Guide
- Rounding decimals to significant figures Study Guide
- Rounding errors Study Guide
- Rounding integers to one significant figure Study Guide
- Rounding integers to significant figures Study Guide
- Rounding to any number of decimal places Study Guide
- Rounding to three decimal places Study Guide
- Securing understanding of rounding Study Guide
- Truncating Study Guide
- Using inequality notation for errors in calculations Study Guide
Browse all guides in the Year 8 Maths guide library.