Curriculum

Middle School Math Modeling Curriculum For In-person, Digital, or Hybrid learning

Topics covered: Ratios & Proportions, Slope & Speed, and Linear Equations

Download Lab PDFs

Curriculum Overview

In order to understand linear equations, students need to have an understanding of the meaning of all the parts of the equation as well as how changes to the equation affect the graph of the equation and the meaning that the graph conveys. By starting with Ratios and Proportions, students are able to differentiate between these two very important mathematical concepts and determine which they are dealing with when they get to linear equations. Thay can begin to internalize what the ratios are representing  in the real world and how changing the ratio changes the graph of the line of the graph and what it represents. 

In the next section, students connect the proportional relationship of constant speed with the slope of the line. They can use the slope of a line to create the equation for the graph of their real world data and then use slopes to graph other lines and begin to understand the story of the graph even without having to collect the data themselves. At this point, students will have an understanding of “m,” the first part of the linear equation. 

In Part 3, students will again use motion to give them context for the Y-intercept part of the linear equation. By knowing that the y-intercept can mean the startinging point, students can combine their understanding of the ratio as the slope of the line, model the proportional relationship on the graph and choose an appropriate starting point for data they are given, data they collect, or a graph they are provided with. 

They can tell the story of what is happening in the graph by understanding the numbers in the equation and create an equation that mathematically explains the motion described by the graph. 

Options for In-Person and Digital Learning

Throughout this curriculum, we’re offering options for conducting classroom activities or discussions both in-person and online, which we hope will be especially useful given the uncertainty of teaching with the ongoing COVID-19 pandemic. We want to provide options for each step of the activities that typically appear in this curriculum. 

The steps in each lesson usually take the following form:  

  1. Conducting a lab
  2. Creating a whiteboard in small groups
  3. Commenting and discussing the class’ whiteboards 
  4. Having a class-wide whiteboard meeting 

Here, we break down what each step looks like in-person or digitally. 

In PersonDigital
Conducting a labSome labs are best conducted digitally, others physically, and others could involve either. We include options in the curriculum for both digital and physical experiments.
In each section, you’ll find recommendations for conducting the lab depending on which modality you’re working in.
Creating a whiteboard in small groupsCreate physical whiteboards and ask students to draw and write. 
Student’s roles can be split up as follows: Recorder – writes on WBPresenter – Starts the discussion about WBLeader – make sure everyone agrees
Create ‘whiteboards’ using a digital tool. You can use some of the options listed below. 
Ask students to screenshot their lab work, upload it to their whiteboards, and write additional details. Instruct students on how to take a screenshot and upload. 
Student’s roles can be split up as follows: Recorder – Shares Screen and writes on WBPresenter – Starts the discussion about WBLeader – make sure everyone agrees, uploads the board
Commenting and discussing the class’ whiteboards Have students walk around the classroom and leave sticky notes on other group’s whiteboards with comments, questions, and thoughts. 
Have students review comments they received on their whiteboards. 
All of the digital whiteboards options below allow students to view their classmate’s boards. Students can also screenshot their work and paste it into a Slides/Powerpoint document in order to have all boards in one place.
You can ask students to view other people’s whiteboards and leave comments with methods specific to whichever whiteboard you choose.
Having a class-wide whiteboard meeting Reconvene as a class for a discussion. When working on definitions or needing to document class work, you can use the slides we provide in this curriculum and project them to the front of the room. 
If you happen to be working without a projector, you can document on your whiteboard and take pictures at the end of class (however we would recommend digital documentation so that you can revisit with your class throughout). 
There are moments in the curriculum in which we will ask students to share their questions with the class and then see if they can answer any of the other students’ questions. For these activities, you can have students post sticky notes at the front of the class then, in smaller groups, cycle through and have students respond to the questions. 
Reconvene on your video-conferencing platform and have a full discussion. 
Use the slides provided in the curriculum or create your own slides/documents to keep track of your class’ thoughts during discussion. Documenting in this way will make lessons easier to revisit. 
There are moments in the curriculum in which we will ask students to share their questions with the class and then see if they can answer any of the other students’ questions. For this activity, you can ask students to write their questions in the chat and then respond in the chat. You could also use some of the chat discussion options provided below. 

Options for Digital Whiteboards

Options for Digital Discussions

Instructional Goals 

Note: Full instructional goals are listed in lessons 

6th Grade

  1. Use ratio and rate reasoning to solve mathematical problems and problems in real-world context (e.g., by reasoning about data collected from measurements, tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). 
  2. Solve unit rate problems including those involving unit pricing and constant speed. 
  3. Use variables to represent two quantities that change in relationship to one another to solve mathematical problems and problems in real-world context.

7th Grade

  1. Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship b. Identify the constant of proportionality (unit rate) c. Represent proportional relationships by equations.
  2. Explain what a point (x, y) on the graph of a proportional relationship means in the situation, with special attention to the points (0, 0) and (1, r) where r is unit rate.

8th Grade

  1. Graph proportional relationships interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. 
  2. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
  3. Given a description of a situation, generate a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or a graph. Track how the values of the two quantities change together. Interpret the rate of change and initial value of a linear function in terms of the situation it models, its graph, or its table of values.

Lesson Sequence

Section 0.0 – Supplemental Materials Checklist 

Section 1.0: Perfect Purple Paint (Ratios and Proportions)

1.1 Introduction

1.2 Create a Model

1.3 Refine Your Model (Whiteboard Discussion)

Suggested Assignment: Intro to Ratios

Suggested Assignment: Help Nico with Ratios 

1.4 Practice Help Giving & Review Talk Moves

1.5 Create Your Own Color

1.6 Discuss your Model

1.7 Integrate Feedback on Model

Suggested Assignment: Proportional Relationships

Suggested Assignment: Solving Proportions

Section 2.0: Buggy Lab (Slope and Speed)

2.1 Proportion Problems Brainstorm

2.2 Accuracy with a Stopwatch

2.3 Buggy Lab: Collect Data 

2.4 Buggy Lab: Create a Whiteboard

2.5 Buggy Lab: Discussion

2.6 Buggy Lab: Board Meeting

Suggested Assignment: Khan Academy Unit Rate

Section 3.0: Row Boats (Linear Equations)

3.1 Row Boat Lab: Collect Data and Make Whiteboards

3.2 Row Boat Lab: Discuss Your Models

3.3 Row Boat Lab: Whiteboard Meeting

3.4 Row Boat Lab: Takaways

Suggested Assignment: Help with Functions Assignment 

Suggested Assignment: Slope-Intercept Form

Section 0.0 Materials Checklist 

Links labeled with lesson numbers are specific to those lessons. Links without a number are used throughout or are suggested materials. 

Physical Materials:

Teacher resources: 

Slides: 

Digital Tools: 

Khan Academy Videos: 

Student Handouts: 

List of Assignments 

1.0 Perfect Purple Paint: 
2.0 Buggy Lab
3.0 Row Boat Lab
Useful Links (not critical to curriculum)