Skip to learning content
← Back to Maths
Free PlanPremium View
🔢
Free PreviewCore30 min

Maths • Number & Operations in Base Ten

Base Ten Operations Mission

Multiply multi-digit whole numbers, divide with remainders, and explain answers using area models and partial quotients.

0

Completed

0/2

Correct

0%

Score

2

Activities

Learning Goals

  • ✓Multiply multi-digit whole numbers using place value.
  • ✓Use an area model to break apart large multiplication problems.
  • ✓Divide whole numbers using partial quotients.
  • ✓Interpret remainders in real-world problems.

Mini Lesson

  1. 1Large multiplication problems become easier when numbers are broken apart by place value.
  2. 2An area model shows each partial product clearly.
  3. 3Division can be solved by subtracting easy groups, called partial quotients.
  4. 4A remainder is what is left after making as many equal groups as possible.
factorproductquotientremainderarea modelpartial quotientplace value

Interactive Activities

Tap an answer choice. The card will show feedback, the correct answer, visual model, and step-by-step explanation.

🎭
Activity 1Multi-Digit Multiplicationquiz

Theater Seat Multiplication

Question

A school theater has 27 rows of seats. Each row has 342 seats. How many total seats are in the theater?

Instruction

Break 342 into 300 + 40 + 2 and break 27 into 20 + 7. Multiply each part, then add all partial products.

💡 Teacher Hint

Use an area model: 20 × 342, then 7 × 342, then add.

👁️ Show Visual Model: Area Model
Model Type: area-model
300      +     40      +    2
        ┌───────────┬───────────┬──────────┐
  20    │   6,000   │    800    │    40    │  → 6,840
        ├───────────┼───────────┼──────────┤
   7    │   2,100   │    280    │    14    │  → 2,394
        └───────────┴───────────┴──────────┘

Total: 6,840 + 2,394 = 9,234 seats
✅ Show Step-by-Step Answer
  1. 1Break 27 into 20 + 7.
  2. 2Break 342 into 300 + 40 + 2.
  3. 3Multiply 20 × 300 = 6,000, 20 × 40 = 800, and 20 × 2 = 40.
  4. 4The first row total is 6,840.
  5. 5Multiply 7 × 300 = 2,100, 7 × 40 = 280, and 7 × 2 = 14.
  6. 6The second row total is 2,394.
  7. 7Add 6,840 + 2,394 = 9,234 seats.
CCSS 5.NBT.B.5
🍎
Activity 2Long Division with Remaindersquiz

Apple Box Division

Question

A farmer has 435 apples. She packs them into boxes that hold 12 apples each. How many full boxes can she pack, and how many apples are leftover?

Instruction

Use partial quotients. Subtract easy multiples of 12 from 435 until fewer than 12 apples remain.

💡 Teacher Hint

Try 12 × 30 first, then see how many more groups of 12 fit.

👁️ Show Visual Model: Partial Quotients Model
Model Type: partial-quotients
12 ⟌ 435
    -360   12 × 30  → 30 boxes
    ────
      75
     -72   12 × 6   →  6 boxes
    ────
       3   leftover apples

Result: 30 + 6 = 36 boxes, remainder 3 apples
✅ Show Step-by-Step Answer
  1. 1Start with 435 apples.
  2. 2Subtract 360 because 12 × 30 = 360.
  3. 3435 - 360 = 75.
  4. 4Subtract 72 because 12 × 6 = 72.
  5. 575 - 72 = 3.
  6. 6Add the partial quotients: 30 + 6 = 36.
  7. 7There are 36 full boxes and 3 apples left over.
CCSS 5.NBT.B.6

Exit Ticket

Why is an area model useful when multiplying large whole numbers?

Show Suggested Answer

It breaks a large multiplication problem into smaller place-value parts, making the partial products easier to see and add.

EthioKids Learning