3.6 Measuring Length, Time, Liquid Volume, and Weight

Unit Goals

  • Students generate and represent length measurement data in halves and fourths of an inch on line plots. They learn about and estimate relative units of measure including weight, liquid volume, and time, and use the four operations to solve problems involving measurement.

Section A Goals

  • Measure lengths using rulers marked with halves and fourths of an inch to generate data for making a line plot.

Section B Goals

  • Measure and estimate weights and liquid volumes of objects.

Section C Goals

  • Solve problems involving addition and subtraction of time intervals in minutes.
  • Tell time to the minute.

Section D Goals

  • Solve problems involving the four operations and measurement contexts.
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Section A: Measurement Data on Line Plots

Problem 1

Pre-unit

Practicing Standards:  2.MD.A.4

What is the length of the pencil in centimeters? Show your reasoning.

Pencil measured by ruler in centimeters.

Solution

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Problem 2

Pre-unit

Practicing Standards:  2.MD.D.9

Here are the lengths of some snakes at the pet store in inches. Use the data to create a line plot.

  • 8
  • 10
  • 13
  • 13
  • 13
  • 15
  • 15
  • 18
  • 21
  • 22

Line plot.

Solution

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Problem 3

Pre-unit

Practicing Standards:  3.NBT.A.2

Find the value of each sum or difference.

  1. \(374 + 455\)
  2. \(259 - 186\)

Solution

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Problem 4

Pre-unit

Practicing Standards:  2.MD.C.7

Write the time shown on each clock.

aAnalog clock showing time.
bAnalog clock showing time.
cAnalog clock showing time.

  1. _______________

  2. _______________

  3. _______________

Solution

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Problem 5

Pre-unit

Practicing Standards:  3.OA.B.5

Find the value of each expression.

  1. \(8 \times 9\)
  2. \(16 \times 6\)
  3. \(72 \div 8\)
  4. \(92 \div 4\)

Solution

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Problem 6

Find the length of each pencil.

  1.  
    Pencil measured by a ruler in inches.

  2.  
    Pencil measured by a ruler in inches.

Solution

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Problem 7

  1. Partition the ruler into halves of an inch and then quarters of an inch.
    Ruler measuring a shaded rectangle in inches.
  2. What is the length of the rectangle? Explain or show your reasoning.

Solution

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Problem 8

Here are the lengths of some pieces of pasta in inches.

Which lengths are the same? Explain or show your reasoning.

  • \(3\frac{2}{4}\)
  • 2
  • \(3\frac{1}{2}\)
  • \(\frac{4}{2}\)

Solution

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Problem 9

The line plot shows the width of some postcards in inches.

Dot plot from 0 to 7 by ones. Postcard widths, inches. Beginning at 4 and a half, the number of X’s above each increment are 2, 5, 2, 3, 2, 1.
 

  1. How many postcards measured \(5 \frac{1}{2}\) inches?

  2. How many postcards measured 6 inches or more?

  3. How many postcards were measured for the line plot?

Solution

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Problem 10

Here are the lengths of some straws in inches. Represent the data on a line plot.

  • \(4\frac{3}{4}\)
  • \(5\frac{1}{2}\)
  • \(4\frac{1}{4}\)
  • \(5\frac{2}{4}\)
  • \(4\frac{1}{2}\)
  • \(3\frac{3}{4}\)
  • \(5\frac{1}{4}\)
  • \(4\frac{2}{4}\)
  • 5
  • \(4\frac{1}{4}\)
  • \(4\frac{1}{2}\)

Dot plot from 0 to 6 by ones. Hash marks by fourths. Horizontal axis, straw lengths, inches.

Solution

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Problem 11

Exploration

You will need a ruler marked in \(\frac{1}{4}\) inches for this problem.

  1. For each length, pick an object in the classroom or at home that you think will be close to that length.

    • \(1\frac{1}{2}\) inches

    • 7 inches

    • 33 inches

  2. Measure each object using a ruler marked in \(\frac{1}{4}\) inches. Was each estimate too high, too low, or just right?

