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.

**Number:**MAFS.5.NBT.2

**Title:**Perform operations with multi-digit whole numbers and with decimals to hundredths. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**5

**Domain-Subdomain:**Number and Operations in Base Ten

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Educational Games

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Tutorials

## Student Resources

## Original Student Tutorials

Help your town build a dog park by multiplying whole numbers by decimals to the tenths place in this interactive tutorial.

Note: this is an introductory tutorial on multiplying whole numbers by decimals before students move on to multiplying decimals by decimals.

Type: Original Student Tutorial

Learn to subtract decimals to the hundredths place using place-value models and written expressions as you fix the topsy-turvy playground in this interactive tutorial.

Type: Original Student Tutorial

Help these aliens clean up the Sweet Treats Factory by learning to add decimals in this interactive mathematics tutorial.

Type: Original Student Tutorial

Learn how the standard algorithm for multiplying numbers works and practice your skills in this interactive tutorial.

Type: Original Student Tutorial

## Educational Games

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

In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

This interactive applet gives students practice in making change in U.S. dollars and in four other currencies. Students are presented with a purchase amount and the amount paid, and they must enter the quantity of each denomination that make up the correct change. Students are rewarded for correct answers and are shown the correct change if they err. There are four levels of difficulty, ranging from amounts less than a dollar to amounts over $100.

Type: Educational Game

## Educational Software / Tool

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

## Problem-Solving Tasks

The purpose of this task is for students to solve multi-step problems 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 can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases.

Type: Problem-Solving Task

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them.

Type: Problem-Solving Task

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Type: Problem-Solving Task

## Tutorials

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division.

Type: Tutorial

In this video tutorial from Khan Academy, view a demonstration of how to set-up an area model for multiplying a two-digit number by a two-digit number on graph or grid paper and then link this to the standard algorithm.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a two-digit number by a two-digit number using the area model. The video makes a connection between partial products and the area model.

Type: Tutorial

In this video tutorial from Khan Academy, view an example and a description of how the distributive property can be used to multiply a two-digit number by a two-digit number. The second example uses the area model with the distributive property.

Type: Tutorial

In this Khan Academy video tutorial, view an example of multiplying a 4-digit number by a 1-digit number by expanding the 4-digit number and multiplying by each digit individually in an area model. This video will help to build an understanding before teaching the standard algorithm. Multiplying with a 4-digit factor is larger than some standards which limit factors to 3-digits.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a 2-digit number by another 2-digit number. Be sure to stick around for the second example! The key is understanding the value of each digit!

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a problem in which a **3-digit** number is being multiplied by a 1-digit number using the standard algorithm.

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a multiplication problem with a two-digit number multiplied by a one-digit number using the standard algorithm.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting with decimals. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

The purpose of this task is for students to solve multi-step problems 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 can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases.

Type: Problem-Solving Task

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them.

Type: Problem-Solving Task

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Type: Problem-Solving Task

## Tutorials

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division.

Type: Tutorial

In this video tutorial from Khan Academy, view a demonstration of how to set-up an area model for multiplying a two-digit number by a two-digit number on graph or grid paper and then link this to the standard algorithm.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a two-digit number by a two-digit number using the area model. The video makes a connection between partial products and the area model.

Type: Tutorial

In this video tutorial from Khan Academy, view an example and a description of how the distributive property can be used to multiply a two-digit number by a two-digit number. The second example uses the area model with the distributive property.

Type: Tutorial

In this Khan Academy video tutorial, view an example of multiplying a 4-digit number by a 1-digit number by expanding the 4-digit number and multiplying by each digit individually in an area model. This video will help to build an understanding before teaching the standard algorithm. Multiplying with a 4-digit factor is larger than some standards which limit factors to 3-digits.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a 2-digit number by another 2-digit number. Be sure to stick around for the second example! The key is understanding the value of each digit!

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a problem in which a **3-digit** number is being multiplied by a 1-digit number using the standard algorithm.

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a multiplication problem with a two-digit number multiplied by a one-digit number using the standard algorithm.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting with decimals. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial