Let’s Learn!
How does the size and shape of the whole affect fractions?
Goal:
Goal:
Donte and Alani have a big project. Their teacher left lots of shapes that are divided into equal parts. Donte and Alani have to look at all of the whole shapes and decide if they are the same whole.
Donte and Alani know that fraction models must be the same whole so they can be compared. To have the same whole, two fraction models must be the same size and shape. They can be divided into different pieces, but their shape and size must be the same.
Donte puts the shapes together, and Alani uses her laser vision to compare the sizes. Click through the slides to see each set of shapes and help Donte and Alani figure out if they are the same whole!
\({ \frac{2}{6} }\)
\({ \frac{4}{6} }\)
Alani looks at both shapes. She can see that they are both circles and are both the same size. She is trying to decide if these are the same wholes.
Are these circles the same whole? Remember, same wholes are the same shape and the same size.
What do you think? Think about your answer, and click the Show Me button to see if you are right.
Yes! Because they are the same shape and same size, they are the same whole.
Donte shows Alani these two square fraction models.
\({ \frac{1}{4} }\)
\({ \frac{1}{4} }\)
Alani looks closely at these shapes with her laser vision. She notices that they both are squares, but she does not think they are the same size. One looks much bigger than the other. She does see that they are both divided into 4 equal parts, but those parts are not the same size!
If these squares are not the same size, can they be from the same whole?
No! These two fraction models are not the same whole because the squares are not the same size.
Donte found 2 number lines in the group of shapes. He tells Alani that these are still fraction models. She uses her laser vision to compare the sizes of the number lines and to count the number of equal parts.
Two number lines from 0 to 1. Both number lines have 8 pieces.
The top number line has 6 pieces shaded.
The bottom number line has 3 pieces shaded.
She finds that both number lines are the same length and have the same number of equal parts. There are 8 equal parts for each number line. Donte points to the denominator for each fraction. It is the same number for both number lines.
Do these number lines have the same whole?
Yes! They are the same length, so they are the same whole.
Alani wants to try again. Here are two more number lines. Can you see if they are the same whole?
Two number lines from 0 to 1. Both number lines have 3 pieces.
The top number line is shorter in length than the bottom number line.
Donte asks Alani if she can tell if these are the same whole. What should she tell Donte?
Alani should say that they are not the same whole. They are not the same length! One is longer than the other.
Donte shows Alani the next set of fraction models. He tells her to be sure to use her laser vision carefully on these. Alani looks very closely at the models.
\({ \frac{4}{6} }\)
\({ \frac{4}{8} }\)
Are they the same whole?
Yes! They are the same size and the same whole, even though they are divided into different numbers of equal parts.
Alani sees that these fraction models have a different number of parts. Even though they are the same whole, the denominators of the fractions will be different. She knows that she can still compare these fractions later on, though, since they are the same whole!
Donte shows Alani the last set of fraction models. He tells her to look carefully at these rectangles. Alani ramps up her laser vision!
\({ \frac{4}{6} }\)
\({ \frac{4}{6} }\)
Are they the same whole?
Donte asks Alani to think about the rectangles as if each were a flatbread pizza. Which would be more, 4 pieces from the first or 4 pieces from the second? The 4 pieces from the second pizza would be more because it is bigger than the first, so they are not the same size.
Your superpowers are growing strong. You can recognize when fractions have the same whole and when they do not.