Day 32 · Thirds and quarters that mean somethingYear 3 Maths · T1 W7–8 · Readers / Days / Day 32

Source review complete · local suitability still needs review.

Give your little display a clear fraction label.

Useful purpose: Recognise one-third and one-quarter and represent their multiples with a strip and an equal-group collection.

1 · Find the starting point

Check equal parts and whole from Day 31 using an unrelated two-part panel. Count twelve drawn marks if wanted; explain that the whole collection includes every mark, not only one row.

2 · Prepare

Offer twelve large paper marks, or describe twelve equal-valued items arranged into three groups of four. Use objects only if safe and familiar. No real distribution to people is required; a fictional display gives a useful purpose.

3 · Brief worked model

MODEL whole is twelve equally counted paper labels. Three equal groups have four labels each. One group is 1/3 of the collection; two groups have eight labels, 2/3. A strip split into three equal lengths shows the same fraction relationship. A different whole of twelve labels split into four groups of three gives 1/4 per group, not 1/3. The grouping changes the denominator.

4 · A different guided try

Use a new collection of eight equally counted marks split into four equal groups of two. Invite one-quarter and three-quarters in groups and in a drawn strip. Compare the representations by the whole and equal grouping, not by matching their decoration.

5 · Your own attempt

Choose thirds or quarters. Make a collection plan, strip or usual-communication description for a fictional label display. Show a unit fraction and a multiple; explain what stays the whole in both versions.

6 · Observe what was actually shown

Record equal grouping, denominator, multiple numerator and connection between representations. Counting eight objects without specifying its whole does not establish 2/3. A helper can place objects while the learner makes the grouping choice.

Specific next teaching

If the number of objects in one group is treated as the denominator, use a new six-item collection with three groups of two. If secure, change from a set to a strip and ask what the parts have in common.

Three choices you can switch between

1 · Display groups

Show one group and then two.

MODEL twelve identical-value labels are grouped 4+4+4. Indicate one-third, then two-thirds. Explain that eight labels means 2/3 of this twelve-label whole, not 2/3 of every collection.

Evidence/observation: Supplied grouped-set interpretation.

Specific next teaching: Use a new nine-item set split into thirds before returning to twelve.

2 · Strip designer

Make thirds or quarters someone can read.

Choose one equal-length strip whole. Draw/describe three or four equal intervals, label one interval and a multiple you choose. Match it with an equal-group collection of a suitable total.

Evidence/observation: Own representation and connection; drawing quality not a criterion.

Specific next teaching: Check the whole/equal intervals with an unrelated model if the two representations disagree.

3 · Repair a label

What does the label need to say?

MODEL eight equal-value cards split into four groups of two. A sign says "two cards is 1/2". Correct it to "two cards is 1/4 of these eight cards", explaining the whole and four groups.

Evidence/observation: Supplied sign repair; no real classroom display asserted.

Specific next teaching: Ask for a different useful label with both numerator and denominator changed.

Short child start · Ordinary cues/full alternatives · Adult preparation