MA.6.NSO.2.3

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Solve multi-step real-world problems involving any of the four operations with positive multi-digit decimals or positive fractions, including mixed numbers.

Clarifications

Clarification 1: Within this benchmark, it is not the expectation to include both decimals and fractions within a single problem.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Number Sense and Operations
Standard: Add, subtract, multiply and divide positive rational numbers.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Area Model
  • Commutative property of Multiplication
  • Dividend
  • Divisor
  • Expression

 

Vertical Alignment

Previous Benchmarks


Next Benchmarks

 

Purpose and Instructional Strategies

In grade 5, students solved multi-step real-world problems involving the four operations with whole numbers as well as addition, subtraction and multiplication for solving real-world problems with fractions and for solving problems with decimals involving money, area and perimeter. In grade 6, students solve multi-step real-world problems with positive fractions and decimals. In grade 7, students will solve real-world problems involving any of the four operations with positive and negative rational numbers. 
  • This benchmark is the culmination of MA.6.NSO.2. It is built on the skills found in MA.6.NSO.2.1 and MA.6.NSO.2.2, so instruction provides practice of these skills within real-world contexts (MTR.5.1, MTR.7.1).
  • Instruction includes engaging in questions such as:
    • What do you know from the problem?
    • What is the problem asking you to find?
    • Are you putting groups together? Taking groups apart? Or both?
    • Are the groups you are working with the same sizes or different sizes?
    • Can you create a visual model to help you understand or see patterns in your problem?
  • Students should have experience using technology with decimals and fractions as they occur in the real world (MTR.7.1). This experience will help prepare students to work with all rational numbers in grade 7 and with irrational numbers in grade 8.

 

Common Misconceptions or Errors

  • Students may incorrectly oversimplify a problem by mechanically circling the numbers, underlining the question, and boxing in key words and then jumping to an answer, or procedure, without taking the time to comprehend the context or situation (MTR.2.1, MTR.4.1, MTR.5.1, MTR.7.1).
  • Students may incorrectly apply rules for adding or subtracting decimals to multiplication of decimals, believing place values must be aligned.
  • Students may confuse the lining up of place values when multiplying or dividing vertically by omitting or forgetting to include zeros as place holders in the partial products or quotients.
  • Students may forget that common denominators are not necessary for multiplying or dividing fractions.
  • Students may incorrectly assume that multiplication results in a product that is larger than the two factors. Instruction continues with students assessing the reasonableness of their answers by determining if the product will be greater or less than the factors within the given context. 
  • Students may incorrectly assume that division results in a quotient that is smaller than the dividend. Instruction continues with students assessing the reasonableness of their answers by determining if the quotient will be greater or less than the dividend within the given context.

 

Strategies to Support Tiered Instruction

  • Instruction includes using visual models to illustrate and make meaning of situations represented in word problems.
  • Instruction includes the use of estimation to ensure the proper placement of the decimal point in the final product or quotient of decimals.
    • For example, if finding the product of 12.3 and 4.8, students should estimate the product to be close to 60, by using 12 and 5 as friendly numbers, then apply the decimal to the actual product of 123 and 48, which is 5904. Based on the estimate, the decimal should be placed after 59 to produce 59.04.
  • Teacher encourages students with a firm understanding of multiplying and dividing fractions to convert decimal values into equivalent fractional forms and then perform the desired operation and convert the solution back to decimal form.
  • Teacher provides opportunities for students who have a firm understanding of multiplying and dividing decimals to convert the provided fractional values to their equivalent decimal form before performing the desired operation and converting the solution back to fractional form.
  • Teacher provides opportunities for students to comprehend the context or situation by engaging in questions such as:
    • What do you know from the problem?
    • Can you create a visual model to help you understand or see patterns in your problem?
  • Teacher provides graph paper to utilize while applying an algorithm for multiplying or dividing to keep numbers lined up and help students focus on place value.
  • Instruction includes providing opportunities to reinforce place values with the use of base ten blocks or hundredths grids.
  • Instruction includes the co-creation of a graphic organizer utilizing the mnemonic device S.I.R. (Same, Inverse Operation, Reciprocal) for dividing fractions, which encourages the use of correct mathematical terminology, and including examples of applying the mnemonic device when dividing fractions, whole numbers, and mixed numbers.
  • Teacher provides students with flash cards to practice and reinforce academic vocabulary.
  • Instead of multiplying by the reciprocal to divide fractions, an alternative method could include rewriting the fractions with a common denominator, dividing the numerators, and then dividing the denominators.
    • For example, 56 ÷ 32 is equivalent to 56 ÷ 96 which is equivalent to 5/91 which is equivalent to 59.
  • Instruction includes the use of a three-read strategy. Students read the problem three different times, each with a different purpose.
    • First, read the problem with the purpose of answering the question: What is the problem, context, or story about?
    • Second, read the problem with the purpose of answering the question: What are we trying to find out?
    • Third, read the problem with the purpose of answering the question: What information is important in the problem?
  • Instruction provides opportunities to assess the reasonableness of answers by determining if the product will be greater or less than the factors within the given context.
  • Instruction provides opportunities to assess the reasonableness of answers by determining if the quotient will be greater or less than the dividend within the given context.

