Looking at the image, this is a “Rational Number Sprinkles” activity where students sort different numbers into three nested categories:
1.
Whole Numbers — These are non-negative integers: 0, 1, 2, 3, ...
2.
Integers — These include whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ...
3.
Rational Numbers — Any number that can be written as a fraction (including decimals that terminate or repeat). This includes all integers and fractions.
The ice cream cone diagram shows three layers:
- The innermost circle = Whole Numbers
- The middle ring = Integers (includes whole numbers)
- The outer ring = Rational Numbers (includes integers and fractions/decimals)
Now let’s go through each “sprinkle” (number) and place it in the correct layer.
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List of sprinkles from the image:
-
5 → positive whole number → belongs in
Whole Numbers
-
0 → whole number → belongs in
Whole Numbers
-
-9 → negative integer → belongs in
Integers (not whole)
-
10/2 → simplifies to 5 → which is a whole number → so
Whole Numbers
-
-3 → negative integer →
Integers
-
-8 → negative integer →
Integers
-
6/11 → fraction, not an integer →
Rational Numbers only
-
2.1 → decimal, terminates → rational →
Rational Numbers
-
-2 5/8 → mixed number = -21/8 → rational, not integer →
Rational Numbers
-
-2.3 → decimal, terminates → rational →
Rational Numbers
-
3/2 → fraction = 1.5 → rational, not integer →
Rational Numbers
Wait — we must also check if any of these could belong in multiple layers. Since the layers are nested:
- All Whole Numbers are also Integers and Rational Numbers.
- All Integers are also Rational Numbers.
- But the diagram likely wants each number placed in the *smallest* category it fits into (i.e., most specific).
So:
→
Whole Numbers: 5, 0, 10/2 (since 10÷2=5)
→
Integers (but not whole): -9, -3, -8
→
Rational Numbers (but not integers): 6/11, 2.1, -2 5/8, -2.3, 3/2
Let me double-check:
- 10/2 = 5 → yes, whole number → correct.
- -2 5/8 = -2.625 → rational, not integer → correct.
- 3/2 = 1.5 → rational, not integer → correct.
- 2.1 and -2.3 → terminating decimals → rational → correct.
- 6/11 → repeating decimal? Actually 6÷11 = 0.545454... → still rational → correct.
All good.
Final sorting:
✔ Whole Numbers: 5, 0, 10/2
✔ Integers: -9, -3, -8
✔ Rational Numbers: 6/11, 2.1, -2 5/8, -2.3, 3/2
Note: The red sprinkle with “3/2” is already placed in the Rational Numbers layer in the image — that’s correct.
Also, the green “-2 5/8” is in Rational — correct.
Yellow “2.1” — Rational — correct.
Blue “-3” — Integers — correct.
Orange “-8” — Integers — correct.
Green “6/11” — Rational — correct.
Red “3/2” — Rational — correct.
Yellow “-2.3” — Rational — correct.
Orange “5” — Whole — correct.
Red “0” — Whole — correct.
Blue “10/2” — Whole — correct.
Yellow “-9” — Integers — correct.
Everything matches.
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Final Answer:
Whole Numbers: 5, 0, 10/2
Integers: -9, -3, -8
Rational Numbers: 6/11, 2.1, -2 5/8, -2.3, 3/2
Parent Tip: Review the logic above to help your child master the concept of classifying rational numbers worksheet.