4 × 26 on the frame: one hundred, no tens and four ones, after two trades.
The big ideaMultiply the ones, trade up, then multiply the tens.
How it works
Multiply one row at a time, and start with the ones.
A row holds only ten beads, so when a row is too full, trade ten of them up for one bead on the next row.
Then multiply the tens and add the tens that traded up. A full tens row trades up for a hundred.
The plan for every sum.After the ones of 4 × 26: 24 ones traded to 2 tens and 4 ones.
Example 1: 3 × 14, one trade
Start with the ones: 3 × 4 = 12 ones.
A row holds ten, so trade ten ones up for one ten. Two ones stay.
Now the tens: 3 × 1 = 3 tens, and the traded ten makes 4 tens.
4 tens and 2 ones: 3 × 14 = 42
3 × 14: four tens and two ones.
Example 2: 5 × 18, the ones row empties
The ones: 5 × 8 = 40 ones.
Forty ones trade up for 4 tens. No ones stay, so the ones row is empty.
The tens: 5 × 1 = 5 tens, and the 4 traded tens make 9 tens.
9 tens and no ones: 5 × 18 = 90
5 × 18: nine tens and an empty ones row.
Example 3: 4 × 26, two trades
The ones: 4 × 6 = 24 ones.
Trade two tens up and keep 4 ones.
The tens: 4 × 2 = 8 tens, and the 2 traded tens make 10 tens.
The tens row is full: ten tens trade up for one hundred.
One hundred, no tens and 4 ones: 4 × 26 = 104
4 × 26: a bead on the hundreds row, none on the tens, four ones.
Example 4: 6 × 47, a bigger one
The ones: 6 × 7 = 42 ones.
Trade four tens up and keep 2 ones.
The tens: 6 × 4 = 24 tens, and the 4 traded tens make 28 tens.
Twenty tens trade up for 2 hundreds, and 8 tens stay.
2 hundreds, 8 tens and 2 ones: 6 × 47 = 282
6 × 47: two hundreds, eight tens and two ones.
Words to know
trade
Ten beads on one row become one bead on the next row up.
ones row
The bottom row. Each bead is worth one.
tens row
The middle row. Each bead is worth ten.
hundreds row
The top row of a three-row frame. Each bead is worth one hundred.
Watch out
A row holds a digit. Twenty-four ones is never 24 beads on the ones row: it is 2 tens and 4 ones.
Start with the ones, so every trade climbs up the frame.
Do not forget the tens that traded up. Three times fourteen is forty-two, not thirty-two.
When the tens row is full with ten tens, it trades up for a hundred.
Try it
What is 4 × 12?
What is 5 × 14?
What is 3 × 38?
Thirty-two ones are on the ones row. What do you do?
Answers: 1. 48 · 2. 70 · 3. 114 · 4. trade up three tens and keep two ones
Try at homeAsk a grown-up to help you set out equal groups, like four plates with fourteen grapes on each. Multiply the ones, trade up, then multiply the tens. Count the grapes one by one to check.
For grown-upsLet your child say each trade out loud as they slide the beads: "twenty-four ones, so two tens and four ones". Check an answer by counting equal groups of real things, like four plates of fourteen grapes.
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