Arrays and Models
Draw a rectangular array or area model to show how to divide 72 by 8. What is the quotient?
72 ÷ 8 = 9
Use the partial-quotients method to compute 84 ÷ 7. Show your partial-quotient steps and the final quotient.
84 ÷ 7 = 12
Mia has 48 stickers. She wants to put them into 6 equal packets. How many stickers in each packet?
48 ÷ 6 = 8
What is the remainder when you divide 43 by 5? Explain what the remainder means in a real-world situation (e.g., distributing apples).
43 ÷ 5 = 8 remainder 3 (3 leftover apples)
100 — Fill in the blank: 6 × ____ = 54, so 54 ÷ 6 = ____.
6 × 9 = 54, so 54 ÷ 6 = 9
Using an area model, represent 144 ÷ 9 and write the quotient. Show the equal groups.
144 ÷ 9 = 16
Solve 156 ÷ 4 with partial quotients. List each subtraction (chunk) and the remaining amount until zero.
156 ÷ 4 = 39
A teacher has 117 pencils and wants to make groups of 9 for classroom sets. How many full sets can she make? If any pencils are left over, state how many remain and explain the remainder.
117 ÷ 9 = 13 remainder 0 (117 = 9×139×13)
Divide 221 by 4. Give the quotient and remainder. Then explain one scenario where you would round the remainder up and one where you would leave it as a remainder.
221 ÷ 4 = 55 remainder 1 — round up if you need whole groups, keep remainder if partial group not allowed
True or False: If a number is divisible by 3, then the sum of its digits is divisible by 3. Use this to decide whether 246 is divisible by 3.
True. Sum digits of 246 = 12; 12 divisible by 3, so 246 is divisible by 3
135 ÷ 5. Explain each step and give the quotient.
135 ÷ 5 = 27
Use partial quotients to divide 289 ÷ 8. Show how you choose chunks and state the quotient and any remainder.
289 ÷ 8 = 36 remainder 1
A baker makes 264 cookies and places them into boxes that hold 8 cookies each. How many boxes are filled? Are there any loose cookies left? Explain in context.
264 ÷ 8 = 33 boxes, 0 leftovers
Calculate 178 ÷ 6. State the quotient and remainder. Describe how you would interpret the remainder if you were packing items into boxes.
178 ÷ 6 = 29 remainder 4 (4 items not packed)
List the multiplication fact you would use to check 189 ÷ 3. Then use it to verify the quotient.
Use 3 × 63 = 189, so 189 ÷ 3 = 63
Given a three-digit dividend 246 ÷ 6, sketch an area model (or array) partitioned by place value to compute the quotient. Show how you break the dividend into hundreds, tens, and ones.
246 ÷ 6 = 41 (since 6×41=2466×41=246)
Compute 325 ÷ 6 using partial quotients. Show each step and explain why partial quotients connect to place value.
325 ÷ 6 = 54 remainder 1
A delivery truck has 473 identical crates to load onto shelves that hold 6 crates each. How many full shelves will be filled and how many crates (if any) will be left unplaced? Interpret the remainder
Find the quotient and remainder for 305 ÷ 7. Then rewrite the result as a mixed number and explain the connection between the mixed number and the quotient-with-remainder form.
305 ÷ 7 = 43 remainder 4
If you know 7 × 8 = 56, explain how that fact helps you quickly find 560 ÷ 7.
560 ÷ 7 = 80 because 7 × 80 = 560
Create an array to solve 378 ÷ 3. Show how the array groups the total into equal rows or columns and state the quotient.
378 ÷ 3 = 126
Use partial quotients to divide 999 ÷ 9. Show reasoning and the final quotient.
999 ÷ 9 = 111
In a school fund-raiser, 999 flyers are handed out in groups of 7 to teams. How many full groups of 7 can be formed and how many flyers remain? Show a solution using place value understanding and explain the remainder in context.
999 ÷ 7 = 142 remainder 5
A coach needs to split 743 players (hypothetical practice tokens) into teams of 8. Find the quotient and remainder and explain what the remainder represents in this context. Suggest one realistic way to handle the leftover players.
743 ÷ 8 = 92 remainder 7 (7 players not assigned; options: form a smaller team or add substitutes)
Explain how place value helps you divide 600 ÷ 3 and 625 ÷ 5. Show quick mental steps you would use.
600 ÷ 3 = 200 (divide each place by 3). 625 ÷ 5 = 125 (since 5×125=6255×125=625)