Comparing fractions: put the numbers on one scale

Where we are on the map

Equivalent fractions now help us order different values.

Begin with a familiar image

Progress along two routes can only be compared fairly when the whole routes and units of measure agree.

Precise meaning

A common denominator makes part sizes equal; a common numerator equalizes selected counts; benchmarks provide a fast magnitude check.

The lesson’s support signal

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

one whole → one scale → points on a line → left/right → benchmark check

Worked example

3/4 = 9/12 and 2/3 = 8/12, so 3/4 > 2/3; both also remain below 1.

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

The larger denominator does not automatically mean a larger fraction. With equal numerators, 3/8 < 3/5 because eighths are smaller.

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. Order 7/8, 5/6, 11/12, and 3/4; verify with a common denominator and benchmarks.

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

Next we perform all four fraction operations from their meanings.

Course contents