 

Instructional Tasks

Instructional Task 1 (MTR.3.1, MTR.6.1)
Janie is at the gas station. She has $53.25 and buys a sandwich that costs $7.68 and a drink for $0.97.
  • Part A. After she buys the sandwich and drink, how much money will Janie have left?
  • Part B. Janie wants to buy 10 gallons of gas with the remaining money. What is the highest price per gallon that she can afford? Use words or numbers to show your work.

 

Instructional Items

Instructional Item 1
Candy comes in 312 pound bags. At a class party, the boys in the class ate 214 bags of candy and the girls in the class ate 113 bags. How many pounds of candy did the class eat?

Instructional Item 2
Tina’s SUV holds 18.5 gallons of gasoline. If she has 4.625 gallons in her car when she stops to fill it up. How much money will she spend to fill up her car if the current price for gas is $2.57 per gallon?

 

*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.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 - 2024, 2024 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.NSO.2.AP.3a: Solve one-step real-world problems involving any of the four operations with positive decimals ranging from the hundreds to hundredth place value.
MA.6.NSO.2.AP.3b: Solve one-step real-world problems involving any of the four operations with positive fractions and mixed numbers with like denominators.

Related Resources

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

Formative Assessments

Multiplying By Ten Three Times:

Students consider why a number multiplied by 10 to the third power will have three zeros in the product.

Type: Formative Assessment

Contextualizing Fraction Division:

Students are asked to write a story context for a given fraction division problem.

Type: Formative Assessment

Lesson Plans

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.

Type: Lesson Plan

Using Box Plots and the Mean Absolute Deviation to Interpret Data:

This lesson explores the use of box plots and the mean absolute deviation to compare two data sets and draw inferences.

Type: Lesson Plan

Florida Food Round Up!:

Most families must buy food and household items that they will need every few weeks. Instead of randomly throwing things into a shopping cart and paying whatever the total is, many families must stick carefully to a predetermined budget to buy all of the items they need. A helpful way to make sure that you are able to buy everything needed is to use a list that is written before going shopping. Families must also determine, if they will purchase "name brand" or "store brand" products. Today, students will practice using a grocery list with a predetermined budget as they add and subtract decimals.

Type: Lesson Plan

Real Life Tax, Tip, and Discount!:

Students calculate the tax, tip, and discount in real-world situations.

Type: Lesson Plan

Snack Time:

In this Model Eliciting Activity, MEA Students will look at a data set to determine which vending machine should be placed in a school. Students have to determine profit and consider other provided data.

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

Perfect Park Planning:

In this Model Eliciting Activity, MEA, students will work in groups to determine a procedure for ranking companies to build a park for a town. Students will need to calculate the area and cost of the park, make decisions based on a data table, and write a letter to the mayor providing evidence for their decisions. Students will need to trade-off between the size and cost of the park as well as park features such as pond or lake, sports field, and playground.

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

For Students by Students:

Students are presented with the task of evaluating several types of fabric based on each of its characteristics. They need to analyze their current uniform needs and decide by choosing which type of fabric will best fit their uniform needs. Then they have to write a report explaining the procedure they used to analyze their choices, reasoning for their ranking and make the requested recommendations.

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.

Type: Lesson Plan

Vacation:

In this Model Eliciting Activity, MEA, the purpose of this lesson is to provide students with the opportunity to solve real-world problems using addition, subtraction, multiplication, and division of multi-digit decimals. They will write arguments to support claims with clear reasons and relevant evidence. Engage effectively in a range of collaborative 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. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Sticks and Stones May Break My Bones:

In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.

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.

Type: Lesson Plan

Manipulating Mathematics (Volume and Surface Area):

This is a lesson designed to teach students how to find the volume and surface areas of right rectangular prisms. It provides an interactive lesson where students get to learn hands-on with cereal boxes and on the computer with a GeoGebra activity.

