# MA.4.M.1.2

Convert within a single system of measurement using the units: yards, feet, inches; kilometers, meters, centimeters, millimeters; pounds, ounces; kilograms, grams; gallons, quarts, pints, cups; liter, milliliter; and hours, minutes, seconds.

### Examples

Example: If a ribbon is 11 yards 2 feet in length, how long is the ribbon in feet?

Example: A gallon contains 16 cups. How many cups are in  gallons?

### Clarifications

Clarification 1: Instruction includes the understanding of how to convert from smaller to larger units or from larger to smaller units.

Clarification 2: Within the benchmark, the expectation is not to convert from grams to kilograms, meters to kilometers or milliliters to liters.

Clarification 3: Problems involving fractions are limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

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 see the relationships between the units they use for measurement. Students should begin to generalize that the smaller the unit is, the more precise measurement they will get, but will also need more of the unit to measure (MTR.5.1). Work in this benchmark builds from grade 3 foundations of using customary measurements (MA.3.M.1.1).
• For instruction, students need to use measuring devices in class to develop a sense of the attributes being measured to have a better understanding of the relationships between units.
• The number of units relates to the size of the unit. Students need to develop an understanding that there are 12 inches in 1 foot and 3 feet in 1 yard. Allow students to use rulers or a yardstick to discover these relationships among units of measurements. Using 12-inch rulers and yardsticks, students will see that three of the 12-inch rulers are the same length as a yardstick, so 3 feet is equivalent to one yard. A similar strategy can be used with rulers marked with centimeters and a meter stick to discover the relationships between centimeters and meters.
• To help students to visualize the size of units, they should be given multiple opportunities to measure the same object with different measuring tools.
• For example, have the students measure the length of a room with one-inch tiles, with one-foot rulers, and with yardsticks. Students should notice that it takes fewer yard sticks to measure the room than rulers or tiles and explain their reasoning.
• During instruction, have students record measurement relationships in a two-column table or t-chart.
• Students are not expected to memorize conversions. Students should be provided conversion tools (e.g., charts) during instruction.

### Common Misconceptions or Errors

• Students can assume that converting from smaller units to larger units (e.g., ounces to pounds), that multiplication is used, and when converting from larger units to smaller units (e.g., pounds to ounces), that division is used. To assist students with this misconception, expect them to estimate reasonable solutions.

### Strategies to Support Tiered Instruction

• Instruction includes demonstrating 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 also includes estimating reasonable solutions. The teacher models a think aloud and records the relationships on a two- column chart.
• For example, “If a ribbon is 11 yards 2 feet in length, how long is the ribbon in feet?”
• “I know that for every 1 yard, there are 3 feet. So, I can multiply the number of yards by 3 to convert to feet. I also know that for every 3 feet, there is one yard. I can divide the number of feet by 3 to convert to yards. Therefore 2 yards convert to 6 feet and 6 feet converts to 2 yards. To find out how many feet there are in 11 yards, 2 feet, I have to multiply the number of yards by 3. 11 yards × 3 = 33 feet. Next, I have to add the extra 2 feet. So, 11 yards, 2 feet converts to 35 feet.”
• Instruction includes using a bar model or tape diagram to show the relationship between the units. The teacher models a think aloud. o For example, “If a ribbon is 11 yards 2 feet in length, how long is the ribbon in feet?”
• “I know that for every 1 yard, there are 3 feet. So, I can multiply the number of yards by 3 to convert to feet. I also know that for every 3 feet, there is one yard. I can divide the number of feet by 3 to convert to yards. Therefore 2 yards convert to 6 feet and 6 feet converts to 2 yards. To find out how many feet there are in 11 yards, 2 feet, I have to multiply the number of yards by 3. 11 × 3 = 33. Next, I have to add the extra 2 feet. So, 11 yards, 2 feet converts to 35 feet.”

Calculate how many minutes there are in 1 week.

