**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Number & Quantity: Quantities

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

**Cluster:**Reason quantitatively and use units to solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting 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

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Lesson Study Resource Kit

## Perspectives Video: Professional/Enthusiasts

## Problem-Solving Tasks

## Unit/Lesson Sequence

## Worksheet

## STEM Lessons - Model Eliciting Activity

The Corn Conundrum MEA provides students with an agricultural problem in which they must work as a team to develop a procedure to select the best variety of corn to grow under drier conditions predicted by models of global climate change. Students must determine the most important factors that make planting crops sustainable in restricted climate conditions for the client. The main focus of this MEA is manipulating factors relating to plant biology, including transpiration and photosynthesis.

The topic of this MEA is work and power. Students will be assigned the task of hiring workers to complete a given task. In order to make a decision as to which workers to hire, the students initially must calculate the required work. The power each worker can exert, the days each worker is available to work each week, the number of sick days each worker has taken over the past 12 months, and the salary each worker commands will then be provided. Full- and/or part-time positions are available. Through data analysis, the students will need to evaluate which factors are most significant in the hiring process. For instance, some groups may select the most efficient workers; other groups may select the group of workers that will cost the company the least amount of money; still other groups may choose the workers that can complete the job in the shortest amount of time. Each group will also be required to provide the rationale that justifies the selection of which workers to hire.

In this MEA students compare data from different commercial floral preservatives. Students are asked to choose which is the best preservative for a certain floral arrangement.

The focus of this MEA is oil spills and their effect on the environment. In this activity, students from a fictitious class are studying about the effects of an oil spill on marine ecosystems and have performed an experiment in which they were asked to try to rid a teaspoon of corn oil from a baking pan filled with two liters of water as thoroughly as possible in a limited timeframe and with limited resources. By examining, analyzing, and evaluating experimental data related to resource usage, disposal, and labor costs, students must face the tradeoffs that are involved in trying to preserve an ecosystem when time, money, and resources are limited.

In the Sugar Scrub MEA students will analyze 5 sugar scrub formulas. In the first part, students are asked to evaluate each formula based on color, scent, and exfoliation. In the second part, students apply their methodology to a cost analysis of the scrubs.

This activity can be used with students in statistics, algebra 2, or a precalculus course who have a good understanding of the statistical methods that are used in describing a given data set.

In this activity, students will utilize measurement data provided in a chart to calculate areas, volumes, and densities of cookies. They will then analyze their data and determine how these values can be used to market a fictitious brand of chocolate chip cookie. Finally, they will integrate cost and taste into their analyses and generate a marketing campaign for a cookie brand of their choosing based upon a set sample data which has been provided to them.

## MFAS Formative Assessments

Students are given a set of data and are asked to choose the scale for the axes, graph the data, and explain why they chose the scales they used.

Students are asked to choose and justify the unit to be used in a formula and are asked to choose and explain the unit used in the answer.

Students are asked to find the approximate number of trees that are saved by using recycled paper.

## Student Resources

## Perspectives Video: Professional/Enthusiast

Get fired up as you learn more about ceramic glaze recipes and mathematical units.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout. Students are asked to determine which product will be the most economical to meet the requirements given in the problem.

Type: Problem-Solving Task

The problem requires students to not only convert miles to kilometers and gallons to liters but they also have to deal with the added complication of finding the reciprocal at some point.

Type: Problem-Solving Task

This task asks students to calculate the cost of materials to make a penny, utilizing rates of grams of copper.

Type: Problem-Solving Task

Students are asked to use units to determine if the given statement is valid.

Type: Problem-Solving Task

This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. Students are given a scenario and asked to determine the number of people required to complete the amount of work in the time described. The task requires students to exhibit MAFS.K12.MP.1.1, Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either MAFS.912.A-CED.1.1 or MAFS.912.N-Q.1.1, depending on the approach.

Type: Problem-Solving Task

This resource poses the question, "how many vehicles might be involved in a traffic jam 12 miles long?"

This task, while involving relatively simple arithmetic, promps students to practice modeling (MP4), work with units and conversion (N-Q.1), and develop a new unit (N-Q.2). Students will also consider the appropriate level of accuracy to use in their conclusions (N-Q.3).

Type: Problem-Solving Task

The task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.

Type: Problem-Solving Task

This task provides students the opportunity to make use of units to find the gas needed (MAFS.912.N-Q.1.1). It also requires them to make some sensible approximations (e.g., 2.92 gallons is not a good answer to part (a)) and to recognize that Felicia's situation requires her to round up. Various answers to (a) are possible, depending on how much students think is a safe amount for Felicia to have left in the tank when she arrives at the gas station. The key point is for them to explain their choices. This task provides an opportunity for students to practice MAFS.K12.MP.2.1: Reason abstractly and quantitatively, and MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others.

Type: Problem-Solving Task

## Parent Resources

## Perspectives Video: Professional/Enthusiast

Get fired up as you learn more about ceramic glaze recipes and mathematical units.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout. Students are asked to determine which product will be the most economical to meet the requirements given in the problem.

Type: Problem-Solving Task

The problem requires students to not only convert miles to kilometers and gallons to liters but they also have to deal with the added complication of finding the reciprocal at some point.

Type: Problem-Solving Task

This task asks students to calculate the cost of materials to make a penny, utilizing rates of grams of copper.

Type: Problem-Solving Task

Students are asked to use units to determine if the given statement is valid.

Type: Problem-Solving Task

This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. Students are given a scenario and asked to determine the number of people required to complete the amount of work in the time described. The task requires students to exhibit MAFS.K12.MP.1.1, Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either MAFS.912.A-CED.1.1 or MAFS.912.N-Q.1.1, depending on the approach.

Type: Problem-Solving Task

This resource poses the question, "how many vehicles might be involved in a traffic jam 12 miles long?"

This task, while involving relatively simple arithmetic, promps students to practice modeling (MP4), work with units and conversion (N-Q.1), and develop a new unit (N-Q.2). Students will also consider the appropriate level of accuracy to use in their conclusions (N-Q.3).

Type: Problem-Solving Task

The task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.

Type: Problem-Solving Task

This task provides students the opportunity to make use of units to find the gas needed (MAFS.912.N-Q.1.1). It also requires them to make some sensible approximations (e.g., 2.92 gallons is not a good answer to part (a)) and to recognize that Felicia's situation requires her to round up. Various answers to (a) are possible, depending on how much students think is a safe amount for Felicia to have left in the tank when she arrives at the gas station. The key point is for them to explain their choices. This task provides an opportunity for students to practice MAFS.K12.MP.2.1: Reason abstractly and quantitatively, and MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others.

Type: Problem-Solving Task