##
* *Reflection: Perseverance
Comparing Investments: A Math Assessment Project Classroom Challenge - Section 3: Collaborative Activity 1 - Matching Investments Plans and Formulas

In this section students are asked to match up different representations of functions depicting simple and compound interest. This task, developed by the Mathematics Assessment Project, worked well in my classroom.

I think that providing a focus area for students to zoom in on is important. In this task, for example, students are not asked to generate graphs or scenarios as they different representations are given to them. This simple, yet ingenious design allows students to dig deep into the connections between the representations.

One pointer when implementing this lesson in the classroom: I find that providing students with a poster board and organizing their space can help initiate and facilitate the process. When the different cards are simply laid out on a desk, they can easily be lost and many students have trouble keeping track of the work they have done as well as maintaining an organized space.

*Motivating Students to Work with Complex Problems*

*Perseverance: Motivating Students to Work with Complex Problems*

# Comparing Investments: A Math Assessment Project Classroom Challenge

Lesson 8 of 10

## Objective: SWBAT identify a linear function as changing at a constant rate over time. SWBAT interpret the structure of expressions. SWBAT interpret expressions for functions based on the scenario they model.

## Big Idea: Students compare simple and compound interest problems as a backdrop for distinguishing between linear and exponential functions across representations!

*90 minutes*

The Formative Assessment Task used in this lesson offers students a great opportunity to connect mathematics to the real world in a meaningful way and there are a number of extensions that can come about as a result of this lesson. For example, students can research house prices in the area and calculate different mortgage payments as the interest rate varies, or research interest rates on different credit cards and how much an item would cost if they bought it with a credit card and paid if off in different time intervals.

To begin the lesson, students complete a pre-assessment called **Making Money** on their own. Before starting the task, I will provide a hook for the lesson - that of asking students about what they know about making money. I may also review the idea of interest and how investments in a bank (or other investments) work.

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After completing the problem on making money, students work in small groups matching different investment scenarios with formulas with the **Comparing Investments Plans and Formulas Sort**

This is a great activity for students to translate between written relationships and formulas that match the scenario. This is an especially valuable exercise for students who struggle with creating equations as it allows them to look for and see structure and connections between formulas and the scenario they model in a manner that is easy to interact with and highly scaffolded.

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Students then work on completing the **Comparing Investments Plans to Tables and Graphs Sort**.

This sort builds off of the previous section of matching verbal descriptions with formulas. For this part of the sort, students are matching the investment plans with matching tables of values and graphs.

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Students take the next 20 minutes to complete the **Comparing Investments: Card Statement Sort** (at this point students have a written description of the investment, a formula, a graph and a table for each investment).

This is a more open ended activity in many ways as it allows students to identify different strategies to differentiate between the different investments. For example, some students may look to the tables to see patterns or proof that one investment matches a particular statement card. Another student may use a graph and the formula together to do the same.

During this time, my job as a teacher is to help provide the right balance of support and challenge to student groups. I want to help students initiate the task by asking a lead in question, but I also do not want to provide too much support to students who can get through the activity with a little perseverance.

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#### Whole Class Discussion

*15 min*

The class then turns to a whole class discussion to check in on progress made thus far and to identify next steps.

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To conclude class, I assign students to complete the I**dea Organizer: Writing and Reflecting on Comparing Investments** to the following prompt:

Choose one card set that your group matched**. **Create a narrative explaining the strategies and reasoning your group used to match the card set. **Use evidence to support your answer!!!**

The intent of this assignment is to help students consolidate and summarize their thinking. in addition, I want students to back up their ideas with evidence, a skill that many of the students I work with have relative difficulties with.

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To wrap up class, students work on the **Making Money Revisited Exit Ticket**. Typically there is not enough time to complete the assignment in class. Therefore, I either assign the task as homework or provide students with some time at the beginning of next class to complete the assignment.

The setup of having a similar pre and post assessment like the Math Assessment Project lesson has is great because it allows teachers to compare student progress focused on the day's objectives.

#### Resources

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Mathematics Assessment Project (2012). *Comparing Investments: A Mathematics Assessment Project Classroom Challenge - A Formative Assessment Lesson*. Shell Center: University of Nottingham. Accessed online on May 26, 2014 at http://map.mathshell.org/materials/download.php?fileid=1250

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- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
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- UNIT 6: Operations on Polynomials
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- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Everything is Relative: An Introduction to Linear Functions
- LESSON 2: Creating Linear Functions to Model State Population Data
- LESSON 3: The Tablet Wars: Comparing Linear Functions in Different Representations
- LESSON 4: Precipitation and Temperature: Estimating Rate of Change Over a Specified Interval
- LESSON 5: Creating and Solving Equations and Inequalities
- LESSON 6: Practice Session on Creating and Solving Equations and Inequalities
- LESSON 7: Running and the Domain of Middle Earth: Modeling a Run and a Hobbit's Journey through Piece-wise Functions
- LESSON 8: Comparing Investments: A Math Assessment Project Classroom Challenge
- LESSON 9: Study Session for Unit Test on Linear Functions
- LESSON 10: Unit Assessment: Linear Functions