### Clarifications

**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.

**Subject Area:**Mathematics

**Grade:**6

**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 Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

**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

## Assessments

## Educational Game

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Teaching Ideas

## Tutorials

## STEM Lessons - Model Eliciting Activity

Students will learn about nutrition and the importance of keeping things balanced in their plate using the FDA recommendations. Students will need to rank meal plans in order to help a restaurateur 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. They will then receive a second letter asking for their help in ranking vegetarian juices from highest to lowest to support an expanded customer base. Students will now have the chance to learn a little more about vegetarians and their food choices.

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.

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 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.

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.

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.

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.

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.

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.

In this MEA, students will work in cooperative groups to discuss and come up with a procedure to rank the banks from best to worst.

The purpose of this lesson is to provide students with the opportunity to solve real-world and mathematical problems using add, subtraction, multiply, and divide multi-digit decimals using the standard algorithm for each operation. They will write arguments to support claims with clear reasons and relevant evidence. Engage effectively in a range of collaborative discussions.

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.

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

Join in on creating a delicious sundae by adding decimals to the thousandths, using the standard algorithm, in this interactive tutorial.

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

## Student Resources

## Original Student Tutorials

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

Type: Original Student Tutorial

Join in on creating a delicious sundae by adding decimals to the thousandths, using the standard algorithm, 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 decimal numbers.

Type: Tutorial

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

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

Type: Tutorial

This video shows an example of subtracting with digits up to the thousandths place.

Type: Tutorial

Just like when add, be sure you align decimals before subtracting.

Type: Tutorial

Learn how to add 9.087 to 15.31. Be careful to use place value!

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