# MAFS.6.NS.2.3Archived Standard Export Print
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

### Remarks

Fluency Expectations or Examples of Culminating Standards

Students 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.
General Information
Subject Area: Mathematics
Domain-Subdomain: The Number System
Cluster: Level 1: Recall
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples. (Additional Cluster) -

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.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Items may include values to the thousandths place. Items may be set up in standard algorithm form.
• Calculator :

No

• Context :

Allowable

Sample Test Items (2)
• 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

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

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

## Educational Game

Ice Ice Maybe: An Operations Estimation 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.

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

## Formative Assessments

Multiplying Multidigit Decimals:

Students are asked to multiply multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Subtracting Multidigit Decimals:

Students are asked to subtract multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Students are asked to add multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Dividing Multidigit Decimals:

Students are asked to divide multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

## Lesson Plans

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

Can You Stand the Wind and Rain?:

In this lesson, students will:

• Investigate how natural disasters have affected human life in Florida.
• Add, subtract, and multiply multi-digit decimals using the standard algorithm.
• Find a percent of a quantity as a rate per 100 and then solve problems involving finding the whole given a part and the percent.

Type: Lesson Plan

Sound Is Not The Only Place You Hear About Volume!:

This lesson introduces the idea of finding volume. Volume in sixth grade math is very "rectangular" (cubes, rectangular prisms) and this lesson brings to light that volume is simply a measure of available space, but can take on many shapes or forms (cylinders for example - graduated cylinders and beakers) in science. Students will be left to design their own data collection and organizing the data that they collect. They will apply the skill of finding volume to using fractional parts of a number (decimals) and finding the product using the volume formula.

Type: Lesson Plan

Students will analyze data to create a route and itinerary, while following time frame guidelines.

Type: Lesson Plan

Where Will We Stay?:

In this lesson, students explore lodging options for their dream family vacation. Students will plan a vacation for a family of four. With a budget of \$5,000 students will prepare a budget to include the cost of transportation, lodging, and attractions. In this lesson, students will focus on preparing the budget for hotel costs. In lesson 1 of this unit lesson, students prepared a budget for transportation. In the subsequent lesson to this lesson, students will prepare a budget for the entertainment/attractions costs portion of their vacation. Teachers can choose to do one, some, or all lessons as they can be completed independently of one another.

Type: Lesson Plan

This is a interdisciplinary MEA lesson for science, writing, and math. This lesson ask students develop a criteria for selecting headphones and develop an equation that supports their choices.

Type: Lesson Plan

Snack Time:

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.

Type: Lesson Plan

A Tasty Treat:

In this lesson, students will be given a list of ingredients and prices they must use to create their own snack mix. Students will have to add, subtract, multiply, and divide decimal numbers. The closure of the lesson focuses specifically on the division strategies students used to solve the problem.

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.

Type: Lesson Plan

:) Where's The POINT? What's The POINT? The Point is... a DECIMAL. "Multiply with Decimals" :):

Multiply efficiently and fluently with multi-digit decimals using the standard algorithm for the operation.

Type: Lesson Plan

I want a cell phone:

Students develop a procedure to select a cell phone based on qualities they think their parents value in a cell phone. Students present their solution in writing to a marketing company, who wishes to use the results to market cell phones to parents of elementary students.

Type: Lesson Plan

Short Hop Airlines:

Short Hop Airlines, a small airline, features flights under 120 minutes. Students are provided a list of songs of varying genre and asked to create a playlist for each of the 9 flights. They will also calculate royalty fees on all songs. Oral presentations of their procedure and song choices will be shared with the class.

Type: Lesson Plan

Out and About: Deciding the Best Field Trip:

Students are asked to decide which field trips would be the most cost effective and be the best one(s) for their grade level to attend. They are given a set dollar amount and asked to consider distance, cost of busses per mile, admission costs, food costs, and also consider feedback from other students regarding how fun and how educational the trip will be.

Type: Lesson Plan

Can You Hear Me Now?:

Students will be given a list of phone rates of 5 different companies and will have to decide which plan(s) are the best according to cost. They will discuss minutes and monthly plan and the cost of each phone. All of the plans are on the prepayment option.

Type: Lesson Plan

Vacation Time:

The students will create a package list for a travel company. They must use all operations with decimals as well as compare decimals.

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.

Type: Lesson Plan

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.

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.

Type: Lesson Plan

Fancy Fractions Catering Company Project:

Fancy Fractions Catering Company will be hosting a party and need your help to make it happen! Your help is needed to find out how much of each ingredient is needed to feed 200 people and the most economical way of doing this (Brand name brands or store brand). You also have the option of omitting up to three ingredients from the recipe.

Type: Lesson Plan

Better Buy: 75 fl oz or 150 fl oz?:

The students will clip out items from ads or by using a PowerPoint to determine the better buy between small quantities and large quantities. The students will answer the question, "Which item costs less per unit?" and demonstrate fluency in dividing with decimals.

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.

Type: Lesson Plan

Sandy's Candy Machine:

In this Model Eliciting Activity (MEA), students will multiply and divide decimals as well as use the resulting data to make a decision about a candy store.

