1. Boxes. 36 tiles. Boxes of 9. How many full boxes, and how many leftover?
Estimate: a bit more than 3 boxes?
Answer
36 ÷ 9 = 4. No leftover. If you said 3, you undercounted a full box.
Math / Sharing the floor
Uncut
How many · cut the rectangle
Sharing the floor
You already counted a rectangle. Now the floor is built and the job is to cut it: how many along one wall, or how many tiles each person gets (division).
Origins
Same floors,
cut up
cut up
Once you can lay a field, you split it: shares of land, shares of grain, tiles per wall. Sharing is not a new kind of number. It is the rectangle read backwards.
When it will
not come even
not come even
Leftovers wait in the next lesson. This page stays on whole tiles, so you can see the cut.
Honesty: nobody invented sharing. People cut piles and floors long before a school name.
Know the floor. Hide one side.
Total tiles stay still. Drag how many across. The other side is what sharing finds: total ÷ across.
If it does not come out even, leftover tiles sit aside. We do not smash them into a fraction yet.
24 tiles · 6 across · 4 down
Whole rows only. Grey tiles are leftover — not a full row.
Same cut, named as people
24 tiles, 4 people. Each person gets a strip. That is the same picture as “24 down a side of 4.”
24 tiles · 4 people · 6 each
Drag people. Each share is total ÷ people, leftover aside.
A cut question, then a job
Calculate 24 ÷ 6.
Nothing is at stake. Nobody is laying tile or splitting a box.
You have 24 tiles. The wall is 6 tiles across. Do you have enough for 4 rows, or do you go back to the shop?
24 ÷ 6 = 4 rows. The wall is covered. That is a job.
Jobs — estimate first
Cover the answer. Say a range. Then open.
2. Seats. 30 seats, tables of 4. How many full tables, leftover chairs?
Estimate: a bit more than 7 tables, some chairs spare.
Answer
7 tables (28 seats), 2 leftover. 8 tables would need 32.
3. Hall. 40 tiles. You want 8 across. How many down?
Estimate: 5?
Answer
40 ÷ 8 = 5 down. Same floor as 8 × 5, read backwards.
Gate — four, all required
Each right gate item is 20 points. Hands-on is 20. Wrong is 0 until you retry and get it. Next unlocks only at 100 — and only if that page exists.
1. What is sharing doing?
2. 24 tiles, 6 across. How many down?
3. 20 tiles, 3 people. Equal whole shares?
4. Which is a real question?