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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.

Arizona Academic Standards learning standard: A1.N-RN.B.3 · comparing rational and irrational 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 Arizona

In the Arizona 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: Arizona Department of Education

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 is irrational?

    • 1.7
    • 7/4
    • −1.75
    • √3

  2. Question 2

    Which number is irrational?

    • 2.5
    • −4
    • √16
    • √15

  3. Question 3

    Which number is irrational?

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

  4. Question 4

    Which statement about π is true?

    • It equals 22/7 exactly
    • It is a whole number
    • It is irrational: its decimal never ends or repeats
    • It is rational because 3.14 is a decimal

  5. Question 5

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

    • 5
    • 0
    • −1
    • 1

  6. Question 6

    Which number is both a natural number and an integer?

    • 8/3
    • −8
    • 8
    • √8

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