Equivalent fractions are not a trick for changing two numbers. They name the same point on the same whole. When one fourth is split into three smaller equal pieces, the size of the fraction has not grown or shrunk; its units have simply been renamed from fourths to twelfths.
MATH-103 · MODULE 02
Equivalent Fractions and Benchmarks
Keep the quantity fixed while changing its name, then compare fractions with evidence.
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
Equivalent fractions keep a quantity fixed while the unit is renamed.
This module develops comparison from meaning. Sometimes a benchmark such as one half settles the question. Sometimes a shared numerator or denominator helps. Sometimes you need a common unit. The important decision is to compare quantities, not to compare isolated digits that happen to be written above and below a bar.
Decimals enter here as another name for base-ten fractions. Tenths and hundredths are fraction units with familiar denominators. By tracing each form to a number-line location, you will gain a way to check that a conversion or comparison still preserves the amount.
Start
Retrieve the size, not a rule
Learning target
Equivalent forms name the same location even when the pieces are partitioned differently.
Start by locating familiar benchmarks: 0, 1/2, and 1. They will help you judge whether a new fraction is reasonable before you calculate anything.
Read or listen to the teaching conversation for this step
Module 2, Start
Transcript: Bring back the number line. Equivalent fractions share one location. The strip may have more pieces, but the amount does not grow just because the pieces get smaller.
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.
Recognize one half
Which fraction is equal to 1/2?
one whole
4/8 equal parts shown