Unit 5, Lesson 27
Solving Problems with Systems of Equations
Accelerated 7
27.1
Warm-up
5 mins
Are We There Yet?
Standards Alignment
Building On
6.EE.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Addressing
Building Toward
Instructional Routines
NoneMaterials
NoneActivity Narrative
The purpose of this Warm-up is to get students to reason about representing a context about distance as an expression. For students who use the equation
Launch
Give students 2 minutes of quiet work time, and follow that with a whole-class discussion.
Activity
NoneStudent Task Statement
A car is driving toward home at 0.5 miles per minute. If the car is 4 miles from home at
Activity Synthesis
Invite students to share their selections and to explain their reasoning. After each explanation ask the rest of the class if they agree or disagree and how the context is represented in the expression.
27.2
Activity
35 mins
Cycling, Fundraising, Working, and ___?
Instructional Routines
MLR8: Discussion SupportsMaterials
To Gather
Tools for creating a visual displayActivity Narrative
In this activity, students reason about situations involving two different relationships between the same two quantities. Then they invent their own problem of the same type. Although students are encouraged by the language of the activity to use a system of equations to solve the problems, they may elect to use a different representation to explain their thinking (MP1, MP3).
As students work through the first three problems, notice the ways in which students reason about the problems with and without systems of equations. Identify some groups with particularly compelling or clear reasoning, and ask them to share later.
Launch
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