### Instructional Items

Instructional Item 1

There are 3 paperclip chains. Chain A is 50 inches long, Chain B is 4 $\frac{\text{1}}{\text{4}}$ feet long. Chain C is 1 yard long. Order the chains from the longest length to the shortest length.
• a. Chain A, Chain B, Chain C
• b. Chain B, Chain C, Chain A
• c. Chain C, Chain B, Chain A
• d. Chain B, Chain A, Chain C
*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.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (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.4.M.1.AP.2a: Explore relative sizes of measurement units within one system of units including yards, feet, inches; pounds, ounces; gallons, quarts, pints, cups; and hours, minutes.
MA.4.M.1.AP.2b: Using a conversion sheet, convert from a larger to a smaller unit within a single system of measurement using the units: yards, feet, inches; pounds, ounces; gallons, quarts, pints, cups; and hours, minutes. 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

Kesha and Juan:

Students are asked to solve a multi-step word problem that requires converting metric length units.

Type: Formative Assessment

Shopping List:

Students are asked to convert units of measure given with fractions and decimals using linear models.

Type: Formative Assessment

Converting Units of Time:

Students complete two tables by converting units of time from hours to minutes and minutes to seconds

Type: Formative Assessment

Conversions in the Metric System Part Two:

Students complete two tables by converting kilometers to meters and liters to milliliters.

Type: Formative Assessment

Conversions in the Metric System:

Students are asked to complete two tables by converting meters to centimeters and kilograms to grams.

Type: Formative Assessment

Conversions in the Customary System:

Students complete two tables by converting from feet to inches and pounds to ounces.

Type: Formative Assessment

## Lesson Plans

The Great Sneaker Design Challenge:

The practice of science is collaborative and exciting. This lesson engages students as a STEM team working collaboratively to provide a company with the best sneaker design.

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

Free Flight in Return for your Ranking!:

In this Model Eliciting Activity, MEA, students will rank four promotional deals that a travel agency is running. Before they make their decision, the students must find the discounted price by multiplying a whole number by a fraction and convert the duration of the trip to the same unit.

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

Park Planning:

Students are asked to plan a playground for a new park within a given budget and area limit. They will analyze the best use of playground equipment using a data table of area requirements and cost. Students will convert units within a single measurement system, calculate the area of a rectangle, and perform addition/subtraction calculations involving money using decimal notation.

Type: Lesson Plan

Let's Think in Small Units:

In this lesson students will make and complete tables to express larger unit measurements in terms of a smaller unit within one system of units. They will use the chart to make comparisons and explain their reasoning.

Type: Lesson Plan

Tennis Lessons:

This MEA asks students to take on the job of a tennis pro and decide which factors are most important in choosing a facility to take tennis lessons. Students will perform math calculations, create a two-column table for hours and minutes, develop a procedure to rank facilities, and provide written feedback through letters to a parent whose child needs group tennis lessons and writes letters to ask for advice. They will rank their choices from "best to worst" tennis lesson facilities. Students will provide a detailed written explanation for how they decided to rank factors and their solution for rating tennis lesson facilities.

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

Walk This Way:

Students will be asked to rank the different floor tiles for the playrooms in activity centers throughout community parks. They will need to take certain factors into consideration when making their rankings. They will also need to calculate the costs of installing the floor tiles using the given measurement of the playroom and the floor tiles. The "twist" will be that the client now needs to include a storage room for some of the playroom's equipment. They will need to decide if to use the same floor tile or different from the playroom and the additional cost of the storage closet. After, they will add the total costs of the playroom and the storage closet. They will report their findings and reasons by writing letters to the 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. 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

Wondrous Water Parks:

This activity requires students to apply their knowledge of unit conversions, speed calculation, and comparing fractions to solve the problem of which water park their class should choose to go on for their 5th grade class trip.

Type: Lesson Plan

Fish Ahoy Fish:

Students will work in groups to assist a client in purchasing different fish for a fish pond. From a data table, they will need to decide which type of fish and how many fish to purchase according to the size of the each pond. After, they will need to revisit a revised data table to make different selection of fish and calculate costs for the purchase of the fish.

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

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

On the Hunt for Measurements: Estimation, Area and Perimeter of Rectangles:

Students look for rectangular objects in the classroom or on the school campus that match the measurements for given clues. Students will estimate the measurements of the object, then take the exact measurements and use this information to determine its area and perimeter.

Type: Lesson Plan

## Original Student Tutorials

Game On Part Two: Measuring Distance with Customary Units:

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting miles to yards and feet in this sports-themed interactive tutorial.

