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

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.

General Information
Number: MAFS.912.N-Q.1
Title: Reason quantitatively and use units to solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Number & Quantity: Quantities

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.912.N-Q.1.AP.1a
Interpret units in the context of the problem.
MAFS.912.N-Q.1.AP.1b
When solving a multi-step problem, use units to evaluate the appropriateness of the solution.
MAFS.912.N-Q.1.AP.1c
Choose the appropriate units for a specific formula and interpret the meaning of the unit in that context.
MAFS.912.N-Q.1.AP.3a
Describe the accuracy of measurement when reporting quantities (you can lessen your limitations by measuring precisely).
MAFS.912.N-Q.1.AP.1d
Choose and interpret both the scale and the origin in graphs and data displays.
MAFS.912.N-Q.1.AP.2a
Determine and interpret appropriate quantities when using descriptive modeling.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

## Formative Assessments

Aquarium Visitors:

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.

Type: Formative Assessment

Notebooks to Trees:

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

Type: Formative Assessment

Density:

Students are given a scenario in which density is calculated and are asked to select the answer that is most appropriate given the degree of accuracy in the initial measurements.

Type: Formative Assessment

Fishy Formulas:

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.

Type: Formative Assessment

Tree Size:

Students are asked to determine if a diameter calculated to seven decimal places is appropriate given the degree of accuracy in the circumference measure used in its calculation.

Type: Formative Assessment

Time to Get to School:

Students are asked to describe potentially important variables that can be used in a model to predict the amount of time required to get to school.

Type: Formative Assessment

Rain Damage Model:

Students are asked to describe potentially important variables that can be used in a model to predict the amount of damage caused by a thunderstorm.

Type: Formative Assessment

## Lesson Plans

Bottled Up Energy:

This experimental design project deals with real life understanding of being assigned a group task, creating a budget, and providing evidence about the completion of the assigned task. The task in this case is that students are being asked to create a model of a car out of supplied materials and to test these designs. After each trial the students will analyze the data collected and make any improvements that are necessary. The teams will test all modifications and after analyzing the results of their trials, they will create a presentation to the class on how their design performed.

Type: Lesson Plan

Earthquake Structures and the Richter Scale:

In this engineering design challenge, students will build an earthquake-proof structure out of spaghetti and marshmallows and then test them with an earthquake shake table. Students will research earthquake damage and how designs have changed with our new technologies and our understanding of earthquakes. After testing and research, students will prepare and present a final presentation on their findings. They will also explore the use of the Richter scale as a measurement of earthquake intensity. This is a culminating activity for a unit on Earth's forces.

Type: Lesson Plan

Compacting Cardboard:

Students with investigate the amount of space that could be saved by flattening cardboard boxes. The analysis includes linear graphs and regression analysis along with discussions of slope and a direct variation phenomenon.

Type: Lesson Plan

Dollars for Density:

This is a guided inquiry activity in which students use simple lab procedures and discussions to develop and apply the concept of density. Students collect and graph data which they use to explore the relationship between mass and volume. Then students use their graph, rather than a memorized formula, to identify the unknown substance.

Type: Lesson Plan

Crime Scene Measurements:

Using a crime scene scenario, students will measure length, mass, volume and temperature. They will calculate area and shoe size using a chart. Students will analyze soil samples using a microscope. Students will use the process of elimination based on their data to determine a suspect.

Type: Lesson Plan

Mass Mole Relationships: A Statistical Approach To Accuracy and Precision:

The lesson is a laboratory-based activity involving measurement, accuracy and precision, stoichiometry and a basic statistical analysis of data using a scatter plot, linear equation, and linear regression (line of best fit). The lesson includes teacher-led discussions with student participation and laboratory-based group activities.

Type: Lesson Plan

Mole Relay:

To be successful in chemistry, students need a solid foundation in solving multi-step (sequential) problems. This activity uses inexpensive materials to strengthening students understanding of stoichiometry problems during an engaging group competition. A student-centered approach develops the reasoning skills needed for scientific thinking. Each student assumes a different role as they complete work in a complex stoichiometry problem. Students may receive immediate feedback from their teammates so that success is felt by all learners.

Type: Lesson Plan

Prom Preparations:

Students will make decisions concerning features of their prom. Students will perform operations with percent and decimals to solve real-world problems involving money.

Type: Lesson Plan

Modeling: Having Kittens:

This lesson unit is intended to help you assess how well students are able to interpret a situation and represent the constraints and variables mathematically, select appropriate mathematical methods to use, make sensible estimates and assumptions, investigate an exponentially increasing sequence and communicate their reasoning clearly.

