# MA.5.M.1.1

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.)
Strand: Measurement
Status: State Board Approved

## Benchmark Instructional Guide

• 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), and becomes a part of a larger context of ratios and rates in grade 6 (MA.6.AR.3.5).
• 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).

### 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).

### 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.

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

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 $\frac{\text{1}}{\text{2}}$ 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

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 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 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
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

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Converting Metric Measurement Units :

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

Type: Formative Assessment

Converting Customary Measurement Units :

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

Type: Formative Assessment

Party Planning:

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

Type: Formative Assessment

Candy and Ribbon:

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

Type: Formative Assessment

## Lesson Plans

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.

Type: Lesson Plan

Mechanical Hands:

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

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Where on Earth is (teacher name)?!:

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

Type: Lesson Plan

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

Type: Lesson Plan

Shot-Put Conversion Activity (Day 1 of 2):

Students will have fun learning how to convert units within the metric system.Â  Students are engaged and will complete hands-on activity to learn how the metric system is based on powers of ten.Â  There are two lessons in this unit.Â  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.Â  Â

Â

Type: Lesson Plan

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.

Type: Lesson Plan

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

Type: Lesson Plan

Workouts That Work:

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

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Interplanetary Zoo:

Students will explore how animal adaptations and habitats are related whenÂ 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.

Type: Lesson Plan

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.

Type: Lesson Plan

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

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

## Original Student Tutorials

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.

Type: Original Student Tutorial

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.

Type: Original Student 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.

Type: Original Student Tutorial

## Perspectives Video: Teaching Idea

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.

Type: Perspectives Video: Teaching Idea

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

Ball Bounce Experiment:

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

Type: Teaching Idea

## Tutorials

Metric System: Units of Volume:

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

Type: Tutorial

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.

Type: Tutorial

Unit Conversion: Ordering Metric Distances Example:

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

Type: Tutorial

## Video/Audio/Animation

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.

Type: Video/Audio/Animation

## STEM Lessons - Model Eliciting Activity

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

Interplanetary Zoo:

Students will explore how animal adaptations and habitats are related whenÂ 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.

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.

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.

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

Workouts That Work:

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

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.

## MFAS Formative Assessments

Candy and Ribbon:

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

Converting Customary Measurement Units :

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

Converting Metric Measurement Units :

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

Party Planning:

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

## Original Student Tutorials Mathematics - Grades K-5

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.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

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.

Type: Original Student Tutorial

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.

Type: Original Student 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.

Type: Original Student Tutorial

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

Metric System: Units of Volume:

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

Type: Tutorial

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.

Type: Tutorial

Unit Conversion: Ordering Metric Distances Example:

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

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.