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Number Trail Grade 5 / Week 09 / Monday
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Week 09 · Fractions that resize

Monday

Bigger or smaller?
// Scaling, fraction stories and sharing with unit fractions
⏱ about 15 min

Monday: Bigger or smaller?

Rosie the Rabbit bounds up the trail with a long ribbon and a big grin.

"Bennie, my bean row is 12 feet long!" she says.

"I want a new row that is only 3/4 as long."

Bennie the Bear sets down his basket of stones.

"Before we multiply, let us make a smart guess," he says.

"Will 3/4 of 12 be more than 12, or less?"

Rosie wiggles her long ears. "Three fourths is less than one whole. So the new row must be shorter!"

"Exactly," says Bennie. "Multiplying by a fraction resizes a number. We call that scaling."

Learn it: compare the fraction with 1

Scaling means resizing a number by multiplying it.

Times a fraction less than 1, the product is smaller than the number.

Times a fraction greater than 1, the product is bigger than the number.

Times a fraction equal to 1, the product stays the same.

Bennie checks Rosie's guess. 3/4 × 12 means 3/4 of 12.

Split 12 into 4 equal parts: 12 ÷ 4 = 3.

Take 3 of those parts: 3 × 3 = 9.

So 3/4 × 12 = 9, and 9 is less than 12.

A number line from 0 to 12, with a dot at 9
BIGGER, SMALLER OR THE SAME?
  • Read the question.
  • Tap your answer.
Without multiplying: is 3/4 × 12 more than, less than or equal to 12?
Without multiplying: is 5/4 × 12 more than, less than or equal to 12?
Without multiplying: is 6/6 × 20 more than, less than or equal to 20?
Without multiplying: is 1 1/2 × 10 more than, less than or equal to 10?
Without multiplying: is 7/8 × 40 more than, less than or equal to 40?
FIND THE PRODUCT
  • Read the question.
  • Tap your answer.
3/4 × 12 = ?
2/3 × 18 = ?
5/6 × 24 = ?
3/5 × 20 = ?
ORDER THE PRODUCTS
  • Each product starts with 8.
  • Put them from least to greatest.
  • Compare each fraction with 1.
11st
22nd
33rd
44th
SentenceTrue or false?
2/3 × 15 < 15?
4/3 × 15 < 15?
5/5 × 15 = 15?
3/4 × 12 = 9?
WHY THIS EXERCISE4/3 is greater than 1, so 4/3 × 15 is more than 15.
Try it
Find a strip of paper or a piece of string.
Fold it into 4 equal parts.
Open it and pinch 3 of the parts together.
Is 3/4 of the strip shorter or longer than the whole strip?
On paper, draw a bar for 12. Split it into 4 equal parts and shade 3 of them.

Great scaling! Tomorrow Rosie stretches numbers with fractions greater than 1.