The tables from ten to twenty

You already know the tables up to nine. Now pic­ture a shop with boxes of $12$ eggs, pack­ets of $15$ bis­cuits and trays of $18$ lad­doos. To count five boxes or seven pack­ets quickly, you need the tables from ten to twenty. This les­son builds each of them from things you already know: adding, tens, and the small tables.

The num­bers are big­ger, but noth­ing new has to be learned. A two-digit num­ber splits into tens and units — $13 = 10 + 3$ — and so does the mul­ti­pli­ca­tion.

13, five times over

$$\begin{aligned}&13 + 13 + 13 + 13 + 13 \\ &= (10 + 10 + 10 + 10 + 10) + (3 + 3 + 3 + 3 + 3) \\ &= 50 + 15 \\ &= 65\end{aligned}$$

Five tens are fifty, and five threes are fif­teen, which you know from the three times table. So the only dif­fi­cult part of the thir­teen times table is a table you learned two lessons ago.

Remem­ber. Split the two-digit num­ber. Ten of any­thing is easy, and the units are a small table you already know.

See it as rows of coun­ters

Put out five rows of coun­ters with $13$ coun­ters in each row. That is $13 \times 5$. Now colour the first ten coun­ters of every row blue and the last three orange.

Count the blue coun­ters: five rows of ten is fifty. Count the orange coun­ters: five rows of three is fif­teen. Put them together and you have sixty-five. You did not have to count all sixty-five one by one.

Every table in this les­son works the same way. The num­ber splits into ten and a small part. The ten part is easy. The small part is a table you learned before. Then you add the two parts.

The ten times table

Start with the eas­i­est of all. Ten of any­thing is the num­ber with a zero after it.

The eleven times table

Eleven is ten and one, so each answer is a lot of tens with the same num­ber of ones along­side.

Look down the answers of the eleven times table up to $11 \times 9$. The tens digit and the units digit are always the same: $22$, $33$, $44$ and so on. That pat­tern is a quick check. It stops at $11 \times 10 = 110$, where the ten tens make a hun­dred.

From the twelve times table onwards, the units part can grow past ten. Look at $12 \times 6$. The units part is $2 \times 6 = 12$, which is more than ten. So you add $60 + 12$, and the answer is $72$. The tables below show every such step in the third col­umn.

The twelve times table

The thir­teen times table

The four­teen times table

The fif­teen times table

The six­teen times table

The sev­en­teen times table

Here is the sev­en­teen times table drawn as a rec­tan­gle. The long side is $17$, split into $10$ and $7$. The short side is $4$.

17 times 8

$$\begin{aligned}17 \times 8 &= (10 \times 8) + (7 \times 8) \\ &= 80 + 56 \\ &= 136\end{aligned}$$

Eight tens are eighty. Eight sev­ens are fifty-six. Eighty and fifty-six make one hun­dred and thirty-six.

The eigh­teen times table

The nine­teen times table

The twenty times table

Twenty is two tens, so this is the two times table with a zero on the end.

Two more ways to check

Split and add

14 times 6

$$\begin{aligned}14 \times 6 &= (10 \times 6) + (4 \times 6) \\ &= 60 + 24 \\ &= 84\end{aligned}$$

Go up to twenty, then come back

Nine­teen is one less than twenty. So nine­teen lots of any­thing is twenty lots, take away one lot.

19 times 7

$$\begin{aligned}19 \times 7 &= (20 \times 7) - 7 \\ &= 140 - 7 \\ &= 133\end{aligned}$$

This matches $19 \times 7 = 133$ in the nine­teen times table. Two dif­fer­ent roads, one answer: that is a good sign your answer is right.

Dou­ble a table you know

Six­teen is dou­ble eight. So six­teen lots of four is dou­ble eight lots of four.

$$\begin{aligned}16 \times 4 &= 2 \times (8 \times 4) \\ &= 2 \times 32 \\ &= 64\end{aligned}$$

Pat­terns to notice

• Every answer in the ten and twenty tables ends in $0$.
• Every answer in the fif­teen table ends in $5$ or $0$.
• Answers in the twelve, four­teen, six­teen and eigh­teen tables are always even.
• Each answer in a table is the one above it plus the table num­ber. In the thir­teen table, $39 + 13 = 52$.

How to prac­tise

Take one table a day. First say it aloud while read­ing the table above. Then cover the answers and say it again, split­ting each fact into its ten part and its small part. Last of all, ask a friend or some­one at home to call out facts in a mixed-up order. When you can answer each one with­out count­ing, that table is yours, and you can move on to the next one tomor­row.

Your turn

Work each one out by split­ting it, then check it against the table above.

Com­mon mis­takes

• For­get­ting to add the ten part. $13 \times 5$ is not $15$; the fifty from the tens must be added.
• Adding the units part wrongly when it goes past ten. In $16 \times 7$ the parts are $70$ and $42$, so the answer is $112$, not $712$.
• Mix­ing up the tables. Say the table name out loud before you start: "four­teen, six times".
• In the go-up-to-twenty short­cut, tak­ing away the wrong amount. $19 \times 7$ is $140 - 7$, not $140 - 1$.

Key terms

Times table

A list of a num­ber mul­ti­plied by $1, 2, 3$ and on up to $10$.

Mul­ti­ply

Add the same num­ber again and again. $13 \times 5$ means five thir­teens added together.

Tens and units

The two parts of a two-digit num­ber. $13$ is one ten and three units.

Split

Break a num­ber into easy parts, such as $17 = 10 + 7$.

Array

Objects set out in equal rows, used to pic­ture a mul­ti­pli­ca­tion.

Dou­ble

Mul­ti­ply by two.

Answers

1. $12 \times 4 = 40 + 8 = 48$
2. $13 \times 6 = 60 + 18 = 78$
3. $14 \times 3 = 30 + 12 = 42$
4. $15 \times 7 = 70 + 35 = 105$
5. $16 \times 5 = 50 + 30 = 80$
6. $17 \times 4 = 40 + 28 = 68$
7. $18 \times 6 = 60 + 48 = 108$
8. $19 \times 3 = 30 + 27 = 57$
9. $11 \times 8 = 80 + 8 = 88$
10. $12 \times 9 = 90 + 18 = 108$
11. $13 \times 7 = 70 + 21 = 91$
12. $20 \times 6 = 60 + 60 = 120$