Learning the Times Tables, One Step at a Time

Fewer facts than it looks

A times-table chart from $2 \times 2$ to $9 \times 9$ has 64 boxes, but many of them are the same fact twice: $3 \times 7$ and $7 \times 3$ are both 21. Once a student knows that the order does not matter, there are only 36 different facts to learn. Facts with 0 and 1 follow simple rules (any number times 1 stays the same, any number times 0 is 0), so they are explained once rather than practised as a table.

The Multiplication worksheets work the same way: one-digit problems start at 2, and the larger number is always written first, so a page shows $9 \times 2$ but never $2 \times 9$. It is worth saying the facts both ways out loud now and then, so that $2 \times 9$ is just as quick.

How the settings choose the facts

On the Multiplication page, the sidebar has two numbers, each with Digits, Min Value and Max Value. Every whole number from Min Value to Max Value is equally likely. For times-table practice:

• Set Number 1 to 1 digit. Min Value 2 and Max Value 9 then cover the whole table.
• Use Number 2 to choose the tables, also with 1 digit. Set Min Value and Max Value to the same number for a single table: Min 7 and Max 7 makes a page of only the 7s. A range mixes several tables: Min 2 and Max 5 mixes the 2s, 3s, 4s and 5s.
• Change Digits first, because changing Digits resets Min Value and Max Value to the full range for that many digits. Then press Generate.

A single table has only 8 facts, from $2 \times 7$ to $9 \times 7$, so a 20-problem page repeats some of them. At this stage that repetition is useful.

A practice order

This order starts with the tables that have a clear pattern and uses each one to learn the next. Each step is one table on its own page, followed by a mixed page once a group of tables is done.

1. The 2s, 5s and 10s. Number 2 at Min 2, Max 2 for the 2s (doubling), then Min 5, Max 5 for the 5s. For the 10s, set Number 2 to 2 digits with Min 10 and Max 10. The 5s are half of the 10s: $5 \times 8$ is half of 80, which is 40.
2. The 4s. Min 4, Max 4. The 4s are double the 2s: $4 \times 7$ is double 14, which is 28.
3. The 3s, then a review. Min 3, Max 3. Once the 3s are steady, Min 2 and Max 5 mixes every table so far on one page.
4. The 6s and 9s. Min 6, Max 6: the 6s are double the 3s. Then Min 9, Max 9: the 9s are one group less than the 10s, so $9 \times 7 = 70 - 7 = 63$.
5. The 7s and 8s. Min 7, Max 7, then Min 8, Max 8. By now most of these are already known from other tables: $7 \times 6$ is in the 6s and $8 \times 9$ in the 9s. Only three facts are new: $7 \times 7 = 49$, $7 \times 8 = 56$ and $8 \times 8 = 64$.
6. All facts, mixed. Min 2 and Max 9 is the full set of 36 facts, the page to keep coming back to. For the hardest corner, set both numbers to Min 6 and Max 9: that page has only the 10 facts from $6 \times 6$ to $9 \times 9$.
7. Optional: the 11s and 12s. If your school expects facts up to $12 \times 12$, set Number 2 to 2 digits with Min 11 and Max 12, or Min 12 and Max 12 for the 12s alone.

When to move on

• Accuracy first. Stay on a setting until a page comes back almost entirely correct.
• Then speed. A fact is learned when it is recalled, not worked out. Writing the time taken at the top of each page shows progress clearly, and a page that gets faster over a few days is ready for the next step.
• Step back without fuss. If a new table brings back mistakes in the old ones, spend a few days on a mixed page of the earlier tables. Changing Min and Max Value takes a second.
• Watch the usual mix-ups. $7 \times 8 = 56$ and $6 \times 9 = 54$ are the pair most often confused; the Multiplication page lists more common mistakes.

After the times tables

Once the facts are automatic, the same page moves on to written multiplication. Set Number 1 to 2 digits and Number 2 to 1 digit for problems with carrying, such as $34 \times 6$, and then two multi-digit numbers for long multiplication. The facts carry straight through: every step of $215 \times 23$ is a times-table fact plus a little addition. They also carry into division and, later, fractions, where finding common denominators is times-table work. The grade-by-grade practice roadmap shows where multiplication fits in the bigger picture.