Units in Scale Drawings

5 min

Narrative

This Warm-up prompts students to review work from grade 5 about converting standard units within a given measurement system. Later in this lesson students will examine equivalent scales; that is, scales that lead to the same size scale drawing. Checking whether or not two scales are equivalent often involves converting given quantities to other units.

Launch

Arrange students in groups of 2. Ask students to use the following numbers and units to record as many equivalent measurements as they can. Tell them that they are allowed to reuse numbers and units. Give students 2 minutes of quiet think time followed by 1 minute to share their equations with their partner.

Student Task

Use the numbers and units from the list to find as many equivalent measurements as you can. For example, you might write “30 minutes is 12\frac12 hour.”

You can use the numbers and units more than once.

1

12

0.4

8

50

12\frac{1}{2}

40

100

3133\frac{1}{3}

30

0.3

24

110\frac{1}{10}

6

2

23\frac{2}{3}

centimeter (cm)

meter (m)

kilometer (km) 

inch (in)

foot (ft)

yard (yd)

Sample Response

Answers vary. Sample responses:

  • 30 cm is 0.3 m, 40 cm is 0.4 m, 50 cm is 12\frac12 m, 100 cm is 1 m
  • 100 m is 110\frac{1}{10} km
  • 6 in is 12\frac12 ft, 8 in is 23\frac23 ft, 12 in is 1 ft, 24 in is 2 ft, 40 in is 3133\frac13 ft
  • 0.3 ft is 110\frac{1}{10} yd, 2 ft is 23\frac23 yd, 6 ft is 2 yd, 24 ft is 8 yd
  • 24 in is 23\frac23 yd
Activity Synthesis (Teacher Notes)

Invite a few students to share equations that they had in common with their partner and ones that were different. Record these answers for all to see. After each equation is shared, ask the class to give a signal if they had the same one recorded. Display the following questions for all to see and discuss:

  • “What number(s) did you use the most? Why?”
  • “If you could include two more cards in this selection, what would they be? Why?”
Anticipated Misconceptions
Some students may write “30 cm is 1 ft” because 30 is often the largest centimeter measurement labeled on a 1-foot ruler. Explain that these values are approximately equal, but not exact. If students want to keep such pairings on their list, prompt them to use a phrase like “is close to.” For example:
  • 30 cm is close to 1 ft
  • 0.3 m is close to 1 ft
  • 40 in is close to 1 m
  • 3133\frac 13 ft is close to 1 m
Standards
Building On
  • 6.RP.3.d·Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
  • 6.RP.A.3.d·Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

15 min