Split a whole into proper-fraction portions

3.NF.A.13.OA.A.2 · take · grade 3

Archetype: Part-Whole Fraction Reasoning · step in a 5-type progression

Jisoo weighed the strawberries she picked at a weekend farm, and they weighed $\dfrac{187}{20}\ \text{kg}$ . She wants to pack the strawberries into boxes holding $2\ \text{kg}$ each and sell them. How many boxes in all can she sell?

Show solution

Understand

Jisoo has 187/20 kg of strawberries. She packs them into 2 kg boxes. We need to count how many complete 2 kg boxes she can fill and sell.

Givens

Total weight of strawberries is 187/20 kg.
Each box holds 2 kg of strawberries.

Unknowns

The number of complete 2 kg boxes she can sell.

Constraints

Only full boxes (each containing 2 kg) can be sold; leftover less than 2 kg cannot make a box.

Plan

#9 Solve an Easier Related Problem · also uses: #5 Look for a Pattern

Turn the improper fraction 187/20 into an easier decimal weight, then repeatedly take away 2 kg (one box at a time) and count how many full boxes come out before less than 2 kg remains.

Execute

#9 Solve an Easier Related Problem 3.NF.A.1

Change the improper fraction 187/20 into a decimal so the weight is easy to picture: 187 divided by 20 is 9.35.

\dfrac{187}{20} = 9.35\ \text{kg}

Seeing 187/20 as 9.35 kg lets a young learner reason with a familiar weight instead of a scary fraction.

#5 Look for a Pattern 3.OA.A.2

Each box uses up 2 kg. Counting boxes is the same as seeing how many whole groups of 2 kg fit inside 9.35 kg: 2, 4, 6, 8 kg fill 4 boxes, and 10 kg would be too much.

2 + 2 + 2 + 2 = 8\ \text{kg} \le 9.35\ \text{kg} < 10\ \text{kg}

Repeatedly subtracting 2 kg is just sharing the strawberries into equal 2 kg boxes.

#9 Solve an Easier Related Problem 3.OA.A.2

After 4 boxes she has used 8 kg, leaving 9.35 - 8 = 1.35 kg. That is less than 2 kg, so it cannot fill another full box. She can sell 4 boxes.

9.35 - 8 = 1.35\ \text{kg} < 2\ \text{kg}

A box must be full to be sold, so the leftover that is not enough for a whole box does not count.

Answer: 4 boxes

Review

9.35 kg of strawberries in 2 kg boxes should be about 9.35 / 2 = about 4.7 boxes, and only whole full boxes count, so 4 boxes is the right size answer.

Guess and check (tool 6): test 4 boxes = 8 kg (fits) and 5 boxes = 10 kg (too much, more than 9.35 kg), confirming 4 is the largest number of full boxes.

Standards · min grade 3

3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Reading the improper fraction 187/20 kg as a real weight (9.35 kg).
3.OA.A.2 Interpret whole-number quotients of whole numbers — Finding how many full groups of 2 kg fit in the total weight.

💡 This only needs Grade 3 sharing-into-equal-groups sense: keep taking out 2 kg until less than 2 kg is left!