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Clarifications
Clarification 1: Within this benchmark, it is not the expectation to include both decimals and fractions within a single problem.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
- MA.6.AR.1.1
- MA.6.AR.2.4
- MA.6.AR.3.2
- MA.6.AR.3.3
- MA.6.AR.3.4
- MA.6.AR.3.5
- MA.6.GR.2
- MA.6.DP.1.2
- MA.6.DP.1.3
- MA.6.DP.1.4
- MA.6.DP.1.6
Terms from the K-12 Glossary
- Area Model
- Commutative property of Multiplication
- Dividend
- Divisor
- Expression
Vertical Alignment
Previous Benchmarks
http://flbt5.floridaearlylearning.com/standards.html
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 the 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?
- With the completion of operations with positive rational numbers in grade 6, students should have experience using technology with decimals and fractions as they occur in the real world (MTR.7.1). This experience will help to prepare students working 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 have incorrectly assumed 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 have incorrectly assumed 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 provides opportunities for students who have a firm understanding of multiplying and dividing fractions to convert the provided decimal values to their equivalent fractional form before performing the desired operation and converting 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 and then dividing the numerators and the denominators.
- For example, ÷ is equivalent to ÷ which is equivalent to which is equivalent to .
- 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 1Candy comes in 3 pound bags. At a class party, the boys in the class ate 2 bags of candy and the girls in the class ate 1 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
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Teaching Idea
Tutorials
STEM Lessons - Model Eliciting Activity
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.
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
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
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.
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.
Uncle Henry's Dilemma is a problem solving lesson to determine the global location for the reading of Uncle Henry's will. The students will interpret data sets which include temperature, rainfall, air pollution, travel cost, flight times and health issues to rank five global locations for Uncle Henry's relatives to travel to for the reading of his will. This is an engaging, fun-filled MEA lesson with twists and turns throughout. Students will learn how this procedure of selecting locations can be applied to everyday decisions by the government, a business, a family, or individuals.
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.
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
Students are asked to write a story context for a given fraction division problem.
Students consider why a number multiplied by 10 to the third power will have three zeros in the product.
Student Resources
Problem-Solving Tasks
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
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
Let's show subtracting with digits up to the thousandths place in this tutorial.
Type: Tutorial
Watch as we align decimals before subtracting in this tutorial.
Type: Tutorial
Learn how to add decimals and use place value in this tutorial.
Type: Tutorial
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
Perspectives Video: Teaching Idea
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
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
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
