Unit Conversions

Lesson 7

Objective

Express customary capacity measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require customary capacity unit conversion.

Materials and Resources

Common Core Standards

Core Standards

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  • 4.MD.A.1 — Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

  • 4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Foundational Standards

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  • 3.MD.A.2

  • 4.OA.A.1

Criteria for Success

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  1. Establish benchmarks for the customary units of a gallon, quart, pint, cup, and fluid ounce. 
  2. Understand that a gallon is four times more capacious than a quart, a quart is twice as capacious as a pint, a pint is twice as capacious as a cup, and a cup is eight times as capacious as a fluid ounce. 
  3. Use these relationships to convert measurements from a larger customary capacity unit to a smaller unit (MP.7, MP.8).
  4. Use these relationships to convert measurements from mixed customary capacity units to a smaller unit (MP.7, MP.8).
  5. Solve one-step word problems that require customary capacity unit conversions (MP.4).

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Anchor Tasks

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Problem 1

Use a gallon, quart, pint, and cup container and water to answer the following question. 

a. What do you notice about the relationship between the capacity of a gallon and the capacity of a quart?

b. What do you notice about the relationship between the capacity of a quart and the capacity of a pint?

c. What do you notice about the relationship between the capacity of a pint and the capacity of a cup?

d. What do you notice about the relationship between the capacity of a cup and the capacity of a fluid ounce?

Guiding Questions

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Problem 2

Fill in the following conversion tables.

Guiding Questions

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Problem 3

Joseph is told to dissolve a medicine he has to take in 1 pint 4 ounces of water. He has a measuring cup marked in ounces. How many ounces of water should he pour?

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Problem 4

Dominica’s mom signs up to bring a gallon of fruit punch to the family potluck. She plans to use the following recipe:

Fruit Punch

This fruit punch is super sweet and yummy, and everyone at your party will love it!

Ingredients:

  • 2 (6 ounce) cans frozen orange juice concentrate

  • 2 (6 ounce) cans frozen lemonade concentrate

  • 1 (3 pint) can pineapple juice

  • 3 cups water

  • 3 cups sugar

  • 1 quart 2 ounces soda

 

Will this recipe yield a gallon of fruit punch? If not, how much more fruit punch would she need to make? If so, how much more than a gallon will she have?

Guiding Questions

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Discussion of Problem Set

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  • How did you figure out how many pints are in a gallon in #2(g)? In four gallons in #2(h)? 
  • If someone wanted to find the number of pints or quarts in 150 gallons, would it make sense to use the conversion table to solve? Why is understanding the conversion rule important? 
  • How did you solve #3? Which strategy is most efficient? 
  • How did you figure out how many cups are in a gallon in #6(i?) How many fluid ounces are in a gallon in #6(j)? 
  • When measuring liquid, such as a bottle of drinking water, which customary unit could I use? Which metric unit could I use? 

Target Task

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Problem 1

Complete the table.

Quarts Cups
1  
2  
3  

 

References

EngageNY Mathematics Grade 4 Mathematics > Module 7 > Topic A > Lesson 2Exit Ticket, Question #1

Grade 4 Mathematics > Module 7 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Bonnie’s doctor recommended she should drink 2 cups of milk per day. If she buys 1 gallon of milk, will it be enough milk to last 1 week? Explain how you know. 

References

EngageNY Mathematics Grade 4 Mathematics > Module 7 > Topic A > Lesson 2Exit Ticket, Question #2

Grade 4 Mathematics > Module 7 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

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