Math · Rung 6 of 7
Division as sharing and as making groups, bigger multiplying, and choosing the right operation for any problem.
Where this sits
Division undoes multiplication. It means sharing (12 cookies between 3 children: how many each?) or making groups (12 cookies, 3 to a bag: how many bags?). Whatever doesn't fit is the remainder, and what to do with it depends on the story.
With division in place, all four operations are working. This rung also stretches multiplication and division to bigger numbers using place value, and finishes with problems that need two steps.
These come from the Adding, subtracting, multiplying rung.
Each step builds on the one before. Most children spend weeks on some steps and days on others.
Share things out equally, one at a time, into groups.
12 grapes between 3 plates → 4 each
Make groups of a given size and count how many groups.
12 grapes, 3 to a plate → 4 plates
Use a times fact to divide.
4 × 6 = 24, so 24 ÷ 6 = 4 and 24 ÷ 4 = 6
What's left over, and what the story needs you to do with it.
14 children, 4 to a car → 3 cars and 2 left, so 4 cars
Split the bigger number into tens and ones.
23 × 4 = 20 × 4 + 3 × 4 = 80 + 12 = 92
Share the tens first, then the ones.
84 ÷ 4: 8 tens → 2 tens each; 4 ones → 1 each → 21
Decide which operations a problem needs and in what order.
"3 packs of 8 markers shared by 4 children" → 3 × 8 = 24, 24 ÷ 4 = 6
Choose how many counters and how many groups, then tap "Share". Ask your child to predict how many each group gets, and how many are left over.
You need: A deck of cards
Deal a pile of cards one at a time between players. Does everyone get the same? Any left over? Try a different number of players.
“Twenty cards between three of us. Does everyone get the same?”
You need: A pile of small treats or stickers, bags or cups
Fill bags with the same number each until you run out. How many bags? What's left over, and what should we do with it?
“Three in each bag. How many bags can we fill?”
You need: A simple recipe
The recipe makes 4 pancakes. Work out how much of each ingredient you need for 8 pancakes, then for 12. Then cook them.
“It makes 4 pancakes and we need 12. What do we do to each amount?”
You need: 24 stones or pinecones
Lay the stones out in equal rows. How many different ways can you do it? Write each one as a times fact and a division fact.
“How many ways can we arrange 24 stones in equal rows?”
You need: A group of children
Split the group into teams of a set size. How many teams? What happens to the children left over?
“18 of us, teams of 4. How many teams? What about the extra 2?”
You need: 25 beans, one die, paper
On your turn, roll the die and share the beans into that many groups. The leftovers are your points. First to 10 points wins.
“25 shared into 3 groups is 8 each, with 1 left. You get 1 point.”
You need: A grocery flyer or a list of prices
Each player has $20. How many of one thing can you buy? How much is left? Can you spend it all?
“Juice is $3. How many can you buy with $20? How much is left?”
Both are division. Act each one out with objects and notice that the answer is the same.
"3 remainder 2" cars isn't an answer. Ask what the story needs: 4 cars.
24 ÷ 6 is not 6 ÷ 24. Read ÷ as "shared into" or "how many groups of".
Share with bundles and loose ones, or with money, first. Write each step beside it.
Ask your child to draw the story before writing anything.
Tick them off as you see them. Saved on this device only.