Type: Lesson Plan

Farming in the Gilded Age: A Simulation:

This video is about a simulation created by a teacher to show the hardships of "gambling" in the world of farming, especially in a past, less civilized time. The students were given 2000 and had to put 500 aside for various expenses. They were then given a list of 11 objects (crops and livestock) that they could chose from to purchase with the remaining 1500. The catch is, they only have a certain amount of space to use, and must plan which items will be more efficient in a set area. To simulate the purchasing of the crops and livestock, the teacher cut out squares with each item on it. He then had each group come up to spend their money on what they found fit for their particular group. After each group chose their ratios of crops and livestock, there was then a simulated growing season that had problems with certain crops and benefits of others. They then repeat the process for the following year with a different scenario for the growing season. At the end of the simulation, the teacher acted as if he was the banker that loaned the 2000 in the beginning. This is where it comes full circle to show why farming was so difficult in the past, and how it declined due to poor weather and the lack of the ability to pay off loans given to start farming in the first place.

Type: Lesson Plan

BIOSCOPES Summer Institute 2013 - Forces:

This lesson is designed to be part of a sequence of lessons. It follows resource 52937 "BIOSCOPES Summer Institute 2013 - Motion" and precedes resource 52910 "BIOSCOPES Summer Institute 2013 - Mechanical Energy." This lesson uses a predict, observe, and explain approach along with inquiry based activities to enhance student understanding of Newton's three laws of motion.

Type: Lesson Plan

BIOSCOPES Summer Institute 2013 - Thermal Energy:

This lesson is designed to be part of a sequence of lessons. It follows resource 52910 "BIOSCOPES Summer Institute 2013 - Mechanical Energy" and precedes resource 52705"BIOSCOPES Summer Institute 2013 - States of Matter." This lesson uses a predict, observe, and explain approach along with inquiry based activities to enhance student understanding of thermal energy and specific heat.

Type: Lesson Plan

BIOSCOPES Summer Institute 2013 - Mechanical Energy:

This lesson is designed to be part of a sequence of lessons. It follows resource 52648 "BIOSCOPES Summer Institute 2013 - Forces" and precedes resource 52957 "BIOSCOPES Summer Institute 2013 - Thermal Energy." This lesson uses a predict, observe, and explain approach along with inquiry based activities to enhance student understanding of the conservation of energy.

Type: Lesson Plan

BIOSCOPES Summer Institute 2013 - States of Matter:

This lesson is designed to be part of a sequence of lessons. It follows CPALMS Resource #52957 "BIOSCOPES Summer Institute 2013 - Thermal Energy" and precedes CPALMS Resource #52961 "BIOSCOPES Summer Institute 2013 - Solutions." The lesson employs a predict, observe, explain approach along with inquiry-based activities to enhance student understanding of states of matter and phase changes in terms of the kinetic molecular theory.

Type: Lesson Plan

Preserving Our Marine Ecosystems:

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.

Type: Lesson Plan

Motion: Speed and Velocity:

In this lesson students should be able to :

• Identify appropriate SI units for measuring speed.
• Compare and contrast average speed and instantaneous speed.
• Interpret position-time graphs.
• Calculate the speed of an object using slopes.

Type: Lesson Plan

Acceleration:

In this lesson students will learn to:

1. Identify changes in motion that produce acceleration.
2. Describe examples of objects moving with constant acceleration.
3. Calculate the acceleration of an object, analytically, and graphically.
4. Interpret velocity-time graph, and explain the meaning of the slope.
5. Classify acceleration as positive, negative, and zero.
6. Describe instantaneous acceleration.

Type: Lesson Plan

Shopping for a Home Mortgage Loan:

Students will analyze the data given to decide which type of loan they will buy. After selecting their options, students will estimate the first loan payment. FHA loans offer a better interest rate than conforming loans, but buying premium insurance is a requirement to qualify for an FHA loan, increasing the upfront cost of the loan. Fixed interest rate loans seem like the best choice because you have the same mortgage payment every month; however, adjustable rate loans offer a better interest rate and it has a cap on the interest rate.

Type: Lesson Plan

Testing water for drinking purposes:

The importance of knowing what drinking water contains. How to know what properties are present in different bottled water. Knowing the elements present in water that is advantageous to growth and development of many things in the body. To know what to be alert for in water and to understand the importance of water in general.

