Fours are double doubles
7 × 4 is double 7 doubled: 14, then 28.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Sam builds 5 tables. Each table needs 4 legs. How many legs in all?
legs
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Threes from twos
7 × 3 is 7 × 2 plus one more 7: 14 and 7 makes 21.
Dividing too
28 ÷ 4 asks what times 4 makes 28. Same facts, read the other way.
Step 2: Try It Yourself
Tap and try it out.
4 + 4 + 4 + 4 + 4 + 4 + 4 = 28
7 × 4 = 28
28 ÷ 7 = 428 ÷ 4 = 7
7 rows of 4 makes 28.
7 × 4 = 28. 7 and 4 are a factor pair of 28.
Pairs you have found
- 4 × 7
Step 3: In Real Life
In a workshop
A table needs 4 legs. For 3 tables, a carpenter orders 3 × 4 = 12 legs. A tricycle needs 3 wheels, a car needs 4. Counting in threes and fours is how a workshop orders its parts.
Step 4: Watch an Example
One step at a time.
Watch Ana Find 8 × 4
Ana is asked for 8 × 4.
- Step 1
Ana sees × 4. She thinks: double, then double again.
Watch Leo Find 9 × 3
Leo is asked for 9 × 3. Leo starts, and you finish.
- Step 1
Leo sees × 3. He thinks: double, then one more group.
Step 5: Your Turn
Practice makes it stick.
The Pencil Shop
Problem 1 of 12
A pencil costs $3. Maya buys 4 pencils. How much does she pay?
dollars
The Garden
Problem 2 of 12
A garden has 3 equal rows. There are 15 plants in all. How many plants in each row?
plants
Threes and Fours
Fours: double twice. Threes: double, then one more group.
Problem 3 of 12
3 × 3 = ?
Problem 4 of 12
4 × 4 = ?
Problem 5 of 12
Ana reads this array as 3 × 2 = 6. Which division says the same thing?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 12
Priya works out 9 × 4. One line is a slip. Which?
Priya's answer for 9 × 4
- 1Double 9 is 18
- 218 and 9 more is 27
- Answer9 × 4 = 27
Problem 7 of 12
What should Priya's answer be?
Problem 8 of 12
Dev works out 30 ÷ 3. One line is a slip. Which?
Dev's answer for 30 ÷ 3
- 130 ÷ 3
- 2Double 30 is 60, and 30 more is 90
- Answer30 ÷ 3 = 90
Problem 9 of 12
What should 30 ÷ 3 be?
Which Way?
Pick the way that fits × 3, × 4, or ÷.
Problem 10 of 12
Sam needs 6 × 3. Which way starts right?
Problem 11 of 12
Noor needs 12 ÷ 4. Which way starts right?
Build the Division
Build it, then check.
Problem 12 of 12
Build 24 ÷ 4 as an array: 4 rows, 24 in all.
1 × 1 = 1
1 ÷ 1 = 1
1 row of 1 makes 1.
Step 6: Quick Check
Show what you know.
Question 1 of 2
8 × 3 = ?
Question 2 of 2
What is multiplying by 4 the same as?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Noor doubles a number, then doubles it again. She gets 40. What was her number?
Stretch 2 of 2
Ana knows 5 × 4 = 20. She wants 5 × 3. Which way gives it?
What You Learned
- Fours are double doubles.
- Threes are twos plus one more group.
- Division uses the same facts backwards.
For the grown-up
This lesson is where the child recalls the 3 and 4 times tables, using doubling for the fours. Multiplication is equal groups before it is a fact to recall. Three fours is three groups of four, and division is the same picture asked from the other end.
Watch for multiplication and division being learned as separate subjects. They are one relationship, and a child who sees that halves what there is to remember.
When they are stuck on a division, ask the multiplication instead: "what times 4 gives 24?" Nearly every child can answer that when they cannot answer 24 divided by 4.
The slip this lesson targets is mixing its two moves: doubling only once for × 4, or adding one more group where a second double was needed. Priya's 9 × 4 = 27 is 9 × 3 in disguise. Have them say the moves aloud before they start — "double, double" for fours, "double, one more" for threes. The other slip is doing a multiplying move on a division: Dev's 30 ÷ 3 = 90 got bigger. Ask whether the answer should be bigger or smaller before any working, then turn the division into "3 times what makes 30?", which is the table they already own.
Building the 3s and 4s from the 2s — The 4 times table is the 2 times table doubled: 6 × 4 is 6 × 2 = 12, doubled to 24. The 3 times table is the 2s plus one more group: 6 × 3 is 6 × 2 = 12, plus 6, giving 18. Every new table can be reached from an older one.
Patterns to lean on — Every answer in the 4 times table is even, and every one is double an answer in the 2s. The 3s alternate odd and even: 3, 6, 9, 12, 15, 18. Their digits also add up in a repeating cycle — 1+2 for 12, 1+5 for 15, 1+8 for 18 gives 3, 6, 9 again.
From working out to knowing — Building a fact from a known one is a good bridge but not the destination. Facts you rebuild every time slow down every longer calculation later. Use the building strategies while you learn, and keep practicing until the answers simply arrive.
Build them from ones you know — × 4 is double, then double again. 6 × 4: 6 doubled is 12, doubled again is 24. × 3 is double it, then add one more group. 6 × 3: 12, plus 6, is 18. Check: 6 × 3 = 18 and 6 × 4 = 24. You never memorized these. You built them from × 2.