standard_description: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Narrative
The purpose of this activity is for students to compare the length of two objects using a third object. When students decide if the teacher's desk will fit through the door or compare other large pieces of furniture, they will need to be precise about which lengths they are measuring as objects like the teacher's desk, a rug, and a bookcase, have a length, width, and in some cases a height (MP6). Next, they will need to select an appropriate third object to use to compare the lengths they have chosen. Teachers may choose to assign different questions for different groups to start with to facilitate student movement around the room. Teachers may also change any question that does not apply to their classroom.
MLR8 Discussion Supports.
Synthesis: For each observation that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to decide which problem to start with and the order to complete the task.
Supports accessibility for: Attention, Social-Emotional Functioning
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group needs measuring materials from the previous activity.
Launch
Groups of 2
Give students access to measuring materials.
“Have you ever seen someone move a large piece of furniture, like a couch, from one room to another? Is it easy to move big pieces of furniture? Why or why not?”
30 seconds: quiet think time
Share responses.
“I have been thinking about getting a new desk. If I do, I will have to move this desk out of the room. I am not sure if this desk will fit through the door. How can we check to see if it will fit?” (We could measure with a string.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“You are all going to check to see if my desk will fit through the door. You are also going to compare the length of some other objects in the room.”
Activity
15 minutes: partner work time
Monitor for a group that measures the width of the teacher's desk and one that measures the length.
Student Facing
Will the teacher’s desk fit through the door?
Show your thinking using drawings, numbers, or words.
Will a student desk fit through the door?
Show your thinking using drawings, numbers, or words.
Which is longer, the bookshelf or the rug?
Show your thinking using drawings, numbers, or words.
Which is longer, the file cabinet or the bookshelf?
Show your thinking using drawings, numbers, or words.
Which is shorter, the bookshelf or the teacher’s desk?
Show your thinking using drawings, numbers, or words.
Will the teacher’s desk fit next to the bookshelf?
Show your thinking using drawings, numbers, or words.
Student Response
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Activity Synthesis
Invite previously identified students to share.
For each student, ask: “How did they compare the length of the objects? What tool did they use? What part of each object did they measure?”


aligns: no