Type: Lesson Plan

The Mystery of Decimals:

This lesson reviews all four operations (adding, subtracting, multiplying, and dividing) with decimals. It is designed to easily provide differentiated instruction for the struggling students, as well as extensions for the high level students. The culmination of the lesson is a computer based assessment set in a mystery format which provides a fun change from a typical pencil and paper test.

Type: Lesson Plan

Dividing Decimals Investigations:

In this introductory lesson, students test how the basic operations performed on the dividend and divisor affect the quotient of a pair of numbers. Students then conclude whether the results of their trials can be applied to solve problems with a decimal divisor.

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

## Original Student Tutorials

Sailing Through Subtracting Decimals:

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

Pennies to Heaven:

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.

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.

Reasoning about Multiplication and Division and Place Value, Part 1:

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.

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.

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.

Students are asked to solve problems from context by using multiplication or division of decimals.

Jayden’s Snacks:

Students are asked to add or subtract decimals to solve problems in context.

## Teaching Ideas

Baby Whale Formula-SeaWorld Classroom Activity:

In this problem solving activity, students will practice measuring and making calculations in the context of providing nutrients to a baby whale that was rescued.

Type: Teaching Idea

Calculating Sharks-SeaWorld Classroom Activity:

• Given data about sharks and the amount of food they eat, students will be able to solve for the unknown in percentage problems.
• Given information about a shark's growth, students will be able to graph coordinates and interpret a linear graph.
• Given the conversion factor, students will be able to convert from metric to English units.

Type: Teaching Idea

## Tutorials

Dividing by a Multi-Digit Decimal:

This video demonstrates dividing two numbers that are decimals.

Type: Tutorial

Multiplying Decimals:

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

This video demonstrates adding decimal numbers to solve a word problem.

Type: Tutorial

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

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

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.

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.

Can You Hear Me Now?:

Students will be given a list of phone rates of 5 different companies and will have to decide which plan(s) are the best according to cost. They will discuss minutes and monthly plan and the cost of each phone. All of the plans are on the prepayment option.

Fancy Fractions Catering Company Project:

Fancy Fractions Catering Company will be hosting a party and need your help to make it happen! Your help is needed to find out how much of each ingredient is needed to feed 200 people and the most economical way of doing this (Brand name brands or store brand). You also have the option of omitting up to three ingredients from the recipe.

This is a interdisciplinary MEA lesson for science, writing, and math. This lesson ask students develop a criteria for selecting headphones and develop an equation that supports their choices.

I want a cell phone:

Students develop a procedure to select a cell phone based on qualities they think their parents value in a cell phone. Students present their solution in writing to a marketing company, who wishes to use the results to market cell phones to parents of elementary students.

Students will analyze data to create a route and itinerary, while following time frame guidelines.

Out and About: Deciding the Best Field Trip:

Students are asked to decide which field trips would be the most cost effective and be the best one(s) for their grade level to attend. They are given a set dollar amount and asked to consider distance, cost of busses per mile, admission costs, food costs, and also consider feedback from other students regarding how fun and how educational the trip will be.

Sandy's Candy Machine:

In this Model Eliciting Activity (MEA), students will multiply and divide decimals as well as use the resulting data to make a decision about a candy store.

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.

Short Hop Airlines:

Short Hop Airlines, a small airline, features flights under 120 minutes. Students are provided a list of songs of varying genre and asked to create a playlist for each of the 9 flights. They will also calculate royalty fees on all songs. Oral presentations of their procedure and song choices will be shared with the class.

Snack Time:

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.

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.

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.

Vacation Time:

The students will create a package list for a travel company. They must use all operations with decimals as well as compare decimals.

## MFAS Formative Assessments

Students are asked to add multidigit decimal numbers and are assessed for both accuracy and fluency.

Dividing Multidigit Decimals:

Students are asked to divide multidigit decimal numbers and are assessed for both accuracy and fluency.

Multiplying Multidigit Decimals:

Students are asked to multiply multidigit decimal numbers and are assessed for both accuracy and fluency.

Subtracting Multidigit Decimals:

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.

Sailing Through Subtracting Decimals:

Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.

## Student Resources

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

## Original Student Tutorials

Sailing Through Subtracting Decimals:

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

Ice Ice Maybe: An Operations Estimation 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.

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

Pennies to Heaven:

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.

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.

Reasoning about Multiplication and Division and Place Value, Part 1:

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.

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.

Students are asked to solve problems from context by using multiplication or division of decimals.

Jayden’s Snacks:

Students are asked to add or subtract decimals to solve problems in context.

## Tutorials

Dividing by a Multi-Digit Decimal:

This video demonstrates dividing two numbers that are decimals.

Type: Tutorial

Multiplying Decimals:

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

This video demonstrates adding decimal numbers to solve a word problem.

Type: Tutorial

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

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

Type: Tutorial

## Parent Resources

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

Pennies to Heaven:

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.

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.

Reasoning about Multiplication and Division and Place Value, Part 1:

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.

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.

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.