Start here: this is not a weakness.
Counting up to reach 3 × 7 means your child understands what multiplication is — that it is groups, added up. Most children who can recite tables fluently cannot do that; they have memorised sounds without meaning. Your child has meaning without speed. That is by far the better problem to have, because meaning cannot be installed later, and speed can.
The step he is missing
There are three stages between not knowing a fact and knowing it cold, and almost everybody tries to skip the middle one.
- 1. Counting. 3 × 7 means seven threes, so count them all. This is where he is now.
- 2. Deriving. 3 × 7 = 3 × 5 (15) + 3 × 2 (6) = 21. This is the missing step, and the whole plan.
- 3. Recall. 3 × 7 = 21, instantly, without thinking.
Drilling tables tries to jump him from 1 straight to 3. It fails, and then he falls back on counting — because under pressure, the method that reliably works is the one you use. Stage 2 is the bridge. Build it and stage 3 arrives on its own, because by then he has met every fact dozens of times through the back door.
Four anchors, not 144 facts
The times tables look like 144 separate things to memorise. They are not. If he owns four anchors — × 1, × 2, × 5 and × 10 — every other fact is one move away. And he almost certainly owns them already: × 10 is obvious, × 5 is the clock face, × 2 is doubling, × 1 is free.
| To get | Use the anchor | Example |
|---|---|---|
| × 4 | double the × 2 | 4 × 7 = double 14 = 28 |
| × 8 | double the × 4 | 8 × 7 = double 28 = 56 |
| × 3 | × 2, then one more group | 3 × 7 = 14 + 7 = 21 |
| × 6 | × 5, then one more group | 6 × 7 = 35 + 7 = 42 |
| × 9 | × 10, take one group away | 9 × 7 = 70 − 7 = 63 |
| × 7 | × 5 plus × 2 | 7 × 7 = 35 + 14 = 49 |
The one question to ask
When he starts counting up, interrupt with the same question every time: “You know 3 × 5. What is it?”He says 15. “So how many more threes do you need?” Two. “So?” 21.
That is the whole intervention, repeated for weeks. You are not teaching him answers. You are teaching him to jump into the middle of the table instead of starting at the beginning.
See the jump, don't just describe it
Our multiplication grid draws any fact as a rectangle of dots, then splits it where you choose — so 3 × 7 visibly becomes a 3 × 5 block and a 3 × 2 block, with the arithmetic underneath. Set it to his hardest fact and let him watch it come apart.
Open the Multiplication Grid →The one change that makes division click
Division trouble is nearly always this: it gets taught as its own topic, when it is really multiplication asked backwards. Fix the wording and most of the difficulty goes with it.
Stop saying “twelve divided by three.”
Start saying “three times what makes twelve?”
Every division question becomes a multiplication question with a hole in it, pointing straight at knowledge he already has. Teach the facts in families of four and one picture does four jobs:
The eight-week plan
Ten to fifteen minutes a day, six days a week. Not more. Short and daily beats long and weekly for anything that must become automatic — and it protects the thing that matters most, which is that he does not come to dread sitting down with you.
Make the four anchors solid
Only the 1, 2, 5 and 10 tables. Doubling practice everywhere — double 6, double 13, double 25. The 5 table read off a clock face. Do not move on until these come out without counting: everything else is built on top of them.
Move on when: He answers 5 × 7 and 2 × 8 straight away, without a pause to work it out.
Teach the jump
Now the derived tables. 4 is double the 2. 8 is double the 4. 3 is the 2 plus one more group. 6 is the 5 plus one more. 9 is the 10 take one away. Every single time, he says out loud how he got there — the reasoning is the skill, the answer is a by-product.
Move on when: He says "six sevens… thirty-five plus seven, forty-two" instead of counting from 6.
Division as the mirror
Nothing new in multiplication. Every fact he owns gets flipped into its family of four: 3 × 4, 4 × 3, 12 ÷ 3, 12 ÷ 4. Bowls and almonds first, symbols after. Remainders come in here, and real life explains them best.
Move on when: Asked for 42 ÷ 6, he reaches for "six times what makes forty-two" rather than freezing.
The hard corners, and speed
By now only a handful are genuinely unmemorised — usually 6 × 7, 7 × 8, 8 × 6 and 7 × 7. Attack those one at a time with a rhyme or a story. Only now start timing him, gently, and only ever against his own last score.
Move on when: Most of the table comes back inside two seconds, and he is not anxious about being asked.
Four things not to do
Don't say “stop counting”
Say “yes, 21 — that's right. Now, faster way?” If he feels his method is being taken away, he will hide it and guess instead. Guessing is a real weakness; counting is not.
Don't ban fingers
Fingers are a tool. They disappear on their own once recall is quicker. Banning them removes the safety net and adds fear.
Don't compare him to anyone
Especially a cousin or a classmate. Nothing shuts down a struggling maths learner faster than being measured against another child.
Don't push harder on a bad day
If a session goes wrong, end it early and cheerfully. Tomorrow is another ten minutes. Eight straight weeks only happens if it stays pleasant.
If the anchors won't stick
If after several weeks of daily practice even the × 2 and × 5 tables stay effortful, mention it to his teacher rather than pushing harder. Persistent difficulty with number facts alongside otherwise sharp reasoning is a specific, recognised thing, and identifying it early helps a great deal. For most children this is not the case — but effort is not the only variable, and it is worth knowing.