##
* *Reflection: Writing Across the Disciplines
Comparing Investments: A Math Assessment Project Classroom Challenge - Section 7: Writing and Reflecting: Comparing Investments

In this section, students worked on completing an Idea Organizer to compare and contrast the different investments modeled in today's performance task.

The writing prompt was a piece of the lesson that I added to the original Performance Assessment Lesson from the Math Assessment Project. Adding a written component to performance tasks and/or group work really can help strike a nice balance between assessing group AND individual understanding of key concepts in the unit.

In reflecting upon how this section played out in the classroom, I keep coming back to the importance of explicit instruction and time in the classroom. Many of my students have never been taught how to write a solid expository piece of writing, never mind how to organize their ideas. I try and take the time in class to teach students how to organize their ideas but also time to practice and apply the skill.

The end result can be powerful. The sample student work are both from my fundamentals section of Algebra I, which is a tracking designated for students who benefit from additional mathematics support (everyday for about 90 minutes as opposed to the CP and Honors sections that meet every other day for the same time). The **Student Work 1 Comparing Investments **shows a group that is doing a nice job of justifying their thinking with evidence. Although there may be other investments that make more money over time, I was pleased to see the use of details and evidence in this group crafting their response. The **Student Work 2 Comparing Investments **is an example of a written response that indicates an emerging understanding of the idea that exponential growth functions will eventually outpace linear functions over time.

Note that students are not simply stating which investment they would choose, but are beginning to learn how to use evidence to justify their claims. As this lesson is taught relatively early in the school year, I am pleased with the progress in mathematical writing that students have made since September.

*Writing Across the Disciplines: Organizing Ideas for Better Written Ouput*

# 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.

*expand content*

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.

*expand content*

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.

*expand content*

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.

*expand content*

#### 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.

*expand content*

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.

*expand content*

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

*expand content*

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

*expand content*

##### Similar Lessons

###### Comparing Growth Models, Day 1

*Favorites(2)*

*Resources(20)*

Environment: Suburban

###### How Much Will College Cost in the Future?

*Favorites(9)*

*Resources(16)*

Environment: Suburban

###### Leap of Faith!

*Favorites(4)*

*Resources(14)*

Environment: Urban

- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- 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
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- 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