The big ideaSharing can leave some over. The remainder is always smaller than the number of shares.
How it works
Sharing can leave some over. What is over is the remainder.
The answer to the share is how many each one gets. The remainder is what is left.
On the frame: start with all the beads, take away what was handed out, and what stays is the remainder.
The remainder is always smaller than the number sharing. If it is as big, deal another round.
14 beads to start.Hand out 12, and 2 stay on the frame: the remainder.
Example 1: 14 shared among 4
Deal one at a time to 4 plates. Three rounds give each plate 3.
Four plates with 3 each use 12: 4 × 3 = 12
Take away what was handed out: 14 − 12 = 2
Two are over, and 2 is smaller than 4, so there is no room for another round.
The remainder is 2.
The 2 that stay on the frame.
Example 2: 22 sweets into 7 bags
Three rounds use 21 sweets: 7 × 3 = 21
Take away 21 from 22: 22 − 21 = 1
One sweet is over, but 7 bags need 7 sweets for another round.
The remainder is 1.
One sweet is over.
Example 3: 18 grapes among 6 plates
Three rounds use all the grapes: 6 × 3 = 18
Take away what was handed out: 18 − 18 = 0
Nothing is over, so the remainder is zero. This is an exact share.
Nothing stays on the frame.
Example 4: 17 shared among 5
Three rounds give each of 5 plates 3. That uses 15: 5 × 3 = 15
Take away: 17 − 15 = 2
Each gets 3 and 2 are over.
17 beads at the start: hand out 15 and 2 stay.
Example 5: 39 shared among 8
Four rounds give each of 8 plates 4. That uses 32: 8 × 4 = 32
Take away: 39 − 32 = 7
A lot is over, but 7 is still fewer than 8, so no more round fits.
Seven are over.
Words to know
remainder
What is over after a fair share.
quotient
How many each one gets.
round
One trip all the way round the plates, one for each.
exact share
A share with nothing over.
Watch out
The remainder must be smaller than the number sharing. If it is not, deal another round.
A remainder of zero means an exact share.
Keep the two answers apart: 3 each is the share, and 2 over is the remainder.
Take away what was handed out, not the number of plates.
Try it
Nineteen marbles are shared among four jars. How many are over?
Sharing among 5. Can the remainder be 5?
Twenty-four cookies are shared among six plates. How many are over?
17 is shared among 5. How many each, and how many over?
Answers: 1. 3 · 2. no · 3. none · 4. 3 each, 2 over
Try at homeAsk a grown-up for a handful of small things, like buttons or raisins. Share them out equally, one at a time, among the people in your family. Say how many each person gets, and how many are over. Then try a different amount!
For grown-upsShare a handful of buttons or raisins among your family, one at a time. Ask how many each person got and how many are over, then try a different amount.
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