Type: Lesson Plan

How Fast Do Objects Fall?:

Students will investigate falling objects with very low air friction.

Type: Lesson Plan

Ramp It Up:

Using inquiry techniques, students, working in groups, are asked to design and conduct experiments to test the Law of Conservation of Energy and the Law of Conservation of Momentum. Upon being provided with textbooks, rulers, measuring tapes, stopwatches, mini-storage containers, golf balls, marbles, rubber balls, steel balls, and pennies, they work cooperatively to implement and revise their hypotheses. With limited guidance from the teacher, students are able to visualize the relationships between mass, velocity, height, gravitational potential energy, kinetic energy, and total energy as well as the relationships between mass, velocity, and momentum.

Type: Lesson Plan

Forced To Learn:

Using inquiry techniques, students, working in groups, are asked to design and conduct an experiment to test Newton's Second Law of Motion. Upon being provided with textbooks, rulers, measuring tapes, mini-storage containers, golf balls, marbles, rubber balls, steel balls, and pennies they work cooperatively to implement and revise their hypotheses. With limited guidance from the teacher, students are able to visualize the direct relationships between force and mass; force and acceleration; and the inverse relationship between mass and acceleration.

Type: Lesson Plan

Riding the Roller Coaster of Success:

Students compete with one another to design and build a roller coaster from insulation tubing and tape that will allow a marble to travel from start to finish with the lowest average velocity. In so doing, students learn about differences between distance and displacement, speed and velocity, and potential and kinetic energy. They also examine the Law of Conservation of Energy and concepts related to force and motion.

Type: Lesson Plan

The Video Game:

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.

Type: Lesson Plan

Efficient Storage:

The topic of this MEA is work and power. Students will be assigned the task of hiring employees to complete a given task. In order to make a decision as to which candidates to hire, the students initially must calculate the required work. The power each potential employee is capable of, the days they are available to work, the percentage of work-shifts they have missed over the past 12 months, and the hourly pay rate each worker commands will be provided to assist in the decision process. 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 prioritize speed of work, while others prioritize cost or availability/dependability.

Type: Lesson Plan

Flower Power:

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Sugar Scrub:

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.

Type: Lesson Plan

Students can organize information about a chemical substance into a menu that will help them establish their thoughts when converting using the concept of the mole. Ordering off their menu narrows the information to only what is relevant and allows them to easily set up factor label conversions.

Type: Lesson Plan

Corn Conundrum:

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.

Type: Lesson Plan

Amusement Park Physics:

Students will research various types of amusement park rides and use their findings to design a feasible ride of their own. They will summarize their findings and present their ride design to the class. Each student will then write a persuasive letter to a local amusement park describing the reasons their ride design is the best.

Type: Lesson Plan

Uncertainty of Measurement:

The students will learn the application of scientific notation, significant figures, accuracy and precision as they pertain to the collection of data (measurement).

Type: Lesson Plan

## Lesson Study Resource Kits

Measurement Matters:

This Lesson Study Resource Kit is an introductory unit on measurement for a Chemistry I course.

Type: Lesson Study Resource Kit

Motion and Forces:

This Lesson Study Resource Kit was adapted from a 2013 BioScopes physical science summer institute. It features a STEM-integrated unit plan that consists of resources and activities aligned to a unit of instruction on that employs Vernier LabQuest probeware in an investigation of Newton's Laws.

Type: Lesson Study Resource Kit

## Perspectives Video: Professional/Enthusiasts

The Science and Math Behind Sour Fizzy Candy:

Master candymaker Wes Raley describes the process and science behind making sour fizzy candy.

Type: Perspectives Video: Professional/Enthusiast

Unit Conversions:

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

Rubber Band Races for Testing Measurement Accuracy:

This activity will send your measurement lab to new distances.

Type: Perspectives Video: Teaching Idea

Ice Cream Van:

The purpose of this task is to engage students, probably working in groups, in a substantial and open-ended modeling problem. Students will have to brainstorm or research several relevant quantities, and incorporate these values into their solutions.

Weed Killer:

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.

Dinosaur Bones:

The purpose of this task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.

Bus and Car:

This task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip.

At a higher level, the task addresses MAFS.912.N-Q.1.3, since realistically neither the car nor the bus is going to travel at exactly the same speed from beginning to end of each segment; there is time traveling through traffic in cities, and even on the autobahn the speed is not constant. Thus students must make judgments about the level of accuracy with which to report the result.

Accuracy of Carbon 14 Dating I:

This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating.

Accuracy of Carbon 14 Dating II:

This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating.

