Formative Assessment: Modeling Population Growth (A Math Assessment Project Classroom Challenge)

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SWBAT interpret and create equations to model a real life scenario involving a geometric sequence. SWBAT create arguments to support their reasoning.

Big Idea

Students model an expanding kitten population with functions!

Entry Ticket: Having Kittens

15 minutes

The pre-test for the Having Kittens Math Assessment Project Classroom Challenge Lesson is a great way to gauge baseline understanding through an open-ended formative assessment. 

Students complete this Pre-Assessment (page 11 of the Math Shell document in this resource) the previous day in class or for homework. The Pre-assessment involves students critiquing a poster from an animal shelter that makes claims about the number of descendants that one cat can produce. The reason to have students complete the task prior to the day's activity is so I can assess student understanding and plan the appropriate level of support and challenge in the lesson. 


Introduction and Questions for Deeper Understanding

10 minutes

To open class, I ask students questions based on their responses to the Pre-assessment. The lesson plan from the Math Assessment Project (resource in this section) provides an excellent table that identifies common misconceptions that students have and suggested prompts and questions to challenge those misconceptions.

I use the MAP Center resources as well as my experience with my students to generate questions. Here are some of the questions that I plan to ask my students:

  • What observations did you make about the poster? 
  • What claims are being made in the poster? Are these claims justified with mathematics/examples/evidence? 
  • What assumptions are being made in the poster? Do the assumptions seem reasonable? Why or why not?




Collaborative Work: Producing a joint solution

20 minutes

Students then work together in small groups comparing and contrasting the work from their group members to create a joint solution (Student Work Example: Joint Solution). This activity gets right at Math Practice 3 as students are set up to communicate their own reasoning and to listen and critique the reasoning of others.

During this time I am observing how groups are working together and also providing groups support in their problem-solving.

It is difficult for many students to initiate with this task. Therefore, I focus my attention to being sure every group is able to begin a conversation about comparing and contrasting ideas from the different group members. To accomplish this task, I check in with groups, and provide reflective prompts. For example, if one student identified an assumption that he/she though was not reasonable, I would point that out to the group and ask a follow up question to help scaffold the group conversation. What other assumptions did the group identify? What evidence did your classmates use to justify their opinion?

Gallery Walk

10 minutes

Once the groups are finished with their posters I have them post them around the classroom. Groups then rotate and assess other groups posters in a short Gallery Walk. I provide students with sticky notes to write constructive criticism for the posters that they visit. 

Teacher's Note: This setup varies slightly from the suggested activity in the Math Assessment Project lesson plan. I use the gallery walk because it meet a similar intent of students reviewing other groups work and providing feedback, and my classes are familiar with the structure of the gallery walk as I use that instructional strategy in other lessons.

Comparing Different Solutions

20 minutes

Once students have completed the gallery walk and given a few minutes to read and process the feedback from their peers. 

The next task at hand is for students to assess sample work in writing. I like the progression of tasks in this lesson from group work to individual work as it is flexible and provides a number of different domains (verbally, written, etc.) for students to think about the concepts in the lesson. 

During this section I provide each student with one of the three sample works (pages 12-14 in the Math Shell document in this section) provided in the lesson plan.

I tend to find there is not enough time for every student to complete feedback on all three pieces of sample work. The nice part about providing each student one of the samples is I can Differentiate Instruction by giving students the sample work that gets at an aspect of the lesson at the level of understanding each student is at. 

Homework for this lesson can also be for students to complete feedback on the two pieces of sample work they did not complete in class.

Whole class discussion: Comparing other solutions

20 minutes

After students have completed their written feedback on the sample work of Alice, Wayne and Ben, I reconvene the class for a whole group discussion.

I like to use the slides provided by the Math Assessment Project as a guide to the discussion. As we progress through each of the three sample works, I have students share their feedback on each piece of work AND have students comment on any similarities or differences between the sample work and their own reasoning/thinking.


Exit Ticket and Reflection: How Did You Work?

10 minutes

To conclude class students complete the "How Did You Work?" worksheet (page 15 of the Having Kittens: A Mathematics Assessment Project Classroom Challenge document in this section as a resource) that provides a nice support for students to engage in all important skill of reflection. Giving students time to reflect on their own work, the good and the bad, allows students to think about what they can improve on and HOW to make those improvements. 


For homework I either assign students to complete the feedback forms for the remaining two sample student work that they did not complete in class OR complete the "How Did I Work?" reflection sheet.

For this class I do not assign homework until the end of class because the assignment depends on progress made in the lesson. If there is not time to complete the reflection I make that the homework, but if the class does complete the reflection I assign the remaining sample work feedback forms.


Mathematics Assessment Project (2012). Modeling: Having Kittens: A Classroom Challenge AFormative Assessment Lesson. Shell Center: University of Nottingham. Accessed online on December 16 at