Multiplication Array Grid
Build any multiplication as a rectangle of dots, then drag the split line to break a hard fact into two easy ones. This is the step most children are missing when they count 3, 6, 9, 12… all the way up instead of just knowing that 3 × 7 is 21.
Try splitting after 5 or after 10 — those are the columns most children already know by heart.
3 × 7 = 21
7 × 3 = 21
How to use this with your child
1. Let him build it first
Say “make me a 3 by 7 rectangle” and let him set the sliders himself. Do the same with Lego, coins or rajma on the table — hands first, screen second. The screen is for the splitting, which is hard to do with real objects.
2. Ask before you split
“You know 3 × 5. How many dots in the first five columns?” He says 15. Now split after column 5. “How many are left?” Six. “So how many altogether?” Let him say 21. He has just done the fact without counting from the start, and he did it himself.
3. Flip it
Swap the rows and columns and watch the total stay the same. Seven groups of three is the same amount as three groups of seven — so he only ever has to learn half the table.
4. Turn it into division
Ask “21 dots, 3 rows — how many in each row?” It is the same rectangle, read backwards. Say “three times what makes twenty-one?” instead of “twenty-one divided by three” and most of the difficulty disappears.
5. Hunt for the square numbers
Ask him to find every rectangle that is a perfect square — 2 × 2, 3 × 3, 4 × 4. Then ask him to make a rectangle with 25 dots that is not 5 × 5. He will discover it only makes 1 × 25. That is prime-ish structure, found with his own hands.
One thing not to do
Don’t say “no, don’t count” when he counts. Counting means he understands what multiplication is, which is the part that cannot be taught later. Say “yes, 21 — that’s right. Now, faster way?” and then split the grid. He keeps his method and gains a quicker one on top of it.
Common questions
My child counts 3, 6, 9, 12… to reach 3 × 7. Is that a problem?
No — it means he genuinely understands that multiplication is repeated groups, which is the harder half to teach. What is missing is a way into the middle of the table. Show him that 3 × 7 is 3 × 5 (which he knows) plus two more threes. Splitting the array on this page makes that visible instead of abstract.
What is an array in multiplication?
An array is objects arranged in equal rows and columns. Three rows of seven dots is 3 × 7. Because the whole rectangle can be counted by rows or by columns, an array also shows why 3 × 7 and 7 × 3 give the same answer.
How does splitting the grid help with times tables?
Splitting 3 × 7 after the fifth column leaves a 3 × 5 block (15) and a 3 × 2 block (6), and 15 + 6 = 21. A child who owns the 2, 5 and 10 tables can reach every other fact this way in one step, instead of counting up from the beginning each time.
What age is this multiplication grid for?
Roughly 6 to 10 years. Children of 6 or 7 use it to see what multiplication means; children of 8 to 10 use the split line to build faster recall of the harder facts like 6 × 7 and 7 × 8.