Math · Rung 5 of 7
Multiplication as equal groups: seeing 4 × 3 as four groups of three, and building the times tables from facts your child already knows.
Where this sits
Multiplication is a shortcut for adding equal groups. It shows up as groups (3 bags of 4 apples), as arrays (rows and columns, like an egg carton) and as skip counting. Understanding comes before memorizing: a child who sees 6 × 7 as 6 × 5 and 6 × 2 more can rebuild any fact they forget.
The goal is the facts up to 10 × 10, and knowing when a problem needs adding, subtracting or multiplying.
These come from the Place value rung.
Each step builds on the one before. Most children spend weeks on some steps and days on others.
Make groups with the same number in each, then find the total.
3 plates, 4 cookies each → 12 cookies
Count by 2s, 5s and 10s, then by 3s and 4s.
5, 10, 15, 20 …
Rows and columns. Turn the array to see that 3 × 4 is the same as 4 × 3.
An egg carton is 2 rows of 6
× 2 is doubling, × 10 is easy, × 5 is half of × 10, × 1 changes nothing, × 0 is zero.
7 × 5 is half of 70 → 35
Split a hard fact into two easy ones.
6 × 7 = 6 × 5 + 6 × 2 = 30 + 12 = 42
Choose whether to add, subtract or multiply.
"5 boxes of 6 crayons. How many crayons?"
Change the rows and the number in each row. Tap "Turn it" to see the same counters the other way round.
You need: Plates, crackers or grapes
Set out plates and put the same number on each. How many altogether? Write it as an addition sentence and as a multiplication sentence.
“Four plates, three crackers on each. How many crackers is that?”
You need: An egg carton, a muffin tin, small things to fill them
Fill each cup. Count the rows and the number in each row, then the total. Turn the tin round and count again.
“How many rows? How many in each row? How many altogether?”
You need: Nothing
Ask quick questions about equal groups: legs on 5 dogs, wheels on 4 bikes, legs on 3 spiders.
“Each spider has 8 legs. How many legs on three spiders?”
You need: Sidewalk chalk
Chalk a line of squares numbered 5, 10, 15 … 50. Jump along saying each number. Try 2s, 3s and 10s on other lines.
“Jump by fives all the way to 50.”
You need: A walk, or a look around the house
Find things in rows and columns: window panes, tiles, garden rows, cars in a parking lot. Say each one as a multiplication sentence.
“That window has 3 rows of 4 panes. How many panes?”
You need: A deck of cards with the face cards taken out (ace counts as 1)
Each player turns over two cards and multiplies them. The bigger answer takes all four cards.
“7 and 6. What's the quickest way to work that out?”
You need: Two dice, graph paper, pencil crayons
Roll two dice and draw that array on the graph paper, writing the multiplication sentence inside it. Keep going until someone can't fit an array. Whoever covered the most squares wins.
“You rolled 4 and 3. Draw 4 rows of 3.”
Build it as groups. "3 groups of 4" says what × means.
Ask them to draw or build a fact. If they can't, go back to equal groups.
Turn an array round. It's the same counters.
"Three plates with nothing on them" is zero cookies.
Build them from anchors: 7 × 8 = 7 × 5 + 7 × 3 = 35 + 21 = 56. Keep a chart of the facts they already know.
Tick them off as you see them. Saved on this device only.