Operations with fractions: name the counting unit first

Where we are on the map

After recognizing and comparing fractions, we calculate with them.

Begin with a familiar image

Half an apple and one third of an apple cannot be counted simply as “two parts” because the part sizes differ.

Precise meaning

Addition and subtraction need a common counting unit. Multiplication takes a part of a number; division asks how many portions of a given size fit.

The lesson’s support signal

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

name the unit → choose a model → calculate → check by inverse or estimate

Worked example

1/2 + 1/3 = 3/6 + 2/6 = 5/6. The answer is below 1 and greater than either addend.

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

Writing 1/2 + 1/3 = 2/5 adds tops and bottoms separately but never creates a common counting unit.

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 workshop has 7/8 of a sheet and uses 3/16 per item. Find the number of complete items and the material left.

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

A relationship between two changing quantities leads to the idea of ratio.

Course contents