### General Information

**Subject Area:**Mathematics

**Grade:**5

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

**Cluster:**Level 2: Basic Application of Skills & Concepts

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

### Test Item Specifications

**Assessment Limits :**

Items may only use factors that result in decimal solutions to the thousandths place (e.g., multiplying tenths by hundredths). Items may not include multiple different operations within the same expression (e.g., 21 + 0.34 x 8.55). Expressions may have up to two procedural steps of the same operation.**Calculator :**No

**Context :**Allowable

### Sample Test Items (3)

**Test Item #:**Sample Item 1**Question:**What is the value of the expression?

5.2 × 10.38

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**An expression is shown.

12.25 + 3.05 +0.6

What is the value of the expression?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 3**Question:**Allen ran 5.4 miles on Monday and 3.28 miles on Tuesday.

How many miles did Allen run altogether?

**Difficulty:**N/A**Type:**EE: Equation Editor

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Educational Games

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Task

## Tutorial

## Virtual Manipulatives

## STEM Lessons - Model Eliciting Activity

This activity allows students to determine the types of items that should be in a hurricane survival kit, use a budget and calculations to determine the items to include in the kit and gain an understanding of hurricanes and the need to prepare for them.

Students need to make decisions about the correct bakery box to send cookies through the mail to fill orders. Students need to consider the capacity, dimensions, and volume of the boxes in terms of how many cookies each box will hold.

This Model Eliciting Activity (MEA) asks students to develop a procedure for choosing a back-up energy source (generator) for an ice cream shop. Students will need to consider Cost of unit, wattage output, size of fuel container, length of time this machine will run, auto turn on, and the number of outlets it can receive. In the second portion of the problem statement, the students will need to prepare and compare the cost of use for 24 hour period. They will need to determine if they have still made the correct choices while adding three more generators for consideration, and make a cost analysis for 24 hours of use. In the culminating activity, the students will write a proposal for the client for the generator of their choice and include the 24 hours cost analysis.

In this MEA, the students will select 5 items from a list to be placed in a bag donated by an organization.

This MEA asks the students to decide which hand dryer model would be the "best and the worst" for Blow Me Away Incorporated to sell.

The students will consider company's cost; selling price; whether hand dryer turns on when hands are placed near it; whether hand dryer stays on when hands are near it; whether hand dryer turns of when hands are moved away; appearance and energy efficiency.

Students will provide "top choice" to Blow Me Away Incorporated and explain how they arrived at the solution.

LEGO Education WeDo Robotics extension activity can follow should a school have the WeDo program.

In teams, students will determine which sailboat the Leeward Family should purchase. They will use their knowledge of multiplying decimals to assist in their problem solving. The criteria will be based on air conditioning, swim out, auto helm, recent bottom job, condition of sails, condition of upholstery, and other twists!

Students will rank fast food restaurants from best to worst based on their nutrition, price, and distance to sport field. Students will need to be able to add, subtract, and multiply decimal numbers. Given the first data set, students will come up with a procedure for ranking restaurants based on the prices and nutrition information given. Students will need to consider what is more important, price or nutrition. They will also need to determine what nutritional elements are more important to consider (fat, calories, sodium). Because some ties can occur, students will have to make tradeoffs for nutrition or price. Given the second data set, students have to reconsider their procedure when given price and coupon information along with distance to the restaurant and budget.

In this MEA, students will choose their top choices of field day activities given the cost, number of adult supervisors needed, the area required for event, safety concerns, clean up required, number of students that can play at a time, and peer comments about the activity. Students will need to make trade-offs in cost when the "twist" provides budget restrictions. Students will calculate area and multiply whole numbers and decimal numbers.

Students will be comparing quantitative and qualitative aspects of technology devices in order to rank them for a particular student's needs.

On this MEA activity, students will create a procedure to rank five lunch bags as to which one is the best in keeping food and drinks at a safe temperature and appealing to the taste, while keeping design and price on target.

This MEA asks students to decide which factors are important in developing a successful frozen yogurt (froyo) store in order to compete with and become the best store in the area. Students will provide feedback to an entrepreneur who is looking to open a frozen yogurt store. They will rank order their choices of the most successful to least successful store. Students will provide a detailed written explanation for how they decided to rank factors and their solution rating existing stores from best to worst.

This MEA asks the students to decide which snack food would be the best for introduction in the school Snack Shack. Students are asked to compare nutritional value per ounce of food based on calories, fat, sodium, cholesterol, protein, and sugar.

