Multiply tens and ones
Split a two-digit number into tens and ones, multiply both parts and recombine.
Begin with the activity ↓How can we count four boxes of 23?
Split each box of 23 into 20 and 3. Count four groups of each part, then combine them.
Each of four boxes contains 23 blocks. Split each box into two tens and three ones. Across four boxes, the tens appear four times and the three ones also appear four times.
Four groups of two tens make eight tens, or 80. Four groups of three ones make 12. Together, 80+12=92. Counting only 20×4 or only 3×4 omits part of each box.
We write (20+3)×4=20×4+3×4. The parentheses group the two parts of one box. Both expressions count the same four boxes, so they give the same value.
Regrouping in written multiplication follows the same idea. The twelve ones in 3×4 become a ten and two ones. Add that ten to the eight tens in 20×4. The important point is what each digit represents, not merely where it is written.
All four boxes must have the same amount to count four groups of 23. If one contains 18, treating every box as 23 gives an incorrect total. Check the equal-group condition first.
Listen one paragraph at a time
If you repeated only one part
Connect the tens and ones inside each box. An additional box adds both parts, not just one.
Now change it yourself
Change the amount per box and the number of boxes. Match the tens and ones parts to the whole calculation.
- Box 120+ 3
- Box 220+ 3
- Box 320+ 3
- Box 420+ 3
23 × 4 = 20 × 4 + 3 × 4 = 80 + 12 = 92
An added box adds both its tens and its ones. Check that neither part is missing.
The activity multiplies a two-digit whole number by 1 to 9. Zero groups would contain zero objects; this meaning extends to multiplying by zero.
Try with paper and objects
Draw four boxes, each containing two tens-rods and three dots. Count rods together and dots together.
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90 · 10×5+8×5=50+40=90.
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Speak, point or draw on paper. Explain the reason, not just the numerical answer.
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Share tens, unpack leftover tens into ones, and account for the remainder in the original total.