Lesson 4 — Whole Numbers, Integers & Fractions

Hands-on · about 10 minutes.

Try these first. They are about how the number families nest inside each other, and how a fraction names a part of a whole.

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The number families, nested like boxes

Counting (natural) numbers: 1, 2, 3, 4, … — what you count objects with.
Whole numbers: the counting numbers plus 0 — 0, 1, 2, 3, …
Integers: the whole numbers and their negatives — …, −3, −2, −1, 0, 1, 2, 3, …

Each family sits inside the next, like nesting boxes: every counting number is a whole number, and every whole number is an integer. The new thing integers add is direction — a way to count below zero.

A number line makes this visible: 0 sits in the middle, positives march to the right, negatives to the left. −3 is three steps left of zero; it is smaller than −1, even though "3 is bigger than 1." The farther left, the smaller the value.

Fractions: naming a part of a whole

A fraction splits a whole into equal pieces. The denominator (bottom) says how many equal pieces the whole is cut into; the numerator (top) says how many of those pieces you have.

Two classroom tools make this concrete:

Fraction circles: a pie cut into equal slices. 3/4 is three of four equal slices shaded — great for showing parts of a single whole.
Fraction squares (bars): a rectangle split into equal strips. Laying a 1/2 bar next to two 1/4 bars shows at a glance that 1/2 = 2/4 — the same amount, named differently.

Equivalent fractions name the same amount: 1/2 = 2/4 = 3/6. You get them by multiplying (or dividing) the top and bottom by the same number — which is just cutting each existing piece into more equal pieces.

Why this matters in the classroom

Negative numbers feel abstract until they are tied to something real — temperature below zero, steps back on a board game, money owed. And fractions are where many students first stumble, almost always because the equal-pieces idea got skipped. Circles and bars keep "equal pieces" front and center, so 1/3 never gets read as "one piece" regardless of size.

True or false? You decide

Decide whether each statement is true or false. Instant feedback either way.

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Quick check

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One sentence summary: counting numbers, whole numbers, and integers nest inside each other on a number line that runs both directions from zero, and a fraction names equal parts of a whole — with equivalent fractions naming the same amount in different pieces.

Next: Rational, Irrational & Real Numbers →