Problem
To divide exactly, drop the leftover or top it up
A weight of walnuts is to be packed into sacks of a fixed size with none left over. We need the smallest amount that must be added.
Number system
Your answer
How to solve
Strategy Guess and Check — Since walnuts can only be added, the target is the next multiple of the sack size above what is there. Find the highest multiple that fits, step up one, and the gap is the answer.
1STEP 1
Find how many sacks fill up
Count how many whole sacks the walnuts already fill without going over.
2.63 × 31 = 81.53
31 sacks fill, with some walnuts left loose.
6.NS.B.2Guess And Check2STEP 2
Step up to the next full sack
The leftover walnuts would be a part-filled thirty-second sack, so aim to fill it.
2.63 × 32 = 84.16
84.16 kg would fill 32 sacks exactly.
6.NS.B.3Work BackwardsThe target is the next multiple of above what is there.
Why?
Filling every sack completely means the weight is a whole number of sacks, so it has to be one of the multiples of .
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Walnuts can only be added, never taken away, so the multiples below what is already there are out of reach.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
3STEP 3
Find the shortfall
Subtract what is there from what is needed.
84.16 - 84.06 = 0.1
Just 0.1 kg more is needed.
6.NS.B.3Identify SubproblemsAnswer
0.1 kg
Check the target: 84.06 + 0.1 = 84.16, and 84.16 ÷ 2.63 = 32 exactly.
Takeaway
When you can only add, aim for the next multiple up -- not the nearest one.
- Find how many sacks fill up
- Step up to the next full sack
- Find the shortfall