Problem Solving
How do you use what you have learned to problem solve?
Goal:
Goal:
Let’s draw models to represent equivalent fractions!
Madelyn is playing video games, but her televisions are glitching. \({ \frac{2}{6} }\) of the boxes on the first TV are blue, and \({ \frac{1}{3} }\) of the boxes on the second TV are blue. Draw models to prove these fractions are equivalent.
Word Problem Solving Steps
- Read the problem.
- Look for important information.
- Draw the models.
- Color or label the models.
- Check your answer.
Read the problem.
What is this word problem telling you? Read through it a few times, and then write it on a piece of paper.
Madelyn is playing video games, but her televisions are glitching. \({ \frac{2}{6} }\) of the boxes on the first TV are blue, and \({ \frac{1}{3} }\) of the boxes on the second TV are blue. Draw models to prove these fractions are equivalent.
Look for important information.
What information is important in this word problem? Underline or circle the important information in the word problem. Then, check your thinking by clicking the Show Me button.
Madelyn is playing video games, but her televisions are glitching. \({ \frac{2}{6} }\) of the boxes on the first TV are blue, and \({ \frac{1}{3} }\) of the boxes on the second TV are blue. Draw models to prove these fractions are equivalent.
\({ \frac{2}{6} }\) and \({ \frac{1}{3} }\) are circled. The last sentence, "Draw models to prove these fractions are equivalent." is underlined.
Here is the most important information in this word problem:
- The televisions are showing \({ \frac{2}{6} }\) and \({ \frac{1}{3} }\) blue boxes.
- We need to prove these fractions are equivalent by drawing models.
Draw the models.
Let’s draw shapes and number lines as our models! Start by drawing 2 rectangles that are the same size and 2 blank number lines that are the same length. Then partition the shapes and number lines to model \({ \frac{2}{6} }\) and \({ \frac{1}{3} }\).
Click on the images below to check your work.
Two rectangles.
Two number lines from 0 to 1.
Two rectangles.
Two number lines.
Top rectangle is partitioned into 6 equal parts. Top number line has 7 marks between 0 and 1.
Bottom rectangle is partitioned into 3 equal parts. Bottom number line has 4 marks between 0 and 1.
Color or label the models.
Color the shapes to model \({ \frac{2}{6} }\) and \({ \frac{1}{3} }\). Then, label the number lines, and draw dots over \({ \frac{2}{6} }\) and \({ \frac{1}{3} }\).
Click on the images below to check your work.
Two rectangles.
Two number lines.
Top rectangle is partitioned into 6 equal parts. Top number line has 7 marks between 0 and 1.
Bottom rectangle is partitioned into 3 equal parts. Bottom number line has 4 marks between 0 and 1.
Two rectangles.
Two number lines.
Top rectangle is partitioned into 6 equal parts with 2 parts filled in. Top number line has 7 marks between 0 and 1. Marks are labeled from \({ \frac{0}{6} }\) to \({ \frac{6}{6} }\) with a dot above \({ \frac{2}{6} }\).
Top rectangle is partitioned into 3 equal parts with 1 part filled in. Top number line has 7 marks between 0 and 1. Marks are labeled from \({ \frac{0}{3} }\) to \({ \frac{3}{3} }\) with a dot above \({ \frac{1}{3} }\).
Check your answer.
Do the colored parts of your rectangles take up the same amount of space? Do the dots on your number lines line up? Draw lines to help you!
Madelyn is playing video games, but her televisions are glitching. \({ \frac{2}{6} }\) of the boxes on the first TV are blue, and \({ \frac{1}{3} }\) of the boxes on the second TV are blue. Draw models to prove these fractions are equivalent.
\({ \frac{2}{6} }\) and \({ \frac{1}{3} }\) are circled. The last sentence, "Draw models to prove these fractions are equivalent." is underlined.
Top rectangle is partitioned into 6 equal parts with 2 parts filled in. Top number line has 7 marks between 0 and 1. Marks are labeled from \({ \frac{0}{6} }\) to \({ \frac{6}{6} }\) with a dot above \({ \frac{2}{6} }\).
Top rectangle is partitioned into 3 equal parts with 1 part filled in. Top number line has 7 marks between 0 and 1. Marks are labeled from \({ \frac{0}{3} }\) to \({ \frac{3}{3} }\) with a dot above \({ \frac{1}{3} }\).
There is a dotted line from the filled parts in the rectangle that match up. There is a dotted line from the dots on the number lines that match up.
Question:
Are \({ \frac{2}{6} }\) and \({ \frac{1}{3} }\) equivalent fractions?
Yes! They are equivalent.
Which number lines show equivalent fractions? Click the number lines below to find out!
Two number lines.
Top number line goes from 0 to 1 with 9 marks between. Marks are labeled from \({ \frac{0}{8} }\) to \({ \frac{8}{8} }\) with a dot on \({ \frac{4}{8} }\).
Bottom number line goes from 0 to 1 with 5 marks between. Marks are labeled from \({ \frac{0}{4} }\) to \({ \frac{4}{4} }\) with a dot on \({ \frac{2}{4} }\).
Two number lines.
Top number line goes from 0 to 1 with 9 marks between. Marks are labeled from \({ \frac{0}{8} }\) to \({ \frac{8}{8} }\) with a dot on \({ \frac{4}{8} }\).
Bottom number line goes from 0 to 1 with 5 marks between. Marks are labeled from \({ \frac{0}{4} }\) to \({ \frac{4}{4} }\) with a dot on \({ \frac{2}{4} }\).
🤔 These number lines are not partitioned into equal parts, so they do not show equivalent fractions.
Two number lines.
Top number line goes from 0 to 1 with 9 marks between. Marks are labeled from \({ \frac{0}{8} }\) to \({ \frac{8}{8} }\) with a dot on \({ \frac{4}{8} }\).
Bottom number line goes from 0 to 1 with 5 marks between. Marks are labeled from \({ \frac{0}{4} }\) to \({ \frac{4}{4} }\) with a dot on \({ \frac{2}{4} }\).
Two number lines.
Top number line goes from 0 to 1 with 9 marks between. Marks are labeled from \({ \frac{0}{8} }\) to \({ \frac{8}{8} }\) with a dot on \({ \frac{4}{8} }\).
Bottom number line goes from 0 to 1 with 5 marks between. Marks are labeled from \({ \frac{0}{4} }\) to \({ \frac{4}{4} }\) with a dot on \({ \frac{2}{4} }\).
😀 Yes! These number lines are partitioned into equal parts. They show \({ \frac{4}{8} }\) and \({ \frac{2}{4} }\) are equivalent fractions because both dots line up.