### Remarks

**Examples of Opportunities for In-Depth Focus**

When students work toward meeting this standard (which is closely connected to 7.NS.1.1 and 7.NS.1.2), they consolidate their skill and understanding of addition, subtraction, multiplication and division of rational numbers.

**Subject Area:**Mathematics

**Grade:**7

**Domain-Subdomain:**The Number System

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

**Cluster:**Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (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 - Archived

**Assessed:**Yes

**Assessment Limits :**

Complex fractions may be used, but should contain fractions with single-digit numerators and denominators**Calculator :**Neutral

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**At 8:00, the temperature was 6 degrees Celsius (°C). Three hours later, the temperature was -13°C.By how many degrees Celsius did the temperature change?

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

**Test Item #:**Sample Item 2**Question:**The change in the price of a certain brand of cereal from 2010 to 2012 is shown in the table.In 2009 the price of cereal was $3.69.

What was the price of the cereal at the end of 2012?

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

**Test Item #:**Sample Item 3**Question:**The total change in the price of a certain brand of cereal from 2008 to 2012 was -$0.20.

Complete the table to show possible price changes in 2010 and 2012.

**Difficulty:**N/A**Type:**TI: Table Item

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Teaching Idea

## Tutorials

## STEM Lessons - Model Eliciting Activity

Students use problem solving skills to determine how much fencing is needed and the type of fencing in order to secure a pool and recreational area.

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.

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Cut It Out Section of the Building and Grounds Maintenance Department of a school district to evaluate several lawn tractor models and help them decide which unit they should purchase.

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.

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from E-Z Go Taxi Cab Service to evaluate several batteries and help them decide which battery they should purchase.

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 MEA, the students will compare data to decide which franchise would be best for a person who is moving into an area and wants to open up their own fried chicken franchise.

Students are asked to rank fabrics designated for a new women's volleyball team. Students must take into account the uniform color, Ultraviolet Protection Factor, weight of the fabric availability of material and cost. They will compare and contrast fabrics on these factors and calculate yardage needed to manufacture the team's 24 uniforms.

In this Model Eliciting Activity, MEA, students will research a list of companies to invest in through purchasing stocks. Students will calculate the amount invested and readjust their investment choices.

Students are asked to rank different types of mulch for a Landscaping company.

The students will need to look at data and make good decisions on which model home will be constructed for victims hurt by natural disasters.

In this 7th grade MEA, students will form teams to rank the best vacation package for the Johansson family vacation. They will have to calculate the total cost of the vacation package making sure they don't go over budget. Teams will suggest what the family should do with any excess money. They will also suggest any deletion of activities if the package is over budget. Teams will make a presentation of the first choice recommendation.

In this 7^{th} grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.

This is a NASA-themed, MEA (Model Eliciting Activity) lesson that challenges students to solve a real world open ended problem, while promoting collaboration through teamwork. This lesson asks each group of students to choose five positions and assign salaries to the positions with a given budget of $500,000. The students' original decision (and "twist") will be based on information from the client's letter(s) and data set(s). Groups are to write a detailed letter to the client of the procedure used.

In this activity, the students are given specifics and data tables to figure out which banking institution best fits the needs of the customer. Student have to figure out the company's monthly banking activities and use this information to rank the banks provided in the table(s) to determine which bank will give them the most service for the least cost. The twist adds a new situation to take into consideration that may or may not change their original recommendation.

Students will select the best type of coating for rockets given a set of data which will include temperature, hardness, resistance to corrosion and drag.

Based on a student-focused scenario encouraging healthier lifestyles, students will perform a close and careful reading of an article encouraging active and healthy lifestyles. During the lesson, students will analyze data from Consumer Reports comparing and contrasting treadmills and elliptical exercisers. Using information gathered, students will compile data and persuade administrators to buy equipment that will align with the provided budget and fit in the given space.

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Simple Photography Classes to evaluate several digital cameras and help them decide which one they should purchase.

Teams of students act as travel agents in order to plan a vacation package for a family of 5. The students must create four vacation packages that include: hotel, car rental, and visits to three theme parks.

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.

The students will have to decide which van is the "best buy" for a family. They will have to figure monthly payments and will also use critical thinking skills to decide which is the best van to purchase.

The Whirl Wind Corporation would like to install Wind Turbines in the Mojave Desert. The company produces various models of these turbines and is looking for help in selecting the best one for the job.

The main problem is that students will help rank products offered at Zany Joke Shop. They will be ranking the products from best overall to least. By helping rank the products, the student will help create a purchase order for the store. They will be expected to create a device to rank the products offered from best to worst. Students will be given tables that show: cost per product, customer rating, profits made and affordability. The second letter offers students a twist since new products are being introduced for the store to sell and a budget constraint will be introduced.

## MFAS Formative Assessments

Students are asked to add, subtract, multiply, and divide positive and negative fractions.

Students are asked to rewrite complex fractions as simple fractions in lowest terms.

Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.

## Original Student Tutorials Mathematics - Grades 6-8

Evaluate numerical expressions with rational numbers expressed as fractions using the order of operations and properties of operations in this interactive tutorial.

This is part 1 in a two-part series.

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

## Student Resources

## Original Student Tutorials

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Evaluate numerical expressions with rational numbers expressed as fractions using the order of operations and properties of operations in this interactive tutorial.

This is part 1 in a two-part series.

Type: Original Student Tutorial

## Problem-Solving Task

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Type: Problem-Solving Task

## Tutorials

Solve a multi-step word problem in the context of a cab fare.

Type: Tutorial

In this example, you determine the volume of frozen water and express the answer as a fraction.

Type: Tutorial

This video demonstrates dividing fractions as multiplying by the reciprocal.

Type: Tutorial

This video demonstrates dividing a whole number by a fraction by multiplying by the reciprocal.

Type: Tutorial

This video tutorial shows examples of writing expressions in simplified form and evaluating expressions.

Type: Tutorial

## Parent Resources

## Problem-Solving Task

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Type: Problem-Solving Task