Standard #: MA.5.M.1.1


This document was generated on CPALMS - www.cpalms.org



Solve multi-step real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement.


Examples


There are 60 minutes in 1 hour, 24 hours in 1 day and 7 days in 1 week. So, there are 60×24×7 minutes in one week which is equivalent to 10,080 minutes.

Clarifications


Clarification 1: Within the benchmark, the expectation is not to memorize the conversions.

Clarification 2: Conversions include length, time, volume and capacity represented as whole numbers, fractions and decimals.



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 5
Strand: Measurement
Standard: Convert measurement units to solve multi-step problems.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • NA

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

  • The purpose of this benchmark is for students to be able to understand the relationship between units of measure through problem solving. This benchmark builds on Grade 4 concepts of converting measurement units (MA.4.M.1.2), where students acquired an understanding of conversion rules (e.g. multiply to change a larger unit to a smaller unit and divide to change a smaller unit to a larger unit.) This foundational concept is applicable to the conversion of any unit of measure. Additionally, in Grade 6 (MA.6.AR.3.5), students further enhance their understanding and establish connections between measurement conversion and the broader context of ratios and rates. During Grade 5, students utilize ratio reasoning to perform unit conversions. The application of ratio reasoning relies on procedures learned through the multiplication and division of fractions, skills that prove valuable in the context of measurement conversion. 
  • Instruction allows students to convert measurements flexibly. 
    • For example, when finding the number of inches in 2 yards, students may start with inches, feet or yards when calculating. Classroom discussion should compare those conversions to explore their similarities and differences (MTR.2.1, MTR.4.1). 
  • For students to have a better understanding of the relationships between units, it is important for teachers to allow students to have practice with tools during instruction. This will show students how the number of units relates to the size of the unit. 
    • For example, for students to discover converting inches to yards, teachers can have them use 12-inch rulers and yardsticks. This will allow students to see that three of the 12-inch rulers are equivalent to one yardstick (3 × 12 inches = 36 inches; 36 inches = 1 yard), so that students understand that there are 12 inches in 1 foot and 3 feet in 1 yard. Using this knowledge, students will be able to determine whether to multiply or divide when making conversions (MTR.2.1). 
  • When moving into real-world problem solving, it is important to begin with problems that allow for renaming the units to represent the solution before using problems that require renaming to find the solution (MTR.7.1). 
  • During instruction, teachers can integrate the relationship between metric units to support student understanding of the place value system. Students utilize their understanding of the patterns of multiplying and dividing with zeros when working with metric conversions. For students to build understanding of metric units, students can list units in order from greatest to least and practice conversion in relation to the place value position. 
  • For students to have a better understanding of measurement conversions and proportional relationships, allow students to have exposure to attributes of items being measured. Students should develop a foundation of the relative size of each unit and should have practice converting from a small unit to a larger unit and from a large unit to a smaller unit.

 

Common Misconceptions or Errors

  • Students confuse renaming units of measurement with the renaming that they do with whole numbers and place value. 
    • For example, when subtracting 6 inches from 3 feet, they get 2 feet 4 inches because they think of subtracting 6 inches from 30 inches. Students need to pay attention to the unit of measurement which dictates the renaming (inches in this example) and the number to use (12 inches in a foot instead of 10 inches in a foot). 
  • Students confuse renaming units of measurements when converting mixed customary measures because, unlike metric measurement, the customary measurements are not expressed using the base-ten system. 
    • For example, when adding 3 feet 5 inches to 4 feet 9 inches, they get 7 feet 14 inches. Students may not understand that 14 inches can be converted into 1 foot 2 inches, for an overall answer of 8 feet 2 inches. 
  • Students may not know which operation to use when converting measurements. During instruction, teachers can use manipulatives and a real-world approach so that students make connections to units. For example, teachers can use containers that equal cups, pints, quarts, and gallons when giving explicit instruction on units of liquid capacity. Real- world application allows students to have a deeper understanding of the relative size of units that may be abstract. 
  • A common mistake that students may make when encountering word problems is when problems contain information in different units. Students should convert different units to one common unit before calculating.

