Lesson 3: Measuring with Different-Sized Units

Let’s measure things.

3.1: Width of a Paper

Your teacher will show you two rods. Does it take more green rods or blue rods lined up end to end to measure the width of a piece of printer paper?

3.2: Measurement Stations

Station 1

  • The larger cubes are 1 cubic inch each. Count how many cubic inches it takes to completely pack the box full without gaps.
  • Empty the box.
  • The small cube is 1 cubic centimeter. Each rod is composed of 10 cubic centimeters. Count how many cubic centimeters it takes to completely pack the box full without gaps.
  • Empty the box.
  cubic inches cubic centimeters
volume of the box    

Station 2

  • Use the meter stick to measure to the nearest meter the length your teacher has indicated.
  • Use rulers to measure to the nearest foot the length your teacher has indicated.
  meters feet
length of ______________________    

Station 3

Watch the video. How many times can a quart bottle be filled from a gallon jug? How many times can a liter bottle be filled from a gallon jug?

quarts and liters from Open Up Resources on Vimeo https://vimeo.com/184901230.

  quarts liters
1 gallon of water    

Station 4

Use the applet to record the weights of different objects in different units.

GeoGebra Applet BhBXHJwV

Record their weights in ounces, pounds, grams, and kilograms.

  object to weigh ounces pounds grams kilograms
object 1          
object 2          
object 3          

Station 5

  • Count how many level teaspoons of salt it takes to fill the graduated cylinder to 20 milliliters, 40 milliliters, and 50 milliliters.
  • Pour the salt back into the original container.
  milliliters teaspoons
volume of salt 20  
volume of salt 40  
volume of salt 50  

After you finish all five stations, answer the following questions with your group.

  1. Which is larger, a cubic inch or a cubic centimeter? Did more cubic inches or cubic centimeters fit in the cardboard box? Why?
  2. Did it take more feet or meters to measure the indicated length? Why?
  3. Which is bigger, a quart or a liter? Explain your reasoning.
  4. Use the data from Station 4 to put the units of weight and mass in order from smallest to largest. Explain your reasoning.

    1. If you continued filling the graduated cylinder with salt to 100 milliliters, about how many teaspoons would it take? Show your thinking.
    2. If you poured 15 teaspoons of salt into an empty graduated cylinder, about how many milliliters would it fill? Show your thinking.
    3. How many milliliters per teaspoon are there?
    4. How many teaspoons per milliliter are there?


The size of the unit we use to measure something affects the measurement.

If we measure the same quantity with different units, it will take more of the smaller unit and fewer of the larger unit to express the measurement. For example, a room that measures 4 yards in length will measure 12 feet.

A pair of tape diagrams for one quantity. The top tape diagram has 4 equal parts and the bottom tape diagram has 12 equal parts.

There are 3 feet in a yard, so one foot is $\frac13$ of a yard.

  • It takes 3 times as many feet to measure the same length as it does with yards.
  • It takes $\frac13$ as many yards to measure the same length as it does with feet.

Practice Problems ▶