This Model Eliciting Activity (MEA) is written at a 5th grade level. In this open-ended problem, students are presented with a variety of steps. Based on the data table given for student review, students must decide which simple machines they want to assemble and rank the stores in order starting with the one they would like to order from. Moreover, students are given special characteristics that they need to consider before describing their reasoning and procedures implemented in reaching their answers.

This Model Eliciting Activity (MEA) asks students to develop a procedure for choosing a reptile or amphibian to place in a school reception area. Students will need to consider safety, price of animal, cost by week to feed animal, size and cost of the enclosure, and the life span of the animals they are considering. In the second portion of the problem statement, the students will need to prepare a budget and cost analysis for the year to consider if they have still made the correct choices while adding three more animals for consideration. The culminating activity for this MEA will have the student write a proposal for the Principal to state their choice of animal, give a year's budget for cost and care for the animal.

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.

This Model Eliciting Activity (MEA) asks students to develop a procedure to select a hurricane shutter company.

This 5th grade MEA is designed to have students do math computations and compare information to provide best answer to the problem based on calculations and information given.

Students work in teams to plan the contents of a covered wagon for a family relocating from Missouri to Oregon. Students must calculate the weight and cost of the wagon by adding, subtracting, and multiplying decimals.

In this MEA, students are challenged to choose the snacks that will be in a vending machine in a school. Students will need to multiply and divide whole numbers and decimal numbers as well as compare fractions and decimal numbers. Students will work in groups to solve the problem and write a letter to the client explaining their thinking.

This is a MEA that looks at the contribution of some women that helped out during the American Revolution.

This activity requires students to apply their knowledge of force, motion, speed, and division to solve the problem of which water park their class should choose to go on for their 5th grade class trip.

Students will create a rating system for workout DVD's according to weight loss, muscle toning, and increased physical condition.

## MFAS Formative Assessments

Students are asked to solve a word problem involving multiplication of a decimal by a whole number using a model or drawing or a strategy based on place value, the relationship between multiplication and division, or properties of operations.

Students are asked to solve a word problem involving division of a whole number by a decimal using a model or drawing, a strategy based on place value, the relationship between multiplication and division, or properties of operations.

Students are asked to solve a word problem that involves adding two decimals by using a strategy based on place value.

Students are asked to solve a word problem that involves subtracting two decimals by using a strategy based on place value.

## Original Student Tutorials Mathematics - Grades K-5

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

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

## 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.

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

## 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 fractions and decimals.

*Percentages: *Identify the percentage of a whole number.

*Fractions: *Multiply and divde a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

This addition game uses mixed decimals to the tenths place. This game encourages some logical analysis as well as addition skills. There may be several ways to make the first couple of circles sum to 3, but there is only one way to combine all the given numbers so that every circle sums to 3.

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

## 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

## 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

## Virtual Manipulatives

With this virtual manipulative, students can explore the meaning of place value and grouping as they add and subtract decimals. Base blocks consist of individual units, longs, flats, and blocks (ten of each set for base 10). These blocks can represent negative as well as positive numbers with one to four decimal places and in five different bases. Students exchange and group the blocks as needed to solve the problem. Problems can be presented to or created by the students. All material is available in Spanish and French as well as English, including instructions for using the manipulative, information about bases and place value, and suggested questions for classroom use.

Type: Virtual Manipulative

Diffy is a virtual manipulative that allows students to practice their subtraction facts with whole numbers, integers, fractions, decimals, or money. It is a puzzle of sorts with four black numbers placed at the corners of a black square. The first goal is to fill in the four blanks in the blue circles in the middle of each side of the black square.

Type: Virtual Manipulative

## Parent Resources

## Educational Game

This addition game uses mixed decimals to the tenths place. This game encourages some logical analysis as well as addition skills. There may be several ways to make the first couple of circles sum to 3, but there is only one way to combine all the given numbers so that every circle sums to 3.

Type: Educational Game

## 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

## 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

## Virtual Manipulatives

With this virtual manipulative, students can explore the meaning of place value and grouping as they add and subtract decimals. Base blocks consist of individual units, longs, flats, and blocks (ten of each set for base 10). These blocks can represent negative as well as positive numbers with one to four decimal places and in five different bases. Students exchange and group the blocks as needed to solve the problem. Problems can be presented to or created by the students. All material is available in Spanish and French as well as English, including instructions for using the manipulative, information about bases and place value, and suggested questions for classroom use.

Type: Virtual Manipulative

Diffy is a virtual manipulative that allows students to practice their subtraction facts with whole numbers, integers, fractions, decimals, or money. It is a puzzle of sorts with four black numbers placed at the corners of a black square. The first goal is to fill in the four blanks in the blue circles in the middle of each side of the black square.

Type: Virtual Manipulative