 

Strategies to Support Tiered Instruction

  • Instruction includes deciding which operation to use when converting from smaller units to larger units (e.g., ounces to pounds) and when converting from larger units to smaller units (e.g., pounds to ounces). Instruction should also include estimating reasonable solutions. 
    • For example, the teacher models a think aloud for which numbers to use based on the units of measurement and record the relationships on a chart. 
      • How many minutes are in 1 week? 
      • There are 60 minutes in 1 hour, 24 hours in 1 day and 7 days in 1 week. So, there are 60 × 24 × 7 minutes in one week which is equivalent to 10,080 minutes. 

chart

  • Instruction includes using a bar model or tape diagram to show the relationship between the units.

 

Instructional Tasks

Instructional Task 1 (MTR.6.1, MTR.7.1) 

Zevah is helping her mom plan her sister’s surprise birthday party. 
  • Part A. The recipe to make one bowl of punch is shown below. How many cups of punch will they be able to serve at the party if they only make one bowl of punch and there is no punch leftover in the bowl? 
  • Part B. At the party, Zevah wants each balloon to have a string that is 250 centimeters long. The string she wants to buy comes in rolls of 30 meters. How many rolls of string does Zevah need to buy if she plans to have 36 balloons at the party?

 

Instructional Items

Instructional Item 1 

  • Michael is measuring fabric for the costumes of a school play. He needs 11.5 meters of fabric. He has 280 centimeters of fabric. How many more centimeters of fabric does he need? 

 

Instructional Item 2 

A recipe requires 24 ounces of milk. Edwin has only a 12 cup measuring cup. How many measuring cups of milk will Edwin need? 
  • a. 6 
  • b. 12 
  • c. 18 
  • d. 24

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.5.M.1.AP.1a Using a conversion sheet, convert within a single system of measurement using the units: miles, yards, feet, inches; pounds, ounces; gallons, quarts, pints, cups; and hours, minutes. Only whole number measurements may be used.
MA.5.M.1.AP.1b Using a conversion sheet, solve one-and two-step real-world problems that involve converting measurement units (i.e., miles, yards, feet, inches; pounds, ounces; gallons, quarts, pints, cups; and hours, minutes) to equivalent measurements within a single system of measurement. Only whole number measurements may be used.


Related Resources

Formative Assessments

Name Description
Converting Metric Measurement Units

Students are asked to make metric measurement conversions involving length and mass.

Converting Customary Measurement Units

Students are asked to make customary measurement conversions involving weight and time.

Party Planning

Students are asked to solve two multi-step word problems that require converting units.

Candy and Ribbon

Students are asked to solve multi-step word problems that require converting units.

Lesson Plans

Name Description
Disaster Relief

Students will analyze data to develop a resupply schedule for a humanitarian mission following a natural disaster. They will apply mathematical operations over multiple steps to minimize the operational cost of the humanitarian mission.

This is an open-ended engineering design lesson where students will develop a model to help them solve a problem. There are no “right” answers as the lesson is focused on the process of developing a solution and the skills and reasoning behind the process. Students should be given the freedom to interpret the problem and parameters in unique ways to pursue their own lines of thinking in producing a solution.

I'll Fly Today

In this Model Eliciting Activity, MEA, students will use the provided data to calculate travel time and total cost after tax. Students will consider this data and other provided criteria to assist a travel agent in determining which airline to choose for a client.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Solving Multi-Step Word Problems With "Undecided" Colonists

Students will be divided into groups and given a set of multi-step real-world problems to solve. The word problems will be specific to topics important to the neutral colonists during the American Revolution. The lesson will conclude with a class discussion of the word problems tying the math and civics together in this integrated lesson plan.

Mechanical Hands

In this STEM design challenge, students will build a working hand model to examine the function of the skeletal and muscular systems.

Marbelous Pool Noodle Ramps

In this lesson, students will build a ramp out of a pool noodle and use it to launch a marble across the room. Students will investigate by adjusting the height and slope of the ramp and record their findings on a data sheet. Students will practice collecting and analyzing data and will investigate the importance of performing repeated experimental trials. Students will practice converting metric units of distance as well as the addition and division of decimals to find the mean of a small data set.

Natural Builders - STEM Engineering Design Challenge

In this lesson, students will investigate and explain balanced and unbalanced forces as they design a building for Miami Beach that is inspired by Florida's natural environment. In this challenge/lesson, students must design a building model that is at least thirty centimeters tall, features two elements that move in the wind, and can also withstand the wind.

Shot-Put Conversion Activity (Day 2 of 2)

This is Lesson 2 of a two-part unit. Resource 73257: Shot-Put Conversion Activity Day 1 of 1 is the first lesson. Students will have fun learning to convert units within the metric system. Students are engaged and will complete hands-on activities to learn how the metric system is based on powers of ten. In this lesson, students will compete against one another by seeing who can throw the shot-put the farthest and convert the distance measured into different metric units.

