# Walking to Win (First Class Period)

## Linear Relationships

Use for CMP2, Problem 2.1 Walking to Win (Day 1 of the Lesson)

Use for CMP3, Problem 2.1 Henri and Emile's Race

This video illustrates the strategies the class uses to solve an open problem that is the first problem of four in this sequence. The summary on this day includes a suggestion from the class that the problem does not make sense. The teacher challenges them to make adjustments to the problem.

The focus is on what the students understand, where the students are in relation to the goals of this Investigation, and what the teacher can do to add mathematical value to the summary phase of the lesson.

The video concludes with the teacher reflecting on the lesson.

Real time is one class period or 55 minutes.

As you view the video, consider the following:

- What is the evidence of students’ understanding and reasoning? What prior understandings do you see students using or building upon?
- What is the evidence of students’ use of the mathematical practices from the Common Core State Standards? To what extent are students growing in their sophistication of their use of the practices?
- Were there any “aha moments” in the video?
- How is the teacher facilitating the development of students’ understanding and reasoning?
- As a teacher, how would you use the information from this lesson to plan the next lesson?

- Full Length Video (23:15)
- CMP2 Problem 2.1
- CMP3 Problem 2.1
- CMP2 Goals for Investigation 2
- Find solutions to a problem using a table or graph
- Understand the connections between linear equations and patterns in the tables and graphs of those relations, including rate of change, and the x- and y-intercepts
- Translate information about linear relations given in a table, a graph, or an equation to one of the other forms
- Connect solutions in graphs and tables to solutions of equations
- Write equations for linear relationships and describe what information the variables and numbers represent

- CMP3 Goals for Investigation 2
- Linear Relationships Recognize problem situations in which two variables have a linear
relationship.
- Identify and describe the patterns of change between the independent and dependent variables for linear relationships represented by tables, graphs, equations, or contextual settings
- Construct tables, graphs, and symbolic equations taht represent linear relationships
- Identify the rate of change between two variables and the x- and y-intercepts from graphs, tables, and equations that represent linear relationships.
- Translate information about linear relationships given in a contextual setting, a table, a graph, or an equation to one of the other forms
- Write equations that represent linear relationships given specific pieces of information, and describe what information the variables and numbers represent
- Make a connection between slope as a ratio of vertical distance to horizontal distance between two points on a line and the rate of change between two variables that have a linear relationship
- Recognize that y = mx represents a proportional relationship
- Solve problems and make decisions about linear relationships using information given in tables, graphs, and equations

- Linear Relationships Recognize problem situations in which two variables have a linear
relationship.
- Suggestions for organizing Professional Development
- Student Work