L5 · Arrays for products and quotients; division as repeated subtraction

Learning goal

“I can use an array to show a product and its quotients. I can divide by subtracting the same number over and over - and count the subtractions.”

Array — objects arranged in rows and columns, like tiles on a floor. An array shows multiplication at a glance.

Row — a line of objects going across the array. The number of rows is one factor.

Column — a line of objects going down the array. The numbers in each row make the other factor.

Repeated subtraction — taking away the same amount again and again until nothing is left. The number of take-aways is the quotient.

Worked example

An array has 4 rows with 6 tiles in each row. Step 1 (product): rows x in-each = 4 x 6 = 24 tiles. Step 2 (turn it): the same array is 6 columns of 4 - 6 x 4 = 24 (L3's commutative property, visible). Step 3 (quotients live here too): 24 tiles in rows of 6 -> how many rows? 24 / 6 = 4. And 24 / 4 = 6. One array holds a whole family: two products and two quotients, all built from 4, 6 and 24.

Check yourself — explain it

One array can show both 24 / 6 and 24 / 4 because...

Paired problem — example still visible

An array of 5 rows of 7: 5 x 7 = 35 (and 35 / 5 = 7, 35 / 7 = 5)

Faded completion — last step is yours

"An array of 3 rows of 9: 3 x 9 = ___ and 27 / 3 = ___" -> 27; 9

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