Where on Earth is (teacher name)?!

Students practice converting metric and customary measurements, while helping their teacher travel on summer vacation in Europe.

Metric Length Madness

This lesson will help students to convert metric units of length, such as kilometers, meters, centimeters, and millimeters.

Shot-Put Conversion Activity (Day 1 of 2)

Students will have fun learning how to convert units within the metric system.  Students are engaged and will complete hands-on activity to learn how the metric system is based on powers of ten.  There are two lessons in this unit.  In the 2nd lesson (Resource 73766), students will compete against one another by seeing who can throw the shot-put the farthest and convert this distance into different metric units.   

 
Mars Exploration Administration

Students will be given the opportunity to design a conductivity tester for astronauts to use on Mars. Students will then get to use a 3D printed tester to check common items for potential conductivity and then to redesign their tester.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Help Save Atreyu!

In this activity students will analyze data about the conditions in a hermit crab habitat to determine which one will be best to meet the animal’s needs.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Workouts That Work

Students will create a rating system for workout DVD's according to weight loss, muscle toning, and increased physical condition.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Museum Dilemma

In this MEA, students evaluate the contributions of various explorers to help a museum select the subject who provided the most impact on Western development for a new exhibit. Students will need to convert units to have the necessary information to help come up with a solution to the problem.

Pounds to Ounces: MEA

The client, Twi N. Key Bakery, wants your students to help them determine which product to sell in your school. Along the way your students will have to convert pounds to ounces as well as survey their peers.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Interplanetary Zoo

Students will explore how animal adaptations and habitats are related when extraterrestrials from an Earth-like planet send the Earth a gift of animals from their planet and the animals must be placed in a zoo. Students will use the characteristics of the animals to figure out the habitat the animals are best adapted to.

X-treme Roller Coasters

This MEA asks students to assist Ms. Joy Ride who is creating a virtual TV series about extreme roller coasters. They work together to determine which roller coaster is most extreme and should be featured in the first episode. Students are presented with research of five extreme roller coasters and they must use their math skills to convert units of measurements while learning about force and motion.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Stand Up and Cheer

This MEA asks the students to compare items to be given to fans attending a college homecoming football game.

Students will use multi-digit multiplication and measurement conversion while comparing data on the items. They will also take into account fan reviews of the items which should create interesting student discussions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Getting Dry

This MEA asks the students to compare hand drying products based on: initial cost, replacement cost and absorbency. Students will provide the "top choice" to the principal of the school and explain how they arrived at the solution. In the twist, students will be asked to consider the environmental impact of the products and reevaluate their conclusions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

New Frozen Yogurt Store

This MEA asks students to decide which factors are important in developing a successful frozen yogurt (froyo) store in order to compete with and become the best store in the area. Students will provide feedback to an entrepreneur who is looking to open a frozen yogurt store. They will rank order their choices of the most successful to least successful store. Students will provide a detailed written explanation for how they decided to rank factors and their solution rating existing stores from best to worst.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Conversion Excursion

This lesson will help students understand the importance of the metric system and see the connection between place value and metric system charts. The students will use a metric system chart to convert between metric units to solve real-world problems.

Give An Inch, Take A Foot

In this activity students practice measuring techniques by measuring different objects and distances around the classroom. They practice using different scales of measurement in metric units and estimation.

Original Student Tutorials

Name Description
A Day at the Park: Time

Learn how to convert time from seconds to minutes, minutes to hours, and hours to days. In this interactive tutorial, you will also practice converting time to fractional amounts.

Healthy Distance: Social Distancing Measurement Conversions

Learn why it's sometimes important to use social distancing to reduce the spread of germs and how to estimate and convert this customary distance with this interactive tutorial.

Measuring to Build a Ramp

Learn how to convert among different-sized customary units of weight, length, capacity, and units of time at the skate park in the this interactive tutorial.

Perspectives Video: Teaching Idea

Name Description
Bicycle Mathematics: Speed and Distance Calculations

Cycling involves a lot of real-time math when you use an on-board computer. Learn about lesson ideas and how computers help with understanding performance.

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Tasks

Name Description
Minutes and Days

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Converting Fractions of a Unit into a Smaller Unit

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

Teaching Idea

Name Description
Ball Bounce Experiment

Students investigate different balls' abilities to bounce and represent the data they collect graphically.

