A fraction is a number, not two numbers stacked together

Where we are on the map

We move from whole numbers to fractional numbers below and above one.

Begin with a familiar image

Cutting one pizza into eight equal pieces and taking three gives 3/8. Equal parts are essential.

Precise meaning

The denominator tells how many equal parts make the whole; the numerator tells how many are selected. a/b is also the number a ÷ b.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

unit → equal parts → size of one part → number of selected parts

Worked example

For 3/8, divide one unit into eight equal parts and take three; its point lies between 0 and 1, three eighths from zero.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

It is wrong to call 3/8 and 3/5 equal because their numerators match: a fifth is larger than an eighth.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. A tank holds 12 equal buckets and already contains 7. Represent the filled amount as a fraction, a division, and a point on a line.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

The next lesson shows how different fraction notations can name the same point.

Course contents