Problem
Divide 12 by 3. Since 3 times 4 is 12, the quotient is 4. So 12 ÷ 3 = 4.
Grade 3 division: 12 split into groups of 3 makes 4 groups.
3.OA.A.2Look For A PatternThe top two dividends must add to 27: 27 − 12 = 15 is the missing middle dividend.
Grade 3 subtraction: since the dividends must add to 27, the missing one is 27 take away 12.
3.NBT.A.2Work BackwardsDivide 15 by 3: 3 times 5 is 15, so 15 ÷ 3 = 5.
Grade 3 division: 15 split into groups of 3 makes 5 groups.
3.OA.A.2Look For A PatternDivide 27 by 3 to get 9. This matches the pattern because the top two quotients add: 4 plus 5 equals 9.
Grade 3: the quotients add the same way the dividends do, confirming 9 is right.
3.OA.A.3Look For A PatternWhen the divisor stays 3, dividing the whole amount 27 gives the same number as adding the two part quotients, so the quotients add just the way the dividends do.
Dividing by 3 counts how many groups of 3 an amount holds, and the whole 27 is only its two dividend parts joined, so its groups of 3 are those two parts' groups counted together.
The two dividend parts are put together with nothing added and nothing left out, so together they are exactly the whole amount.
Each dividend part is a whole number of groups of 3, so the groups that fill the whole are the first part's groups set next to the second part's groups.
An amount divided by 3 is just the count of equal groups of 3 that build it, so each part supplies its own count of groups.
Some groups of 3 from one part plus some groups of 3 from the other part make that many groups of 3 altogether, because joining equal-size groups keeps the group size 3.
When the divisor stays the same, dividends add and quotients add, so the boxes are 4, 15, 5, and 9!