Tutorials

Name Description
Metric System: Units of Volume

This Khan Academy tutorial video illustrates the conversion equivalence of liters, milliliters, and kiloliters.

Unit Measurement Word Problem: Distance (US Customary)

This Khan Academy tutorial video develops a visual diagram to use to solve a distance problem that requires converting feet to yards and other computations.

Unit Conversion: Ordering Metric Distances Example

This Khan Academy tutorial video demonstrates a strategy for ordering four different-sized metric length units.

Video/Audio/Animation

Name Description
Soybean growth rate response to touch

A time-lapse video showing differential growth rates for touch-treated seedlings and control seedlings. This would be appropriate for lessons about plant growth responses to environmental stress and graphing growth rate. Plants were grown in a vermiculite soilless medium with calcium-enhanced water. No other minerals or nutrients were used. Plants were grown in a dark room with specially-filtered green light. The plants did not grow by cellular reproduction but only by expansion of existing cells in the hypocotyl region below the 'hook'.
Video contains three plants in total. The first two plants to emerge from the vermiculite medium are the control (right) and treatment (left) plants. A third plant emerges in front of these two but is removed at the time of treatment and is not relevant except to help indicate when treatment was applied (watch for when it disappears). When that plant disappears, the slowed growth rate of the treatment plant is apparent.
Treatment included a gentle flexing of the hypocotyl region of the treatment seedling for approximately 5 seconds. A rubber glove was used at this time to avoid an contamination of the plant tissue.
Some video players allow users to 'scrub' the playback back and forth. This would help teachers or students isolate particular times (as indicated by the watch) and particular measurements (as indicated by the cm scale). A graph could be constructed by first creating a data table and then plotting the data points from the table. Multiple measurements from the video could be taken to create an accurate graph of the plants' growth rates (treatment vs control).
Instructions for graphing usage:
The scale in the video is in centimeters (one cm increments). Students could observe the initial time on the watch in the video and use that observation to represent time (t) = 0. For that value, a mark could be made to indicate the height of the seedlings. As they advance and pause the video repeatedly, the students would mark the time (+2.5 hours for example) and mark the related seedling heights. It is not necessary to advance the video at any regular interval but is necessary to mark the time and related heights as accurately as possible. Students may use different time values and would thus have different data sets but should find that their graphs are very similar. (Good opportunity to collect data from real research and create their own data sets) It is advised that the students collect multiple data points around the time where the seedling growth slows in response to touch to more accurately collect information around that growth rate slowing event. The resulting graph should have an initial growth rate slope, a flatter slope after stress treatment, and a return to approximately the same slope as seen pre-treatment. More data points should yield a more thorough view of this. This would be a good point to discuss. Students can use some of their data points to calculate approximate pre-treatment, immediate post-treatment, and late post-treatment slopes for both the control and treatment seedlings.
This video was created by the submitter and is original content.
Full screen playback should be an option for most video players. Video quality may appear degraded with a larger image but this may aid viewing the watch and scale for data collection.

Student Resources

Original Student Tutorials

Name Description
A Day at the Park: Time:

Learn how to convert time from seconds to minutes, minutes to hours, and hours to days. In this interactive tutorial, you will also practice converting time to fractional amounts.

Healthy Distance: Social Distancing Measurement Conversions:

Learn why it's sometimes important to use social distancing to reduce the spread of germs and how to estimate and convert this customary distance with this interactive tutorial.

Measuring to Build a Ramp:

Learn how to convert among different-sized customary units of weight, length, capacity, and units of time at the skate park in the this interactive tutorial.

Problem-Solving Tasks

Name Description
Minutes and Days:

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Converting Fractions of a Unit into a Smaller Unit:

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

Tutorials

Name Description
Metric System: Units of Volume:

This Khan Academy tutorial video illustrates the conversion equivalence of liters, milliliters, and kiloliters.

Unit Measurement Word Problem: Distance (US Customary):

This Khan Academy tutorial video develops a visual diagram to use to solve a distance problem that requires converting feet to yards and other computations.

Unit Conversion: Ordering Metric Distances Example:

This Khan Academy tutorial video demonstrates a strategy for ordering four different-sized metric length units.



Parent Resources

Problem-Solving Tasks

Name Description
Minutes and Days:

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Converting Fractions of a Unit into a Smaller Unit:

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.



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