Solution

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Problem 12

Exploration

Choose a collection of objects to measure at school or at home. Make a line plot of the length of the objects.

Solution

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Section B: Weight and Liquid Volume

Problem 1

  1. Circle the items that might weigh about 1 gram.

    a piece of gum

    a turtle

    a dollar bill

    a chair

    a pen

  2. Circle the items that might weigh about 1 kilogram.

    a giant tortoise

    a pencil

    a pineapple

    a large book

    a full lunchbox

Solution

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Problem 2

For each item, decide whether it holds more than a liter, less than a liter, or about a liter.

  1. a bathtub

    ________________________________________

  2. a cup

    ________________________________________

  3. a swimming pool

    ________________________________________

  4. a small pot for a plant

    ________________________________________

Solution

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Problem 3

  1. What is the volume of liquid shown in the container?

    Container of water showing measurement in liters.

  2. Shade the image of the empty container to show \(1\frac{3}{4}\) liters of water.

    Container with measurements in liters.

Solution

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Problem 4

Exploration

Kiran thinks that weight and volume go together. The bigger something is, the heavier it is and the heavier something is the bigger it is. Do you agree with Kiran? Give some examples to explain your thinking.

Solution

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Problem 5

Exploration

You have a 3 liter jug of water and a 5 liter jug of water. How can you measure out 4 liters of water precisely using these two jugs?

Solution

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Section C: Problems Involving Time

Problem 1

  1. Han drew this clock and says it shows 2:16 p.m. Do you agree with Han? Explain your reasoning.
    Analog clock showing time.

  2. Draw the hands on this clock to show 5:55 p.m.

    Analog clock.

Solution

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Problem 2

Mai left to walk the dog at 6:50 a.m. and she returned at 7:44 a.m. How much time did Mai spend walking the dog?

Solution

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Problem 3

Andre started soccer practice at 3:45 p.m. He left school 75 minutes earlier. 

  1. Show the time Andre left school on the clock.
  2. Andre was at soccer practice for 110 minutes. What time did soccer practice end? Explain or show your reasoning.
Analog clock with no hands.

Solution

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Problem 4

Exploration

  1. What time do you usually go to bed at night?

  2. What time do you usually get up in the morning?

  3. How many minutes do you spend in bed? Explain or show your reasoning.

Solution

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Problem 5

Exploration

Priya drew this clockface to show 3:15.

Do you think Priya’s clock face is accurate? Explain or show your reasoning.

Analog clock showing time.

Solution

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Section D: Measurement Problems in Context

Problem 1

Lin’s class got 8 pumpkins for a pumpkin carving contest. Each pumpkin weighed 12 pounds.

  1. Which tape diagram represents the situation?

    Diagram. Rectangle divided into 12 equal parts, each labeled 8. Total, question mark.
    Diagram. Rectangle divided into 8 equal parts, each labeled 12. Total, question mark.
  2. How many pounds did the pumpkins weigh altogether? Explain or show your reasoning.

Solution

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Problem 2

A family brought two pigs to the fair. The first pig weighed 153 kg. The second pig weighed 66 kg less. How much did the second pig weigh?

Solution

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Problem 3

One day, a lemonade stand at the fair sold 56 liters of lemonade in 4-liter packs. How many 4-liter packs did they sell?

Solution

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Problem 4

Jada arrived at the fair at 10:15 a.m. She left the fair at 11:47 a.m. How many minutes did Jada spend at the fair? Explain or show your reasoning.

Solution

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Problem 5

Exploration

Analog clock with no numbers.

Jada sees this image of a clock in a mirror. What time is it? Explain your reasoning.

Solution

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Problem 6

Exploration

Three pumpkins at the fair weigh a total of 1,000 kg.

  1. What is one possibility for the 3 pumpkin weights?
  2. The lightest of the 3 pumpkins is 255 kg. What is a possibility now for the 3 pumpkin weights?
  3. The heaviest of the 3 pumpkins is 428 kg. How much does the 3rd pumpkin weigh?

Solution

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