# MA.4.M.2.1

Solve two-step real-world problems involving distances and intervals of time using any combination of the four operations.

### Clarifications

Clarification 1: Problems involving fractions will include addition and subtraction with like denominators and multiplication of a fraction by a whole number or a whole number by a fraction.
Clarification 2: Problems involving fractions are limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.
Clarification 3: Within the benchmark, the expectation is not to use 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

• NA

### Purpose and Instructional Strategies

The purpose of this benchmark is to connect concepts of unit conversions to time and distance and solve problems with these conversions. In grade 3, students solved one- and two-step elapsed time problems without converting units of time or crossing from a.m. to p.m. or p.m. to a.m. (MA.3.M.2.2).
• For distance problems, students may need to understand multiplicative comparison (e.g., 20 is twice as many as 10).
• For instruction, an open number line is a strategy students can use to solve elapsed time problems.
• Students need to spend time solving problems crossing between a.m. and p.m., and vice- versa.
• Students should also have a firm understanding of the terms quarter hour (15 minutes) and half hour (30 minutes).

### Common Misconceptions or Errors

• Students can confuse when time crosses the hour because it does not follow the base-ten pattern where they are familiar. For example, students can misinterpret that the elapsed time between 9:55 a.m. and 10:05 a.m. and state that the elapsed time is 50 minutes because they have found the difference from 55 to 105. The use of number lines and clocks side-by-side help students build understanding about how elapsed time is calculated.

### Strategies to Support Tiered Instruction

• Instruction includes the use of number lines and clocks side-by-side to help students build understanding about how elapsed time is calculated.
• Instruction includes using a number line and counting by ones to demonstrate what happens when time crosses the hour because it does not follow the familiar base ten pattern.
• For example, use a number line to find the elapsed time between 9:55 a.m. and 10:05 a.m. and explain what happens when time crosses the hour at 10:00 a.m.
• Instruction includes demonstrating what happens when time crosses the hour because it does not follow the familiar base ten pattern.
• For example, instruction may include using a geared manipulative (Judy) clock to find the elapsed time between 9:55 a.m. and 10:05 a.m. Students move the minute of the hand one minute at a time from 9:55 to 10:00. After each minute, the teacher asks the students to record what time it is. The teacher has students pay special attention to what happens when the minute hand moves from 9:59 to the next minute.

Steve drove 2,465 miles away to college. On Parents’ Weekend, his parents drove the distance round trip from home, with an additional 385 miles traveled to visit his sister on their return trip. How many total miles did his parents drive on Parents’ Weekend?

### Instructional Items

Instructional Item 1

After lunch, Billy walked the dog for 17 minutes and then immediately after, did his chores for 58 minutes. If he finished his chores at 12:15 p.m., what time did he start walking the dog?
• a. 1:30 p.m.
• b. 1:13 p.m.
• c. 11:17 a.m.
• d. 11:00 a.m.

*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.2.AP.1a: Solve one- and two-step real-world problems involving distances (i.e., inches, feet, yards, miles) in whole numbers using any combination of the four operations.
MA.4.M.2.AP.1b: Solve one-step real-world problems involving intervals of time in whole numbers using any of the four operations.

## Related Resources

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

## Formative Assessment

Piano Lessons:

Students are asked to use a number line to answer elapsed time questions.

Type: Formative Assessment

## Lesson Plans

Help Me Build a Roller Coaster:

Students will evaluate different factors for building the right roller coaster.

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

All-Star Track Runners:

Students will help a track coach determine which shoe is the best to purchase for his team. Students will be required to convert measurements initially and then rank the shoes from best to worst based on the data provided.

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

## Tutorials

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

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

## 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

All-Star Track Runners:

Students will help a track coach determine which shoe is the best to purchase for his team. Students will be required to convert measurements initially and then rank the shoes from best to worst based on the data provided.

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

Help Me Build a Roller Coaster:

Students will evaluate different factors for building the right roller coaster.

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

Piano Lessons:

Students are asked to use a number line to answer elapsed time questions.

## Student Resources

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

## Tutorials

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

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

## Parent Resources

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

## 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