16 × 12 on the frame: one hundred, nine tens and two ones.
The plan for a two-digit sum.
Ten rows of 16: every bead moves up one row, 160.
Worked examples
16 × 12, ten rows and two rows
Split 12 into 10 and 2.
Ten rows of 16: every bead moves up a row, so 10 × 16 = 160.
Two rows of 16: 2 × 16 = 32.
Join the parts: hundreds with hundreds, tens with tens, ones with ones.
160 + 32 = 192
16 × 12: 160 and 32 joined.
14 × 13, ones part first
Split 13 into 10 and 3.
Build the ones part first: 14 × 3 = 42. Keep the beads.
Add the tens part on top: 14 × 10 = 140.
42 + 140 = 182
23 × 12, hundreds and tens
Split 12 into 10 and 2.
The ones part: 23 × 2 = 46. Keep the beads.
The tens part: 23 × 10 = 230.
46 + 230 = 276
21 × 14, an easy ones part
Split 14 into 10 and 4.
The ones part: 21 × 4 = 84.
The tens part: 21 × 10 = 210.
84 + 210 = 294
A taste of the worksheets
These are some of the questions on the sets. The printable sheets have more, with the bead frame drawn for each, and an answer key.
True or false? To find 12 × 23, you can find 10 × 23 and 2 × 23, then add the two parts.
Ben worked 12 × 15. He added 150 and 20 and got 170. What went wrong? Ten rows of 15 should be 105 / He should have taken the parts away / Two rows of 15 make 30, not 20
Ben multiplies a number by 13. Which split is easiest to build on the frame? ten and three / six and seven / five and eight
Stretch: build 21 × 14. Ten rows of 21 is 210 and four rows of 21 is 84. Together: ___
Which sum is too big for three rows of the frame? forty-five times twenty-five / fourteen times thirteen / twenty-two times thirteen
Words to know
split
Break a number into easy parts, like 12 into 10 and 2.
ones part
The part you build first, like 14 × 3.
tens part
The part you add on top, like ten rows of 14.
row of chairs
In the story, a line of the same number of chairs: twelve rows of sixteen.
Watch out for
Keep the beads. Do not clear the frame between the two parts.
Add place by place: hundreds with hundreds, tens with tens, ones with ones.
Ten is just a move up a row, so splitting 13 into 10 and 3 is easier than splitting it into 6 and 7.
Mind the ones part. Two rows of fifteen make thirty, not twenty.
Try it
What is 12 × 11?
132. Split 11 into 10 and 1: 10 × 12 = 120 and 1 × 12 = 12. Then 120 + 12 = 132.
Which split of 13 is easiest to build?
10 and 3. Ten is just a move up a row.
What is 13 × 12?
156. The ones part is 13 × 2 = 26, and the tens part is 13 × 10 = 130. Then 26 + 130 = 156.
What is 22 × 13?
286. The ones part is 22 × 3 = 66, and the tens part is 22 × 10 = 220. Then 66 + 220 = 286.
For grown-ups
Ask a grown-up to help you set out rows of cushions or books, like eleven rows of twelve. Count ten rows first, then the one row left, and add the two parts together.
Set out rows of cushions or books, like eleven rows of twelve. Count ten rows first, then the one row left, and join the two parts.
