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Week 04 Β· Missing numbers

Wednesday

Turn around and group
// Unknowns, turn-arounds and break-aparts
⏱ about 15 min

Wednesday: Turn around and group

Samantha sets out acorns in an array: 4 rows of 6.

Then she spins around to look from the side.

"Now I see 6 rows of 4!" she squeaks.

"Did my acorns change?"

Bennie laughs kindly. "No, it is the same array."

"So 4 Γ— 6 and 6 Γ— 4 make the same product."

"That is a turn-around fact," says Samantha.

Learn it: turn-around facts

This grid shows 4 rows of 6. That is 4 Γ— 6 = 24.

A rectangle of unit squares, four rows of six

Turn it on its side. Now it shows 6 rows of 4. That is 6 Γ— 4 = 24.

A rectangle of unit squares, six rows of four

Changing the order of the factors does not change the product.

If you know 4 Γ— 6, you also know 6 Γ— 4.

Learn it: group the factors

Three factors can be grouped in either way.

Try 3 Γ— 5 Γ— 2.

First 3 Γ— 5 = 15. Then 15 Γ— 2 = 30.

Or first 5 Γ— 2 = 10. Then 3 Γ— 10 = 30.

Making a 10 first is often easier.

USE THE TURN-AROUND FACT
  • Read the question.
  • Tap your answer.
A rectangle of unit squares, six rows of four6 Γ— 4 = 4 Γ— ?
7 Γ— 3 = ? Γ— 7
9 Γ— 2 = 2 Γ— ?
8 Γ— 5 = 40. What is 5 Γ— 8?
GROUP THE FACTORS
  • Read the question.
  • Tap your answer.
3 Γ— 5 Γ— 2 = ?
2 Γ— 4 Γ— 5 = ?
5 Γ— 2 Γ— 7 = ?
Which way makes 2 Γ— 5 Γ— 9 easier?
WHICH IS THE SAME?
  • Read the question.
  • Tap your answer.
A rectangle of unit squares, three rows of eightWhich has the same product as 3 Γ— 8?
Which has the same product as 6 Γ— 7?
Which has the same product as (4 Γ— 2) Γ— 5?
SentenceTrue or false?
4 Γ— 6 = 6 Γ— 4?
3 Γ— 5 Γ— 2 = 3 Γ— 10?
7 Γ— 2 = 7 + 2?
2 Γ— 9 Γ— 5 = 9 Γ— 10?
WHY THIS EXERCISE7 Γ— 2 = 14, but 7 + 2 = 9.
Try it
Build an array of 2 rows of 5 with spoons or blocks.
Walk around to the side and look again.
Say the multiplication you see now.
Did the number of things change?
On paper, draw 3 rows of 5 dots. Then draw 5 rows of 3. Write both facts.

Terrific turning! Tomorrow Chris tells a break-apart story.

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