L1-01 · Fractions describe part of a whole
A fraction compares a part with the whole. The top number counts the part. The bottom number counts all the equal parts in the whole. Different fractions can name the same amount.
Level 1 · Grades 4–6 · about 40 minutes
Big idea. A fraction compares a part with the whole. The top number counts the part. The bottom number counts all the equal parts in the whole. Different fractions can name the same amount.
Before this lesson. L0-01, L0-05
Grown-ups. The guide for adults is at the end of this page.
What you will learn¶
I can write a fraction for part of a strip or part of a group.
I can show that one half, two fourths, and four eighths are the same amount.
I can say what the whole is before I write a fraction.
Story: Sharing a strip and a bag of marbles¶
Maya and Leo have one long strip of paper. They fold it in half and color one part. One part is colored, and there are 2 equal parts in all. That is 1 out of 2, or one half.
Leo folds the strip in half again. Now there are 4 equal parts, and 2 of them are colored. That is 2 out of 4. Maya folds it once more. Now there are 8 equal parts, and 4 are colored: 4 out of 8. “The colored part never changed,” says Leo. “We only cut it into smaller pieces.” So 1 out of 2, 2 out of 4, and 4 out of 8 are the same amount.
Next they open a bag of 12 marbles. 3 of the marbles are green. Leo writes 3 out of 12 as a fraction: 3/12. The numerator, 3, counts the green marbles. The denominator, 12, counts all the marbles.
Maya puts the marbles into 4 equal groups of 3. She puts the 3 green marbles together in one group. Now 1 out of 4 groups is green. So 3 out of 12 is the same as 1 out of 4.
“What if the bag had only 6 marbles, with 3 green?” asks Leo. Then 3 out of 6 would be green, which is one half. The part is the same, but the whole is smaller. That is why you always say what the whole is.
The same shaded amount, cut into 2, 4, and 8 equal parts, and then 12 marbles sorted into 4 equal groups.
What the animation shows. A bar is cut into 2 equal parts, and 1 part is shaded: 1 out of 2. New cut lines make 4 parts, then 8, and the shaded amount stays 2 out of 4, then 4 out of 8. Next, 12 marbles appear, and 3 are green: 3 out of 12. They move into 4 groups of 3, and the green ones make 1 out of 4 groups.
Hands-on: Fold, shade, and group¶
About 20 minutes.
You need:
Three strips of paper, all the same length
Colored pencils or crayons
A ruler
12 counters, beans, or buttons, with 3 of one color
Steps:
Fold the first strip in half. Open it and shade one part, starting from the left end. Write 1/2 on it.
Fold the second strip in half, then in half again. Open it. Shade 2 parts next to each other from the left end. Write 2/4.
Fold the third strip in half three times. Open it. Shade 4 parts next to each other from the left end. Write 4/8.
Line up the three strips, one under the other. Use the ruler to check that the shaded parts are the same length.
Put out the 12 counters. Write a fraction for the 3 counters of the other color.
Sort the counters into 4 equal groups of 3. Put the 3 counters of the other color together in one group. Write the new fraction for the groups.
Write two fractions that name the same amount, like 3/12 and 1/4.
Practice together¶
A tray has 10 pieces of fruit. 2 are pears and the rest are apples. What fraction of the fruit is pears? What fraction is apples?
Check your answer
The whole is all 10 pieces of fruit. Pears are 2 out of 10, or 2/10. Apples are the other 8, so they are 8 out of 10, or 8/10. Together, the two parts make the whole tray.
Try it yourself¶
1. A box has 6 red blocks and 9 blue blocks. What fraction of the blocks are red?
Check your answer
There are 15 blocks in all. The red blocks are 6 out of 15, or 6/15. The bottom number counts all the blocks, not just the blue ones.
2. Leo shades 3 parts of a strip folded into 4 equal parts. Maya shades 6 parts of a strip folded into 8 equal parts. Did they shade the same amount?
Check your answer
Yes. Leo shaded 3/4 of his strip. Maya shaded 6/8. Each of Leo’s parts is the same as two of Maya’s parts, so 3/4 and 6/8 are the same amount.
Talk about it¶
Why must the parts be equal before you can name a fraction?
Is 3 green marbles a lot or a little? What do you need to know to decide?
Where do you see fractions at home or at school?
Check yourself¶
1. A class has 20 students, and 5 of them are left-handed. What fraction of the class is left-handed?
A. 20/5
B. 5/20
C. 5/15
Show the answer
B. 5/20
The whole class has 20 students, and the part is the 5 who are left-handed. So the fraction is 5 out of 20, or 5/20.
2. Which fraction is the same amount as one half?
A. 4/8
B. 1/4
C. 2/8
Show the answer
A. 4/8
A strip folded into 8 equal parts with 4 shaded is half shaded. So 4/8 is the same amount as one half.
3. In a fraction, what does the denominator count?
A. The part you are looking at
B. The parts that are left over
C. All the equal parts in the whole
Show the answer
C. All the equal parts in the whole
The denominator is the bottom number. It counts all the equal parts in the whole. The numerator, on top, counts the part.
Words to know¶
- fraction
- A number that compares a part with a whole, like 3 out of 12, written 3/12.
- numerator
- The top number of a fraction. It counts the part you are looking at.
- denominator
- The bottom number of a fraction. It counts all the equal parts in the whole.
For grown-ups: about this lesson
Why it matters. The lesson builds the two fraction ideas of the Common Core that the rest of Level 1 needs: a fraction as a part of a whole cut into equal parts (3.NF.1), and equal fractions shown with a visual model, such as folded strips (4.NF.1) NGA Center and CCSSO, 2010. Later lessons turn counts into probabilities and conditional fractions, which only make sense if the child first asks what the whole is.
Watch for these mix-ups.
A bigger bottom number means a bigger fraction. (Eighths are smaller pieces than halves, so 1/8 is less than 1/2.)
Any split into 4 pieces makes fourths. (The pieces must be equal for each to be one fourth.)
3 green marbles is always the same fraction. (It depends on the whole: 3 out of 12 is not 3 out of 6.)
Equal fractions must use the same numbers. (2/4 and 4/8 use different numbers but name the same amount.)
To make it easier. Use only halves and fourths, and a group of 4 counters with 1 of a different color.
To make it harder. Fold a strip into thirds and then sixths, and find a fraction equal to 2/3. Or sort 12 counters with 4 of one color into equal groups, and show that 4/12 is the same as 1/3.
Limits. Fractions of a group describe that group only. A bag with 3 green marbles out of 12 says nothing about another bag. The lesson uses small whole numbers and only equal parts; it does not yet cover comparing fractions by size.
On the computer. Grown-ups can see where this idea leads later in Lab: Chance and repeated trials, written for older learners.
Sources for this guide. NGA Center and CCSSO, 2010
Next: L1-02 · Build a probability model
- NGA Center and CCSSO. (2010). Common Core State Standards for Mathematics. Common Core State Standards Initiative. https://learning.ccsso.org/wp-content/uploads/2022/11/Math_Standards1.pdf