Tuesday
Tuesday: Layers of cubes
Hazel the Hedgehog builds a tall box of cubes on her desk.
"Counting every cube one at a time takes so long," she sighs.
Bennie the Bear points to the bottom of her box.
"Look at the first layer," he says. "It has 4 rows of 3 cubes."
Hazel counts carefully. "That is 12 cubes in one layer."
"And how many layers are there?" asks Bennie.
"Two," says Hazel. "So 12 + 12 = 24. Or 12 × 2 = 24!"
Bennie nods. "Length times width gives one layer. Times the height gives the volume."
Learn it: base layer times layers
The bottom layer covers the base. It holds 4 × 3 = 12 cubes.
There are 2 layers, so the box holds 12 × 2 = 24 cubes.
Volume = length × width × height.
So 4 × 3 × 2 = 24 cubic units.
- Read the question.
- Tap your answer.
How many unit cubes make this box?
How many unit cubes make this box?- Read the question.
- Tap your answer.
Learn it: group the factors any way
(4 × 3) × 2 means the base layer first, then the layers.
4 × (3 × 2) means a side face first: 3 × 2 = 6 cubes.
Then it takes 4 of those slices.
Both give 24. We can multiply the factors in any order.
| Sentence | True or false? |
|---|---|
| (4 × 3) × 2 = 4 × (3 × 2) | ? |
| 5 × 2 × 3 = 25 | ? |
| (2 × 5) × 6 = 60 | ? |
| 3 × 3 × 3 = 9 | ? |
- Think about how Hazel found 24.
- Tap the steps in order.
How many blocks are in the layer?
Stack 3 more layers just like it on top.
Find the volume by multiplying, then count to check.
You found volume with layers! Tomorrow we use the formula with bigger boxes.