Lesson 4Converting Units

Learning Goal

Let’s convert measurements to different units.

Learning Targets

I can convert measurements from one unit to another, using double number lines, tables, or by thinking about “how much for 1.”
I know that when we measure things in two different units, the pairs of measurements are equivalent ratios.

Warm Up: Number Talk: Fractions of a Number

Find the values mentally.

$\frac{1}{4}$ of 32
$\frac{3}{4}$ of 32
$\frac{3}{8}$ of 32
$\frac{3}{8}$ of 64

Activity 1: Road Trip

Elena and her mom are on a road trip outside the United States. Elena sees this road sign.

Elena’s mom is driving 75 miles per hour when she gets pulled over for speeding.

Problem 1

The police officer explains that 8 kilometers is approximately 5 miles.

How many kilometers are in 1 mile?
How many miles are in 1 kilometer?

Problem 2

If the speed limit is 80 kilometers per hour, and Elena’s mom was driving 75 miles per hour, was she speeding? By how much?

Activity 2: Veterinary Weights

A veterinarian uses weights in kilograms to figure out what dosages of medicines to prescribe for animals. For every 10 kilograms, there are 22 pounds.

Problem 1

Calculate each animal’s weight in kilograms. Explain or show your reasoning. If you get stuck, consider drawing a double number line or table.

Fido the Labrador weighs 88 pounds.
Spot the Beagle weighs 33 pounds.
Bella the Chihuahua weighs $5 \frac{1}{2}$ pounds.

Problem 2

A certain medication says it can only be given to animals over 25 kilograms. How much is this in pounds?

Activity 3: Run a Mile or Two

A rectangular field is 90 yards long and $42 \frac{1}{4}$ yards wide. Priya says that 6 laps around the field is more than a mile. Do you agree with Priya?
Explain or show your reasoning.
A different rectangular field is $408 \frac{1}{2}$ feet long and $240 \frac{1}{4}$ feet wide. How many laps around this field would Priya need to run if she wants to run at least 2 miles?

Activity 4: Walk All Day

Lin has a watch that counts the number of steps she takes during the day and displays those steps in centimeters, meters, or kilometers.

Here is a list of activities Lin did on Monday. Next to each activity, write whether it would make sense to display the distance in cm, m, or km.
- walked to her friend’s desk
- walked to the front of the classroom
- walked from her classroom to the bus
- ran twice around the playground
The table shows the amount of steps Lin’s watch displayed for each activity. If each of her steps is 50 centimeters, how many centimeters and meters did Lin walk for each activity?
activity
number of steps
distance (cm)
distance (m)
walked to her friend’s desk
$5$
walked to the front of the classroom
$12$
walked from her classroom to the bus
$250$
ran twice around the playground
$1, 000$
At the end of the day, Lin’s watch displayed 8,500 steps. Would it make sense for her watch to record the distance in centimeters, meters, or kilometers? Why?
How many kilometers did Lin walk that day?

activity	number of steps	distance (cm)	distance (m)
walked to her friend’s desk	$5$
walked to the front of the classroom	$12$
walked from her classroom to the bus	$250$
ran twice around the playground	$1, 000$

Lesson Summary

When we measure something in two different units, the measurements form an equivalent ratio. We can reason with these equivalent ratios to convert measurements from one unit to another.

Suppose you cut off 20 inches of hair. Your Canadian friend asks how many centimeters of hair that was. Since 100 inches equal 254 centimeters, we can use equivalent ratios to find out how many centimeters equal 20 inches.

Using a double number line:

A double number line with 6 evenly spaced tick marks. The top number line is labeled “length, in inches” and starting with the first tick mark 0, 20, 40, 60, 80, and 100 are labeled. The bottom number line is labeled “length, in centimeters” and starting with the first tick mark 0, 50 point 8, 101 point 6, 152 point 4, 203 point 2, and 254 are labeled. There is one circle around the second tick marks in each line and one circle around the last tick mark in each line.

Using a table:

length (in)	length (cm)
100	254
1	2.54
20	50.8