Type: Lesson Plan

Can You Find the Relationship?:

In this lesson students will first define in their own words what the greatest common factor (GCF) and least common multiple (LCM) mean. They will take this understanding and apply it to solving GCF and LCM word problems. Students will then illustrate their understanding by creating posters based on their word problems. There are examples of different types of methods, online games, a rubric, and a power point to summarize this two-day lesson.

Type: Lesson Plan

Makeover, Home Edition Final Part IV:

This is the final part of the lesson "Makeover, Home Edition." This lesson is designed to teach students the applicability of finding the area of composite figures as well as understanding the importance of ratios in the real world. Part I (#48705) dealt with determining backyard dimensions for fence installation. Part II (#48967) concentrated on inserting a pool and patio into this backyard. Part III (#49025) dealt with creating a scale drawing of the backyard.

Type: Lesson Plan

Batteries Included:

In this Model Eliciting Activity, MEA, students will evaluate batteries using empirical data and customer comments to help a Taxi Cab Service decide which battery brand to purchase. In this real-world scenario, students will communicate with the client in letter format stating their suggested ranking. They will also provide calculations and justification for each decision.

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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Bake Sale:

Students will apply and develop strategies to write and solve equations for mathematical and real world situations. Students will be encouraged to use various strategies, including using inverse operations, to find a solution.

Type: Lesson Plan

A Healthy Outlook:

In this Model Eliciting Activity, MEA, students will learn about nutrition and the importance of keeping things balanced on their plate using the FDA recommendations. Students will need to rank meal plans and shake plans in order to help a restaurant catering company keep a successful business going. After students have evaluated and created rankings for their meal choice, they will write a letter explaining their rationale and thinking and find the bundle price. They will then receive a second letter asking for their help in ranking vegetarian shakes from highest to lowest to support an expanded customer base and find the bundle price. Students will now have the chance to learn a little more about vegetarians and their food choices.

 

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.

Type: Lesson Plan

Feel the Heat!:

This MEA is a great way to implement Florida State Standards for math and language arts. It also supports cooperative learning groups and encourages student engagement. Students will explore different types of materials to determine which absorbs the least amount of heat. Students will also calculate the surface area to determine the cost for constructing the buildings using the materials.

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

The Classroom Money Vault:

This activity has students predict the number of one hundred dollar bills that can fit inside the classroom. The students use volume measurements to explain their estimation.

Type: Lesson Plan

Scuba Diving Mask Search:

This MEA asks the students to decide which company would be the “best and the worst” to use to purchase scuba diving masks for Tino’s Scuba Diving School to provide to their diving certification students. Furthermore, the students are asked to suggest which type of scuba diving masks should be purchased in term of multiple panes – single pane mask, double pane mask, full face mask, skirt color, fit, durability, and price. Students must provide a "top choice" scuba diving mask to the company owner and explain how they arrived at their solution.

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.

Type: Lesson Plan

Teen Cell Phone Plans:

In this Model Eliciting Activity, MEA, the purpose of this lesson is to solve real-world and mathematical problems. Students will also use operations with multi-digit decimals to solve problems. They will write arguments to support claims with clear reasons and relevant evidence. Students will engage effectively in a range of collaborative 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. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Sugar Scrub:

In the Sugar Scrub MEA students will analyze 5 sugar scrub formulas. In the first part, students are asked to evaluate each formula based on color, scent, and exfoliation. In the second part, students apply their methodology to a cost analysis of the scrubs.

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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx.

Type: Lesson Plan

You Can Never Have Too Many Shoes!:

This lesson teaches Least Common Multiples.

Type: Lesson Plan

Batter Up Travel Plans:

A traveling baseball team coach is asking a group of engineers to provide a travel plan from Boston to Jacksonville, Florida with the hopes of attending Major League baseball games along their route. The students will design the route on a large US map highlighting their travel plan and submit the map and a written rationale of their plan.

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.

Type: Lesson Plan

Finding the Greatest Crush Factor:

This lesson uses a real-life approach to exploring the use of Greatest Common Factors (GCF). The students will utilize math practice standards as they analyze math solutions and explain their own solutions.

Type: Lesson Plan

Factoring out the Greatest:

This lesson teaches students how to find the GCF and LCM by factoring. This is a different method than is normally seen in textbooks. This method easily leads to solving GCF word problems and using the distributive property to express a sum of two whole numbers.

