Unit 3: Multiplication
Multiplication as equal groups and as a rectangle's area, from times tables to multi-digit products.
7 topics · 29 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What Multiplication Really Means
- How it worksHow does multiplication add the same group over and over to get a total fast?
- Common mistakeWhy isn't 3 times 4 the same total as 3 plus 4?
- Worked exampleFind the total number of wheels on 6 cars if each car has 4 wheels.
- Going furtherWhat happens to the total if you multiply the same two numbers in the opposite order, like 4 times 6 instead of 6 times 4?
- Ties togetherHow does multiplying as repeated addition connect to the addition facts you already know?
Your turn1 of 2
A parking lot has 9 cars, and each car has 6 wheels. How many wheels are there in all?Arrays and the Area Model
- How it worksHow do you arrange 5 rows of 3 dots into an array to show 5 times 3?
- How it worksHow does an array of dots for 4 times 6 turn into a rectangle with the same area sitting right next to it?
- Worked exampleFind the total dots in an array with 7 rows and 8 columns.
- Common mistakeWhy isn't the area of a rectangle found by adding its length and width instead of multiplying them?
Your turn1 of 2
An art project glues buttons onto a grid with 9 rows and 8 columns. How many buttons are there in total?Times Tables as Patterns
- How it worksHow does skip counting by 5s build the entire 5 times table on a number line?
- Worked exampleFind the next three numbers in the pattern 6, 12, 18, 24 from the 6 times table.
- Ties togetherHow does skip counting connect to the repeated addition behind multiplication?
Your turn1 of 2
Nina is filling in a chart with the 9 times table. What is the 5th multiple of 9 -- that is, 9 times 5?The Distributive Property of Multiplication
- How it worksHow do you split 7 times 12 into 7 times 10 plus 7 times 2 and add the pieces back together?
- Common mistakeWhy isn't 6 times 14 solved by multiplying 6 times 1 and 6 times 4 separately?
- Common mistakeWhy doesn't splitting 8 times 23 into 8 times 20 and 8 times 3 mean you can skip adding the two results?
- Worked exampleFind the product of 9 and 15 by splitting 15 into 10 plus 5.
- Going furtherWhat happens if you split the first number instead of the second when multiplying 23 by 6?
Your turn1 of 2
A classroom has 7 shelves with 16 books on each shelf. How many books are there in total?Multiplying by Multiples of Ten and a Hundred
- How it worksHow do you multiply 7 by 30 by first multiplying 7 by 3 and then adding a zero?
- Worked exampleFind the product of 8 and 400.
- Common mistakeWhy isn't 5 times 20 found by just multiplying 5 times 2 without changing anything else?
- Going furtherWhat happens when you multiply a number by 100 instead of by 10?
Your turn1 of 2
A warehouse has 7 boxes, each holding 6 hundred paperclips. How many paperclips are there altogether?Multiplying a Multi-Digit Number by a One-Digit Number
- How it worksHow do you multiply 3 by each digit of 246 and carry the extra tens as you go?
- Worked exampleFind the product of 328 and 4.
- Common mistakeWhy isn't 7 times 58 equal to 356 if you forget to add the carried ten to the tens digit?
Your turn1 of 2
A factory packs 658 pencils into each box and fills 7 boxes. How many pencils does it pack in all?Multiplying Two Multi-Digit Numbers
- How it worksHow do you multiply 23 by 14 by breaking 14 into 10 and 4 and adding two partial products?
- How it worksHow do you line up the partial products with a placeholder zero when multiplying 34 by 26?
- Worked exampleFind the product of 47 and 32.
- Common mistakeWhy isn't 12 times 15 found by multiplying 1 times 1 and 2 times 5 separately?
- Going furtherWhat happens to the number of partial products you need when you multiply a two-digit number by a three-digit number?
Your turn1 of 2
A farm has 67 rows of corn with 63 plants in each row. How many corn plants are there altogether?