A fraction begins with a defined whole. The denominator names the size of one equal part of that whole; the numerator counts how many of those equal units are present. Without the whole and equal parts, a fraction picture cannot prove anything. This is why a number line is so useful: it fixes the whole, the unit, and the location in one place.
MATH-103 · MODULE 01
Fractions Have Location
Treat a fraction as one quantity with a size, a whole, and a place on a number line.
A rational number toolkit
Make the relationship visible before the procedure tries to hide it.
This course begins every module with a teaching conversation and treats fractions, decimals, percents, and ratios as connected ways to describe quantity. Work one decision at a time, choose a representation that fits, then check whether the result belongs in a sensible range.
Restoring this module…
Before you begin
Fractions are locations and quantities—not two unrelated whole numbers.
You will use fraction strips, equal shares, and a number line to connect several ideas that are often separated. A fraction can name part of one whole, a fair share from division, or an amount greater than one. Seven fourths is not an error because the numerator is bigger; it is one whole and three fourths more.
Before each question, ask: What is one whole here? What size is one unit? Where would this amount lie relative to zero, one half, and one? Those questions make fraction reasoning visible and prevent you from treating the top and bottom digits as a rule to memorize.
Start
Name the whole before naming the fraction
Learning target
A fraction only has meaning when its whole and equal-sized unit are clear.
The denominator tells how many equal units make one whole. The numerator tells how many of those same-sized units are being counted. The two numbers work together to name one quantity.
Read or listen to the teaching conversation for this step
Module 1, Start
Transcript: Begin by naming the whole. Then ask how many equal parts make that whole, and how many of those equal parts are being counted. A fraction is a quantity, not two separate whole numbers stacked together.
Guided practice
Make one decision, get a useful response, then continue.
A response counts as independently complete only when it is correct. Hints and recovery routes remain available whenever you need them.
Find the defined whole
A supply box holds 12 identical markers. Three markers are set aside. What fraction of the box is set aside?
12 markers
3/12 equal parts shown