Type: Lesson Plan

How much can it hold?:

This lesson uses a discovery approach to exploring the meaning of volume. The students will work with cubes as they construct and analyze the relationship between the length, width, and height to the total amount of cubes. Students will be able to apply this concept to real world applications of other right rectangular prisms and compare them to determine which will hold the most volume. 

 

Type: Lesson Plan

The Survey Says...:

Students will work in groups to conduct class surveys, using the results of the survey to calculate various measures of central tendency.

Type: Lesson Plan

Which Food Should I Feed My Cat?:

The students will convert fractions into decimals and multiply to determine the amount of food to feed their assigned cat. Using this amount, they will calculate (division of decimals) the number of servings and the price per serving of cat food. Students will work with three brands of food and enter the data into their charts. Finally, the students will analyze the data to determine the most affordable food.

Type: Lesson Plan

Here's a tip!:

Students will solve problems involving sales tax and tips; students will apply the properties of operations with numbers in decimal, percent, and fraction form. Students will convert between numbers in any form as appropriate.

Type: Lesson Plan

Dividing by Fractions Discovery:

This lesson allows students to derive an algorithm for dividing fractions using visual fraction models and equations to represent the problem.

Type: Lesson Plan

Sweet Surface Area:

In this lesson, students will explore the relationship between volume and surface area through real-world problem solving. They will work with a partner as they are tasked with finding the least expensive packaging (smallest surface area) for a given number of caramels (volume). Students will justify their packaging strategy in a group discussion.

Type: Lesson Plan

“Dinner with Friends”:

The students will determine what to order at a dinner with friends yet stay within a budget. The students will try to maximize their budgets and order as much food as they possibly can with their given amount of money.

Type: Lesson Plan

Data Doctors:

Have your students become "Data Doctors" by examining and analyzing means of central tendency. This lesson is a great introduction to mean, median, mode and range. Students will be sets of data, get to work in small groups examining the sets, view a poem that will help them remember each term, and take surveys to get real data sets.

Type: Lesson Plan

Lotsa Lotion Lab's Sunscreens:

Lotsa Lotion Labs requests the help of your team to rank a group of sunscreens, explain the process and justify how you chose which is 'best.' An additional hands-on lesson investigating solar energy and sunscreens is included as an extension activity.

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

Using Box Plots to Interpret Data:

This lesson explores the creation of box plots to compare two data sets and draw inferences.

Type: Lesson Plan

Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Overview:

Why did the math teacher KROS the ocean? Because it made for a wonderful way to engage students and do something unique.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Movie Tickets:

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students are asked to compare the buying power of $20 in 1987 and 2012, at least with respect to movie tickets.

Type: Problem-Solving Task

Setting Goals:

The purpose of this task is for students to solve problems involving multiplication and division of decimals in the real-world context of setting financial goals. The focus of the task is on modeling and understanding the concept of setting financial goals, so fluency with the computations will allow students to focus on other aspects of the task.

Type: Problem-Solving Task

Tutorials

Subtracting Decimals 2:

Let's show subtracting with digits up to the thousandths place in this tutorial.

Type: Tutorial

Subtracting Decimals 1:

Watch as we align decimals before subtracting in this tutorial.

Type: Tutorial

Adding Decimals Example:

Learn how to add decimals and use place value in this tutorial. 

Type: Tutorial

Creating Common Denominators:

This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).  The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion.

Type: Tutorial

STEM Lessons - Model Eliciting Activity

A Healthy Outlook:

In this Model Eliciting Activity, MEA, students will learn about nutrition and the importance of keeping things balanced on their plate using the FDA recommendations. Students will need to rank meal plans and shake plans in order to help a restaurant catering company keep a successful business going. After students have evaluated and created rankings for their meal choice, they will write a letter explaining their rationale and thinking and find the bundle price. They will then receive a second letter asking for their help in ranking vegetarian shakes from highest to lowest to support an expanded customer base and find the bundle price. Students will now have the chance to learn a little more about vegetarians and their food choices.

 

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.

Batter Up Travel Plans:

A traveling baseball team coach is asking a group of engineers to provide a travel plan from Boston to Jacksonville, Florida with the hopes of attending Major League baseball games along their route. The students will design the route on a large US map highlighting their travel plan and submit the map and a written rationale of their plan.

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.

Batteries Included:

In this Model Eliciting Activity, MEA, students will evaluate batteries using empirical data and customer comments to help a Taxi Cab Service decide which battery brand to purchase. In this real-world scenario, students will communicate with the client in letter format stating their suggested ranking. They will also provide calculations and justification for each decision.

