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Number Trail Grade 4 / Week 08 / Monday
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Week 08 · Add and subtract fractions

Monday

Fractions are made of unit fractions
// Join and take away parts of the same whole
⏱ about 15 min

Monday: Fractions are made of unit fractions

Donnie the Deer walks softly along the meadow path with his satchel.

He stops beside a fence made of 8 equal boards.

"I have painted 5 of the 8 boards," he says slowly.

"Yesterday I painted 2 boards. Today I painted 3 more."

Bennie the Bear counts the painted boards one at a time.

"One eighth, two eighths, three eighths, four eighths, five eighths."

"So 5/8 is five 1/8s," Bennie says. "And 2/8 + 3/8 makes 5/8."

Donnie smiles. "One fraction, many ways to build it."

Learn it: unit fractions

A bar cut into eight equal parts, five shaded

A unit fraction has 1 as its numerator, like 1/8.

5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8.

We can also group the parts: 5/8 = 2/8 + 3/8, or 5/8 = 1/8 + 4/8.

Breaking a fraction into parts is called decomposing.

HOW MANY UNIT FRACTIONS?
  • Read the question.
  • Tap your answer.
How many 1/8s make 5/8?
How many 1/5s make 3/5?
How many 1/12s make 7/12?
1/6 + 1/6 + 1/6 + 1/6 = ?
DECOMPOSE THE FRACTION
  • Read the question.
  • Tap your answer.
? + 3/8 = 5/8
4/6 = 1/6 + ?
7/10 = 2/10 + 2/10 + ?
? + 1/4 = 4/4
WHICH SUM EQUALS THE FRACTION?
  • Read the question.
  • Tap your answer.
A bar cut into eight equal parts, five shadedWhich one equals 5/8?
A bar cut into four equal parts, three shadedWhich one equals 3/4?
Which one equals 6/10?
Which one equals 4/5?

Learn it: a whole is a fraction too

8/8 is one whole. So is 4/4, and so is 10/10.

A mixed number like 1 3/8 is 1 whole and 3/8 more.

1 3/8 = 8/8 + 3/8 = 11/8.

A number line from 0 to 2 in eighths, with a dot at 11/8
SentenceTrue or false?
1/8 + 1/8 + 1/8 = 3/8?
2/8 + 3/8 = 5/8?
1/4 + 2/4 = 3/8?
1 3/8 = 11/8?
WHY THIS EXERCISE1/4 + 2/4 is 3/4. The parts are still fourths.
ORDER THE FRACTIONS
  • Count the eighths in each one.
  • Put them from least to greatest.
11st
22nd
33rd
44th
Try it
Line up 8 spoons, socks or blocks in a row.
Turn 5 of them a different way. That shows 5/8.
Split the turned ones into two groups. Write the sum you made.
Find a different way to split them.
Draw a bar for 7/10. Color it in two colors to show a sum.

Beautifully built! Tomorrow we add and subtract fractions.