Fraction Models · Set 3 of 4 · Grade 3
Roots of Reason
rootsofreason.org
Every Fraction Has a Picture
Stuck?
Scan for the anchor chart
A fraction is a number, and numbers have pictures.
This set teaches the three pictures of three fourths.
This set teaches the three pictures of three fourths.
1
The shape picture
Cut one whole into 4 equal parts. Shade 3 of them.
2
The strip picture
Same idea, stretched into a bar. 4 equal pieces, 3 shaded.
3
The number line picture
Cut the space between 0 and 1 into 4 equal jumps. Land on the 3rd mark.
Same rule as always:
"If you can't draw it, you don't get it."
Roots of Reason
Fraction Models · Shape pictures
Name
Date
Shade It, Say It
The shaded part is the fraction.
Count parts in all, then count shaded parts.
Count parts in all, then count shaded parts.
1.Shade it. The cuts are already fair. Shade each shape to match its fraction.
shade 1/2
shade 3/4
shade 2/3
2.Say it. Write the fraction each picture shows. Bottom number first: how many parts in all?
Say each one out loud: "3 out of 4 equal parts."
Roots of Reason
Fraction Models · Strip pictures
Name
Date
Fraction Strips
Strips are the same whole, cut different ways.
Stack them and the pieces compare themselves.
Stack them and the pieces compare themselves.
1.All three strips are the same size. Cut the first into 2 equal parts, the second into 3, the third into 4. Then shade one part of each strip and label it.
one part is one
one part is one
one part is one
2.Look at your strips. Which piece is bigger, one third or one fourth? Circle one.
one third
one fourth
More pieces from the same whole means each piece is
Roots of Reason
Fraction Models · Number line pictures
Name
Date
Fractions Live on the Number Line
A fraction is a place between 0 and 1.
Equal jumps, just like equal parts.
Equal jumps, just like equal parts.
1.The line is already cut into 4 equal jumps. Write the fraction that names each mark.
0
1
2.Your turn to cut. Make 2 equal jumps on this line, then put a dot exactly at one half.
Is three fourths closer to 0 or to 1? How do you know from the line?
Roots of Reason
Fraction Models · Putting it together
Name
Date
One Fraction, Three Pictures
Show two thirds every way you know.
If all three pictures agree, you own this fraction.
If all three pictures agree, you own this fraction.
1.Draw 2/3 three ways. Start each picture from what is given.
shape
strip
number line
2.Think about it. Which picture is easiest for you to draw? Which one helps you most when fractions get hard? Why?
Number lines hide in rulers and measuring cups.
Roots of Reason
rootsofreason.org
Fraction Models · Set 3 of 4 · Grade 3
Answer Key and Teacher Notes
Shade it, say it (page 2)
1. Any correct count of shaded parts works: 1 of 2, 3 of 4, 2 of 3 2. 1/4 · 2/3 · 1/4. Insist on the sentence "out of equal parts", not just the digits.
Fraction strips (page 3)
1. Fair cuts into 2, 3, 4; one part shaded on each; labels half, third, fourth 2. one third is bigger; more pieces means each piece is smaller. This inverts whole-number intuition, so expect hesitation.
Number line (page 4)
1. Marks left to right: 1/4, 2/4, 3/4 2. One tick in the middle, dot at 1/2; 3/4 is closer to 1 because it is 1 jump from 1 but 3 jumps from 0.
One fraction, three pictures (page 5)
1. Circle in 3 equal parts, 2 shaded; strip in 3 equal parts, 2 shaded; line cut into 3 equal jumps with a dot at the 2nd mark 2. Any honest reflection counts. Push past "the circle is easiest" to a reason.
The number line is the picture students avoid and the one that matters most later: it is how fractions become numbers rather than pieces of pizza. If page 4 wobbles, put a strip directly above a number line of the same length and show the tick marks lining up with the cuts. Do not move on to comparing or adding fractions until all three pictures of the same fraction agree on page 5.