This is Part 2 of a two-part series. Click HERE to open Part 1: Measuring Length with Customary Units.

Type: Original Student Tutorial

Game On Part One: Measuring Length with Customary Units:

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting yards to feet and inches, in this sports-themed interactive tutorial.

Type: Original Student Tutorial

## Tutorials

Unit Conversion: Ordering Metric Distances Example:

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

Type: Tutorial

Time Word Problem: When to Leave to Get Home on Time:

In this Khan Academy tutorial video Chris is told to be home by 6:15. You know the number of minutes it takes him to get home. What time should he leave?

Type: Tutorial

U.S. Customary Units: Distance:

This Khan Academy tutorial video presents conventional examples that use specific customary units

Type: Tutorial

How to convert kilograms to milligrams and tons to ounces:

In this tutorial video from Khan Academy, explore the differences and similarities involved when converting between measurements in the metric and customary systems.

Type: Tutorial

How to convert gallons to quarts, quarts to pints, pints to cups, and cups to ounces:

In this video tutorial from Khan Academy, explore converting between gallons, quarts, pints, cups, and fluid ounces.

Type: Tutorial

How to convert kilometers to meters and meters centimeters:

In this video tutorial from Khan Academy, explore conversion within metric units of length, such as: kilometers, meters and centimeters.

Type: Tutorial

How to convert hours to minutes and minutes to seconds:

In this video tutorial from Khan Academy, explore conversion of units of time between hours, minutes and seconds.

Type: Tutorial

U.S. customary units: fluid volume:

In this video tutorial from Khan Academy, explore U.S. customary units of fluid volume (teaspoon, tablespoon, fluid ounce, cup, pint, quart, and gallon).

Type: Tutorial

U.S. customary units: weight:

In this video tutorial from Khan Academy, explore pounds, ounces and tons.

Type: Tutorial

## STEM Lessons - Model Eliciting Activity

Fish Ahoy Fish:

Students will work in groups to assist a client in purchasing different fish for a fish pond. From a data table, they will need to decide which type of fish and how many fish to purchase according to the size of the each pond. After, they will need to revisit a revised data table to make different selection of fish and calculate costs for the purchase of the fish.

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

Free Flight in Return for your Ranking!:

In this Model Eliciting Activity, MEA, students will rank four promotional deals that a travel agency is running. Before they make their decision, the students must find the discounted price by multiplying a whole number by a fraction and convert the duration of the trip to the same unit.

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

Park Planning:

Students are asked to plan a playground for a new park within a given budget and area limit. They will analyze the best use of playground equipment using a data table of area requirements and cost. Students will convert units within a single measurement system, calculate the area of a rectangle, and perform addition/subtraction calculations involving money using decimal notation.

Tennis Lessons:

This MEA asks students to take on the job of a tennis pro and decide which factors are most important in choosing a facility to take tennis lessons. Students will perform math calculations, create a two-column table for hours and minutes, develop a procedure to rank facilities, and provide written feedback through letters to a parent whose child needs group tennis lessons and writes letters to ask for advice. They will rank their choices from "best to worst" tennis lesson facilities. Students will provide a detailed written explanation for how they decided to rank factors and their solution for rating tennis lesson facilities.

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

The Great Sneaker Design Challenge:

The practice of science is collaborative and exciting. This lesson engages students as a STEM team working collaboratively to provide a company with the best sneaker design.

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

Walk This Way:

Students will be asked to rank the different floor tiles for the playrooms in activity centers throughout community parks. They will need to take certain factors into consideration when making their rankings. They will also need to calculate the costs of installing the floor tiles using the given measurement of the playroom and the floor tiles. The "twist" will be that the client now needs to include a storage room for some of the playroom's equipment. They will need to decide if to use the same floor tile or different from the playroom and the additional cost of the storage closet. After, they will add the total costs of the playroom and the storage closet. They will report their findings and reasons by writing letters to the 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. 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

Wondrous Water Parks:

This activity requires students to apply their knowledge of unit conversions, speed calculation, and comparing fractions to solve the problem of which water park their class should choose to go on for their 5th grade class trip.

