A child who can chant the times tables does not yet know what multiplication is. Four rows of three, drawn as an array, is what makes the fact mean something — and shows why it matches three rows of four.
Grade 3 · medium
Count the rows and the columns. Write the multiplication sentence and the total.
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Difficulty is a real change to the numbers or the layout, not a label.
Arrays up to 5 × 5.
Up to 8 × 8.
Up to 10 × 10.
Tap a grade you can use for a page of everything a child that age can practise here.
Four rows of six dots is 4 × 6. Turn your head and it is 6 × 4. That is how commutativity stops being a word and becomes something a child noticed for themselves. It is also visibly repeated addition, four sixes, which connects multiplication to the operation they already know.
That is a lot of conceptual work for a page of dots, and it is why arrays belong before drill.
Past about 6 × 8 the counting takes longer than the multiplication and the picture stops helping. Arrays are a bridge to the facts, not a substitute for knowing them, and by Grade 3 most of the time should be going into recall.
The grade ranges here reflect that: arrays are a Grade 2 to 3 tool, with the larger sizes available for a child who still wants the picture.
An array shows the structure: rows of equal groups. That is what makes 4 × 3 and 3 × 4 obviously the same total rather than two facts to memorise.
Grades 2 to 5. Grade 2 is held to arrays no larger than 5 × 5, which is the range it is taught.
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