Mathematics·Number Representation & Place Value·conceptual
Number Sets & Infinity
Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers
Suggested ages 13–14
Evidence of understanding
- Explain that rational numbers can be written as a fraction of two integers and have terminating or repeating decimals
- Give examples of irrational numbers and explain why their decimal expansions neither terminate nor repeat
- Appreciate that between any two numbers there are infinitely many other numbers
Assessment prompt
Can Number Sets & Infinity explain that numbers like √2 and π can't be written as exact fractions — and that their decimal expansions go on forever without repeating?
Standards alignment
8.NS.1US · ccss-math
Know irrational numbers and decimal expansions
Common Core State Standards for Mathematics · 8
8.NS.2US · ccss-math
Approximate irrational numbers
Common Core State Standards for Mathematics · 8
KS3.Maths.Num.16GB · uk-nc-2013
Infinite Nature of Number Sets
The national curriculum in England: Key stages 1 and 2 framework document · Key Stage 3