## MFAS Formative Assessments

Conversions in the Customary System:

Students complete two tables by converting from feet to inches and pounds to ounces.

Conversions in the Metric System:

Students are asked to complete two tables by converting meters to centimeters and kilograms to grams.

Conversions in the Metric System Part Two:

Students complete two tables by converting kilometers to meters and liters to milliliters.

Converting Units of Time:

Students complete two tables by converting units of time from hours to minutes and minutes to seconds

Kesha and Juan:

Students are asked to solve a multi-step word problem that requires converting metric length units.

Shopping List:

Students are asked to convert units of measure given with fractions and decimals using linear models.

## Original Student Tutorials Mathematics - Grades K-5

Game On Part One: Measuring Length with Customary Units:

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting yards to feet and inches, in this sports-themed interactive tutorial.

Game On Part Two: Measuring Distance with Customary Units:

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting miles to yards and feet in this sports-themed interactive tutorial.

This is Part 2 of a two-part series. Click HERE to open Part 1: Measuring Length with Customary Units.

## Student Resources

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

## Original Student Tutorials

Game On Part Two: Measuring Distance with Customary Units:

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting miles to yards and feet in this sports-themed interactive tutorial.

This is Part 2 of a two-part series. Click HERE to open Part 1: Measuring Length with Customary Units.

Type: Original Student Tutorial

Game On Part One: Measuring Length with Customary Units:

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting yards to feet and inches, in this sports-themed interactive tutorial.

Type: Original Student Tutorial

## Tutorials

Unit Conversion: Ordering Metric Distances Example:

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

Type: Tutorial

Time Word Problem: When to Leave to Get Home on Time:

In this Khan Academy tutorial video Chris is told to be home by 6:15. You know the number of minutes it takes him to get home. What time should he leave?

Type: Tutorial

U.S. Customary Units: Distance:

This Khan Academy tutorial video presents conventional examples that use specific customary units

Type: Tutorial

How to convert kilograms to milligrams and tons to ounces:

In this tutorial video from Khan Academy, explore the differences and similarities involved when converting between measurements in the metric and customary systems.

Type: Tutorial

How to convert gallons to quarts, quarts to pints, pints to cups, and cups to ounces:

In this video tutorial from Khan Academy, explore converting between gallons, quarts, pints, cups, and fluid ounces.

Type: Tutorial

How to convert kilometers to meters and meters centimeters:

In this video tutorial from Khan Academy, explore conversion within metric units of length, such as: kilometers, meters and centimeters.

Type: Tutorial

How to convert hours to minutes and minutes to seconds:

In this video tutorial from Khan Academy, explore conversion of units of time between hours, minutes and seconds.

Type: Tutorial

U.S. customary units: fluid volume:

In this video tutorial from Khan Academy, explore U.S. customary units of fluid volume (teaspoon, tablespoon, fluid ounce, cup, pint, quart, and gallon).

Type: Tutorial

U.S. customary units: weight:

In this video tutorial from Khan Academy, explore pounds, ounces and tons.

Type: Tutorial

## Parent Resources

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

## Tutorials

How to convert kilograms to milligrams and tons to ounces:

In this tutorial video from Khan Academy, explore the differences and similarities involved when converting between measurements in the metric and customary systems.

Type: Tutorial

How to convert gallons to quarts, quarts to pints, pints to cups, and cups to ounces:

In this video tutorial from Khan Academy, explore converting between gallons, quarts, pints, cups, and fluid ounces.

Type: Tutorial

How to convert kilometers to meters and meters centimeters:

In this video tutorial from Khan Academy, explore conversion within metric units of length, such as: kilometers, meters and centimeters.

Type: Tutorial

How to convert hours to minutes and minutes to seconds:

In this video tutorial from Khan Academy, explore conversion of units of time between hours, minutes and seconds.

Type: Tutorial

U.S. customary units: fluid volume:

In this video tutorial from Khan Academy, explore U.S. customary units of fluid volume (teaspoon, tablespoon, fluid ounce, cup, pint, quart, and gallon).

Type: Tutorial

U.S. customary units: weight:

In this video tutorial from Khan Academy, explore pounds, ounces and tons.

Type: Tutorial