Let’s Learn!
Can you create equivalent fractions?
Goal:
Goal:
Madelyn knows her dollhouses are similar. Both houses have pink rooms! She thinks both houses have the same fraction of rooms that are pink. Let’s see how she checks to see!
24 of the rooms are pink
36 of the rooms are pink
Are 24 and 36 equivalent fractions? Equivalent fractions are two or more fractions that name the same amount. Madelyn wants to create partitioned shapes and number lines to see if these are equivalent fractions. Shapes and number lines are also called fraction models. Click through the slides below to create models that represent 24 and 36 to see if they are equivalent.
Equivalent Shapes
Let’s draw partitioned shapes to represent the equivalent fractions 24 and 36. Begin by drawing 2 shapes that are the same size and shape. You could draw 2 circles, 2 squares, or 2 rectangles. We will use rectangles.
Two rectangles. Top rectangle is labeled 24. Bottom rectangle is labeled 36.
We will use the top rectangle to draw 24 and the bottom rectangle to draw 36.
Partition each of the rectangles in equal parts to match the denominators. Look at the denominator of each fraction. Remember, this tells us the number of parts the shape is divided into.
Two rectangles. Top rectangle is labeled 24 and the denominator 4 is circled. Bottom rectangle is labeled 36 and the denominator 6 is circled.
The top rectangle is partitioned into 4 parts, and the bottom rectangle is partitioned into 6 parts.
Color the parts of each rectangle to match the numerator. The numerators tell us either the parts that are shaded or the parts left unshaded. Right now, the numerators tell us how many parts are shaded.
Two rectangles. Top rectangle is labeled 24 and the numerator 2 is circled. The rectangle is partitioned into 4 equal parts and 2 parts are filled in. Bottom rectangle is labeled 36 and the numerator 3 is circled. The rectangle is partitioned into 6 equal parts and 3 parts are filled in.
2 parts of the top rectangle are shaded, and 3 parts of the bottom rectangle are shaded.
Both rectangles are the same shape and size. The colored parts take up the same amount of space. That means we have created equivalent fraction models!
Two rectangles. Top rectangle is labeled 24 and the numerator 2 is circled. The rectangle is partitioned into 4 equal parts and 2 parts are filled in. Bottom rectangle is labeled 36 and the numerator 3 is circled. The rectangle is partitioned into 6 equal parts and 3 parts are filled in. Both rectangles have a dotted line after their filled parts that match up for both rectangles.
Equivalent Number Lines
Let’s draw number lines to represent the equivalent fractions 24 and 36. Begin by drawing 2 lines with an arrow at each end. Label each side of each number line with 0 and 1. It is important to make sure these numbers line up on both number lines. This ensures you that the numbers lines are the same length.
Two number lines. Top number line from 0 to 1 labeled 24. Bottom number line from 0 to 1 labeled 36.
We will use the top number line to draw 24 and the bottom number line to draw 36.
Partition the number lines to match the denominators. The spaces should be equally spaced out.
Two number lines. Top number line from 0 to 1 labeled 24. The denominator 4 is circled. Five marks between 0 and 1. Bottom number line from 0 to 1 labeled 36. The denominator 6 is circled. Seven marks between 0 and 1.
The top number line is partitioned into 4 equal parts, and the bottom number line is partitioned into 6 equal parts.
Label the fractions on each number line.
Two number lines. Top number line from 0 to 1 labeled 24. Five marks between 0 and 1 from 04 to 44. Bottom number line from 0 to 1 labeled 36. Seven marks between 0 and 1 from 06 to 66.
Now draw the dots! Draw a dot at 24 on the top number line and another dot at 36 on the bottom number line.
Two number lines. Top number line from 0 to 1 labeled 24 with the numerator 2 circled. Five marks between 0 and 1 from 04 to 44 and a dot above 24. Bottom number line from 0 to 1 labeled 36 with the numerator 3 circled. Seven marks between 0 and 1 from 06 to 66 and a dot above 36.
Both number lines have a 0 and 1 that line up, so they are the same length. Both dots line up with each other. That means we have created equivalent fraction models!
Two number lines. Top number line from 0 to 1 labeled 24 with the numerator 2 circled. Five marks between 0 and 1 from 04 to 44 and a dot above 24. Bottom number line from 0 to 1 labeled 36 with the numerator 3 circled. Seven marks between 0 and 1 from 06 to 66 and a dot above 36. Dotted line from the top number line's dot to the bottom number line's dot. Both dots match up.
Question:
Draw shapes to model to see if 34 and 68 are equivalent fractions.
Two rectangles. Top rectangle is partitioned into 4 equal parts with 3 parts filled in. Labeled 34. Bottom rectangle is partitioned into 8 equal parts with 6 parts filled in. Labeled 68.
Yes! These squares are the same shape and size. The colored parts take up the same amount of space, so 34 and 68 are equivalent fractions!