Bounds and error intervals – Year 9 maths lesson
Lesson 3 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 9 (ages 13–14)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why does the error interval use < at the top and ≤ at the bottom?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using the wrong half unit (7.4 to 1 d.p. as 7.3 to 7.5). Half of one tenth is 0.05.
- Using the upper bound for both numbers in a division. Big answer: big ÷ small.
Tip for home: Talk about rounded figures in the news: what could the real number be?
What your child will learn
We are learning to find upper and lower bounds and write error intervals.
Success looks like
- I can find upper and lower bounds.
- I can write an error interval.
- I can use bounds in calculations.
Key words
- upper bound
- the largest value that rounds to the number
- lower bound
- the smallest value that rounds to the number
- error interval
- the range of possible values
- truncate
- cut off digits without rounding
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Measure a length to the nearest centimetre and talk about what the real length could be.
The big ideas (for the adult)
A rounded number could have been anything within half a unit either side. 7.4 to 1 decimal place is between 7.35 and 7.45.
Write this as an error interval: 7.35 ≤ x < 7.45. The upper bound itself would round up, so it uses <.
In calculations, choose the bounds that give the largest or smallest answer: for a maximum quotient, divide the upper bound by the lower bound.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 9 maths lessons
- Prime factors, HCF and LCM
- Rounding and estimation
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Venn diagrams and conditional probability
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 9: “use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b”
GCSE subject content N15: “round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.