IM 6.4.12 Lesson: Fractional Lengths

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

Find the product mentally.

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

If your teacher gives you the data card:

Silently read your card and think about what information you need to be able to answer the question.
Ask your partner for the specific information that you need.
Explain how you are using the information to solve the problem. Continue to ask questions until you have enough information to solve the problem.
Share the problem card and solve the problem independently.
Read the data card and discuss your reasoning.

Silently read your card.
Ask your partner “What specific information do you need?” and wait for them to ask for information. If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions.
Read the problem card and solve the problem independently.
Share the data card and discuss your reasoning.

Lin has a work of art that is 14 inches by 20 inches. She wants to frame it with large paper clips laid end to end.

If each paper clip is inch long, how many paper clips would she need? Show your reasoning and be sure to think about potential gaps and overlaps. Consider making a sketch that shows how the paper clips could be arranged.

How many paper clips are needed if the paper clips are spaced inch apart? Describe the arrangement of the paper clips at the corners of the frame.

A second-grade student is 4 feet tall. Her teacher is 5 ⅔ feet tall.

How many times as tall as the student is the teacher?

What fraction of the teacher’s height is the student’s height?

Find each quotient. Show your reasoning and check your answer.

Write a division equation that can help answer the question. Then find the answer. If you get stuck, consider drawing a diagram.

A runner ran miles on Monday and miles on Tuesday. How many times her Monday’s distance was her Tuesday’s distance?

A cyclist planned to ride miles but only managed to travel miles. What fraction of his planned trip did he travel?

The photo shows a situation that involves fractions. Complete the sentences. Be prepared to explain your reasoning.

The length of the long tube is about ______ times the length of a short tube.

The length of a short tube is about ______ times the length of the long tube.

If the length of the long paper roll is inches, what is the length of each short paper roll?