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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Feel the Heat!:

This MEA is a great way to implement Florida State Standards for math and language arts. It also supports cooperative learning groups and encourages student engagement. Students will explore different types of materials to determine which absorbs the least amount of heat. Students will also calculate the surface area to determine the cost for constructing the buildings using the materials.

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

For Students by Students:

Students are presented with the task of evaluating several types of fabric based on each of its characteristics. They need to analyze their current uniform needs and decide by choosing which type of fabric will best fit their uniform needs. Then they have to write a report explaining the procedure they used to analyze their choices, reasoning for their ranking and make the requested recommendations.

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.

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.

Lotsa Lotion Lab's Sunscreens:

Lotsa Lotion Labs requests the help of your team to rank a group of sunscreens, explain the process and justify how you chose which is 'best.' An additional hands-on lesson investigating solar energy and sunscreens is included as an extension activity.

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

Perfect Park Planning:

In this Model Eliciting Activity, MEA, students will work in groups to determine a procedure for ranking companies to build a park for a town. Students will need to calculate the area and cost of the park, make decisions based on a data table, and write a letter to the mayor providing evidence for their decisions. Students will need to trade-off between the size and cost of the park as well as park features such as pond or lake, sports field, and playground.

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

Scuba Diving Mask Search:

This MEA asks the students to decide which company would be the “best and the worst” to use to purchase scuba diving masks for Tino’s Scuba Diving School to provide to their diving certification students. Furthermore, the students are asked to suggest which type of scuba diving masks should be purchased in term of multiple panes – single pane mask, double pane mask, full face mask, skirt color, fit, durability, and price. Students must provide a "top choice" scuba diving mask to the company owner and explain how they arrived at their solution.

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.

Snack Time:

In this Model Eliciting Activity, MEA Students will look at a data set to determine which vending machine should be placed in a school. Students have to determine profit and consider other provided data.

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.

Sticks and Stones May Break My Bones:

In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.

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.

Sugar Scrub:

In the Sugar Scrub MEA students will analyze 5 sugar scrub formulas. In the first part, students are asked to evaluate each formula based on color, scent, and exfoliation. In the second part, students apply their methodology to a cost analysis of the scrubs.

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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx.

Teen Cell Phone Plans:

In this Model Eliciting Activity, MEA, the purpose of this lesson is to solve real-world and mathematical problems. Students will also use operations with multi-digit decimals to solve problems. They will write arguments to support claims with clear reasons and relevant evidence. Students will engage effectively in a range of collaborative 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. Click here to learn more about MEAs and how they can transform your classroom.

Vacation:

In this Model Eliciting Activity, MEA, the purpose of this lesson is to provide students with the opportunity to solve real-world problems using addition, subtraction, multiplication, and division of multi-digit decimals. They will write arguments to support claims with clear reasons and relevant evidence. Engage effectively in a range of collaborative 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. Click here to learn more about MEAs and how they can transform your classroom.

MFAS Formative Assessments

Contextualizing Fraction Division:

Students are asked to write a story context for a given fraction division problem.

Multiplying By Ten Three Times:

Students consider why a number multiplied by 10 to the third power will have three zeros in the product.

Student Resources

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

Problem-Solving Tasks

Movie Tickets:

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students are asked to compare the buying power of $20 in 1987 and 2012, at least with respect to movie tickets.

Type: Problem-Solving Task

Setting Goals:

The purpose of this task is for students to solve problems involving multiplication and division of decimals in the real-world context of setting financial goals. The focus of the task is on modeling and understanding the concept of setting financial goals, so fluency with the computations will allow students to focus on other aspects of the task.

Type: Problem-Solving Task

Tutorials

Subtracting Decimals 2:

Let's show subtracting with digits up to the thousandths place in this tutorial.

Type: Tutorial

Subtracting Decimals 1:

Watch as we align decimals before subtracting in this tutorial.

Type: Tutorial

Adding Decimals Example:

Learn how to add decimals and use place value in this tutorial. 

Type: Tutorial

Creating Common Denominators:

This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).  The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion.

Type: Tutorial

Parent Resources

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

Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Overview:

Why did the math teacher KROS the ocean? Because it made for a wonderful way to engage students and do something unique.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Movie Tickets:

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students are asked to compare the buying power of $20 in 1987 and 2012, at least with respect to movie tickets.

Type: Problem-Solving Task

Setting Goals:

The purpose of this task is for students to solve problems involving multiplication and division of decimals in the real-world context of setting financial goals. The focus of the task is on modeling and understanding the concept of setting financial goals, so fluency with the computations will allow students to focus on other aspects of the task.

Type: Problem-Solving Task