Subscribe

9th grade · Math · Unit 6 of 17

Number Sets

Whole, rational and irrational

What your child practices

Natural numbers, whole numbers, integers, rational and irrational numbers, how they fit inside each other, and why there are always more numbers between any two rational numbers.

Minnesota K-12 Academic Standards benchmark: 9.3.5.3 · the number systems from whole numbers to the real numbers

How we explain it

Children can open this short lesson before they practice.

  1. Natural numbers count: 1, 2, 3. Integers add 0 and negatives.
  2. Rational numbers can be written as fractions. Irrational numbers cannot.
  3. Between any two rational numbers there is always another one.

Example: Is 0.25 rational or irrational? 0.25 = 25/100 = 1/4. It is a fraction of whole numbers. Answer: Rational

Number Sets in Minnesota

In the Minnesota K-12 Academic Standards, this is unit 6 of 17 in 9th grade Math, after Statistics in Society and before Expressions.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Minnesota Department of Education (MDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Which number belongs to the whole numbers but is not a natural number?

    • 5
    • −1
    • 0
    • 1

  2. Question 2

    Which pair are both irrational?

    • √6 and π
    • √9 and 0.5
    • 1/3 and 0.25
    • −2 and √4

  3. Question 3

    Between 2.1 and 2.2, there is…

    • an infinite number of rational numbers
    • no number
    • exactly nine numbers
    • exactly one number

  4. Question 4

    Which number is irrational?

    • √10
    • −2/9
    • √25
    • 0.125

  5. Question 5

    As n gets very large, what happens to 1/n?

    • It becomes negative
    • It gets larger and larger
    • It reaches exactly 0
    • It gets closer and closer to 0

  6. Question 6

    What is the largest natural number?

    • There is no largest one: they go on forever
    • 1
    • 999,999,999
    • 1,000,000

More 9th grade