4.MD.2 - About the Math, Learning Targets, and Rigor

Grade 4 Measurement and Data

4.MD.2

About the Math

Full Standard

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.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

4th Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

  

Report Card Measurement Topic: Demonstrates understanding of patterns, expressions, equations, and algebraic thinking.
3rd Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

 

Report Card Measurement Topic: Solves one and two-step word problems with any operation.

 

Learning Targets

  • Represent measurement quantities using number lines with measurement scales.
  • Represent measurement word problems.
  • Solve measurement word problems with any operation that include whole numbers, fractions, and decimals. Note: Computation with fractions and decimals is limited to the expectations of 4th grade standards.
  • Convert larger units into equivalent smaller units to solve a problem.

 

About the Math

This standard includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, and dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems. Essential vocabulary for this standard includes: customary units, metric system, inch, feet, yard, pound, ounce, ton, gallon, pint, cup, ounces, second, minute, hour, day, week, month, year, millimeter, centimeter, meter, gram, kilogram, milliliter, and liter (online dictionary Links to an external site.).  Note: The standard is specific to the units noted in 4.MD.1.  However, it is completely appropriate for students to work with other measurement units, but students are not expected to have mastery of these additional units.

Example:
Charlie and 10 friends are planning for a pizza party. They purchased 3 quarts of juice. If each glass holds 8oz will everyone get at least one glass of juice? possible solution:

  • Charlie plus 10 friends = 11 total people
  • 11 people x 8 ounces (glass of juice) = 88 total ounces 1quart=2pints= 4cups=32ounces
  • Therefore 1 quart = 2 pints = 4 cups = 32 ounces 2 quarts = 4 pints = 8 cups = 64 ounces
  • 3 quarts = 6 pints =12 cups = 96 ounces
  • If Charlie purchased 3 quarts (6 pints) of juice there would be enough for everyone at his party to have at least one glass of juice. If each person drank 1 glass then he would have 1- 8 oz glass or 1 cup of juice left over.

 

Additional Examples with various operations:

Division/fractions: Susan has 2 feet of ribbon. She wants to give her ribbon to her 3 best friends so each friend gets the same amount. How much ribbon will each friend get? Students may record their solutions using fractions or inches. (The answer would be 2/3 of a foot or 8 inches. Students are able to express the answer in inches because they understand that 1/3 of a foot is 4 inches and 2/3 of a foot is 2 groups of 1/3.)

Addition: Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40 minutes on Wednesday. What was the total number of minutes Mason ran?

Subtraction: A pound of apples costs $1.20. Rachel bought a pound and a half of apples. If she gave the clerk a $5.00 bill, how much change will she get back?

Multiplication: Mario and his 2 brothers are selling lemonade. Mario brought one and a half liters, Javier brought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did the boys have?

Number line diagrams that feature a measurement scale can represent measurement quantities. Examples include: ruler, diagram marking off distance along a road with cities at various points, a timetable showing hours throughout the day, or a volume measure on the side of a container.

 

Math In Minutes:  Below is a video highlighting strategies for elapsed time.

 

 

 

Progression of Standard within Grade 4

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
   

 
  • Represent measurement quantities using number lines with measurement scales.
  • Represent measurement word problems.
  • Solve measurement word problems with any operation that include whole numbers, fractions, and decimals.
  • Convert larger units into equivalent smaller units to solve a problem.

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 3 Grade 5
  • Solve one-step word problems involving masses or volumes (3.MD.2)
  • Fluently x/÷ facts (3.OA.7 )
  • Convert among standard measurement units and use to solve multi-step problems (5.MD.1)
  • Interpret a fraction as division (5.NF.3)
  • Interpret multiplication as scaling (resizing) (5.NF.5)
  • Word problems with x of fractions (5.NF.6)

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction. 

  • Use Cuisenaire rods to create a bar model to help students visualize the connection between different units of measurement. For example, tell students that the blue rod represents 1 yard. Ask them to use what they know about conversions to find which rod represents 1 foot. After students have identified the light green rod as 1 foot, provide the following prompt: The width of a 4th grade classroom is 9 yards. How many feet is the width of the classroom? Students can either use the Cuisenaire rods, create their own bar models, or a different conceptual explanation to answer the prompt.
  • If I saw a movie that was 2 hours and 37 minutes long, what time could I have entered the theatre and what time could I have left the theatre?
  • Julianna bought a bag of candy at the movie theatre. She spent less than 75/100 of a dollar but more than 5/10 of a dollar. How much money could Julianna have spent on candy? Give your answer in decimal form. What is another possible answer?
  • Malachi rode his bike 268 meters to his friends house. He then rode his bike half a kilometer to the park. How many total meters has Malachi ridden on his bike? Represent your answer using a model, drawing, or other representation.
  • 1,000 pounds is the answer, what could be a story problem for this answer?
  • At the fair, the puppet show started at 8:38am and ended at 10:45am. Storytime was ¾ hour longer than the puppet show. How long was storytime?
  • Four jugs have water in them: Jug A has 36.5 quarts, Jug B has 144 cups and Jug C has 8 ¾ gallons. Order the jugs from least to greatest
  • Yesterday, Brittany ran less than 5 kilometers but more than 1,200 meters. How far could Brittany have run? Andrea says Brittany ran 1.5 kilometers. Steven says Brittany ran 3,200 meters. Who do you agree with and why?

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 15 • Measurement and Problem Solving

Solve Problems Involving Measurement:

 

 

Additional Tasks

These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.] 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics 3-5 Rectangle Comparison-No Units, Activity 9.3, Page 261 


 
Groundworks Reasoning About Measurement

4

 

 1-87
Brain-Compatible Activities for Mathematics 4-5 110-114
Problem Driven Math

4

 26-28, 68-70, 97-99

Math In Practice

Teaching Fourth-Grade Math

4

 Module 11

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

 

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Assessment

Learning Targets

rubric

  • Represent measurement quantities using number lines with measurement scales.
  • Represent measurement word problems.
  • Solve measurement word problems with any operation that include whole numbers, fractions, and decimals. Note: Computation with fractions and decimals is limited to the expectations of 4th grade standards.
  • Convert larger units into equivalent smaller units to solve a problem.

 

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.  

 

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.