Fuel Efficiency:

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.

How Much Is a Penny Worth?:

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

Runner's World:

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

Harvesting the Fields:

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 , 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.

Traffic Jam:

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).

Selling Fuel Oil at a Loss:

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.

Felicia's Drive:

This task provides students the opportunity to make use of units to find the gas needed (). 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.

Calories in a Sports Drink:

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. An unexpected surprise awaits in this case, however, as no reasonable interpretation of the level of accuracy makes sense of the information reported on the bottles in parts (b) and (c). Either a miscalculation has been made or the numbers have been rounded in a very odd way.

## Teaching Ideas

Now That is a Dense Graph:

Students will first measure and plot the total mass vs liquid volume in a graduated cylinder. They will then use slope and the mathematical formula for the plot to determine the density of the liquid, the density of a solid added to the liquid, and the mass of the graduated cylinder.

Type: Teaching Idea

Pump Up the Volume:

This activity challenges students to analyze the statistical distribution of volume measurements from a partially filled graduated cylinder. The free app, GeoGebra is used to create a box plot to aid in the analysis.

Type: Teaching Idea

Pump Up the Volume:

This activity is a statistical analysis of recorded measurements of a single value - in this case, a partially filled graduated cylinder.

Type: Teaching Idea

Now That is a Dense Graph:

In this activity, the density of ethanol is found by graphical means. In the second part, the density of sodium thiosulfate is found, also by graphical means. The values found are then analyzed statistically.

Type: Teaching Idea

A Certain Uncertainty:

Students will measure the mass of one nickel 10 times on a digital scale precise to milligrams. The results will be statistically analyzed to find the error and uncertainty of the scale.

Type: Teaching Idea

All Numbers Are Not Created Equal:

Although a sheet of paper is much thinner than the divisions of a ruler, we can make indirect measurements of the paper's thickness.

Type: Teaching Idea

## Unit/Lesson Sequence

Sample Algebra 1 Curriculum Plan Using CMAP:

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

### Using this CMAP

To view an introduction on the CMAP tool, please .

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

Type: Unit/Lesson Sequence

## Worksheet

Practice with Dimensional Analysis:

This is a worksheet that can be used for students individually or as a cooperative learning resource for practice with dimensional analysis. Answers are in red as a separate copy of the worksheet.

Type: Worksheet

## Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

## Perspectives Video: Professional/Enthusiast

Unit Conversions:

Type: Perspectives Video: Professional/Enthusiast

Weed Killer:

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.

Dinosaur Bones:

The purpose of this task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.

Bus and Car:

This task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip.

At a higher level, the task addresses MAFS.912.N-Q.1.3, since realistically neither the car nor the bus is going to travel at exactly the same speed from beginning to end of each segment; there is time traveling through traffic in cities, and even on the autobahn the speed is not constant. Thus students must make judgments about the level of accuracy with which to report the result.

Accuracy of Carbon 14 Dating I:

This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating.

Accuracy of Carbon 14 Dating II:

This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating.

Fuel Efficiency:

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.

How Much Is a Penny Worth?:

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

Runner's World:

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

Harvesting the Fields:

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 , 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.

Traffic Jam:

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).

Selling Fuel Oil at a Loss:

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.

Felicia's Drive:

This task provides students the opportunity to make use of units to find the gas needed (). 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.

Calories in a Sports Drink:

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. An unexpected surprise awaits in this case, however, as no reasonable interpretation of the level of accuracy makes sense of the information reported on the bottles in parts (b) and (c). Either a miscalculation has been made or the numbers have been rounded in a very odd way.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

## Perspectives Video: Professional/Enthusiast

Unit Conversions:

Type: Perspectives Video: Professional/Enthusiast

Weed Killer:

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.

Dinosaur Bones:

The purpose of this task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.

Bus and Car:

This task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip.

At a higher level, the task addresses MAFS.912.N-Q.1.3, since realistically neither the car nor the bus is going to travel at exactly the same speed from beginning to end of each segment; there is time traveling through traffic in cities, and even on the autobahn the speed is not constant. Thus students must make judgments about the level of accuracy with which to report the result.

Accuracy of Carbon 14 Dating I:

This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating.

Accuracy of Carbon 14 Dating II:

This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating.

Fuel Efficiency:

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.

How Much Is a Penny Worth?:

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

Runner's World:

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

Harvesting the Fields:

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 , 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.

Traffic Jam:

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).

Selling Fuel Oil at a Loss:

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.