standard_description: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^(2) + y^(2))^(2) = (x^(2 )– y^(2))^(2) + (2xy)^(2 )can be used to generate Pythagorean triples.
problem_activity: Activity
The purpose of this activity is for students to use the four operations on rational numbers solve real-world problems. Monitor for students who solved the problem using different representations and approaches.
Launch
Arrange students in groups of 2–4. Given them 4 minutes of quiet work time, followed by small group and then whole-class discussion.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy. For example, “First, I _____ because _____. Then, I…,” “I noticed _____ so I…” and “I tried _____ and what happened was…”
Supports accessibility for: Language; Social-emotional skills
Reading: MLR6 Three Reads.
Use this routine to support reading comprehension of this word problem, without solving it for students. In the first read, students read the problem with the goal of comprehending the situation (e.g., A utility company charges for energy use.). In the second read, ask students to identify the quantities and relationships, without focusing on specific values. Listen for, and amplify, the quantities that vary in relation to each other in this situation: electricity used, in kilowatt-hours; amount spent on electricity used, in dollars; electricity generated and not used, in kilowatt-hours; amount credited for electricity generated and not used, in dollars. Invite students to draw a diagram to represent the relationships among these quantities. After the third read, ask students to brainstorm possible strategies to answer the questions. This helps students connect the language in the word problem and the reasoning needed to solve the problem, maintaining the intended level of cognitive demand in the task.
Design Principle(s): Support sense-making​
Student Facing
A utility company charges
$
0.12 per kilowatt-hour for energy a customer uses. They give a credit of
$
0.025 for every kilowatt-hour of electricity a customer with a solar panel generates that they don't use themselves.
A customer has a charge of
$
82.04 and a credit of -
$
4.10 on this month's bill.
What is the amount due this month?
How many kilowatt-hours did they use?
How many kilowatt-hours did they generate that they didn't use themselves?
Student Response
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Student Facing
Are you ready for more?
Find the value of the expression without a calculator.
\((2)(\text-30)+(\text-3)(\text-20)+(\text-6)(\text-10) -(2)(3)(10)\)
Write an expression that uses addition, subtraction, multiplication, and division and only negative numbers that has the same value.
Student Response
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for free access to Extension Student Response.
Activity Synthesis
Select students to share their solution. Help them make connections between different solution approaches.


aligns: no