Remarks
Fluency Expectations or Examples of Culminating StandardsStudents fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. This is the culminating standard for several years’ worth of work relating to the domains of Number and Operations in Base Ten, Operations and Algebraic Thinking, and Number and Operations — Fractions.
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
- Assessment Limits :
Items may include values to the thousandths place. Items may be set up in standard algorithm form. - Calculator :
No
- Context :
Allowable
- Test Item #: Sample Item 1
- Question:
An expression is shown.
What is the value of the expression?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 2
- Question:
An expression is shown.
What is the value of the expression?
- Difficulty: N/A
- Type: EE: Equation Editor
Related Courses
Related Access Points
Related Resources
Educational Game
Formative Assessments
Lesson Plans
Original Student Tutorials
Problem-Solving Tasks
Teaching Ideas
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.
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.
Fancy Fractions Catering Company will be hosting a party and need your help to make it happen! Your help is needed to determine which recipe would be best for them to use in their pasta dish taking into account ingredient cost and customer preference.
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
In this Model Eliciting Activity (MEA), students will use the 4 operations with decimal numbers and calculate profit (including negative numbers) as well as use the resulting data to help a business owner make decisions about their candy stores.
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 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.
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.
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.
The students will create a package list for a travel company. They must use all operations with decimals as well as compare decimals.
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
MFAS Formative Assessments
Students are asked to add multidigit decimal numbers and are assessed for both accuracy and fluency.
Students are asked to divide multidigit decimal numbers and are assessed for both accuracy and fluency.
Students are asked to multiply multidigit decimal numbers and are assessed for both accuracy and fluency.
Students are asked to subtract multidigit decimal numbers and are assessed for both accuracy and fluency.
Original Student Tutorials Mathematics - Grades 6-8
Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial.
Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.
Student Resources
Original Student Tutorials
Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.
Type: Original Student Tutorial
Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial.
Type: Original Student Tutorial
Educational Game
This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.
Various levels of difficulty make this game appropriate for multiple age and ability levels.
Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.
Multiplication/Division: The multiplication and addition of whole numbers.
Percentages: Identify the percentage of a whole number.
Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.
Type: Educational Game
Problem-Solving Tasks
The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.
Type: Problem-Solving Task
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
Given the fact 13 x 17 = 221, students are asked to reason about and explain the decimal placement in multiplication and division problems where some of the numbers involved have been changed by powers of ten.
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
Students are asked to solve problems from context by using multiplication or division of decimals.
Type: Problem-Solving Task
Students are asked to add or subtract decimals to solve problems in context.
Type: Problem-Solving Task
Tutorials
This video demonstrates dividing two numbers that are decimals.
Type: Tutorial
This video demonstrates adding decimal numbers to solve a word problem.
Type: Tutorial
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
Parent Resources
Problem-Solving Tasks
The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.
Type: Problem-Solving Task
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
Given the fact 13 x 17 = 221, students are asked to reason about and explain the decimal placement in multiplication and division problems where some of the numbers involved have been changed by powers of ten.
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
There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly. Easily recognizing contexts that require division is a necessary conceptual prerequisite to more complex modeling problems that students will be asked to solve later in middle and high school.
This task also has a natural carryover to work with ratios and rates, so students should also be building connections between these kinds of division problems and finding unit rates.
Type: Problem-Solving Task
Students are asked to solve problems from context by using multiplication or division of decimals.
Type: Problem-Solving Task
Students are asked to add or subtract decimals to solve problems in context.
Type: Problem-Solving Task