options: Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

Work with equal groups of objects to gain foundations for multiplication.

Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

Interpret the structure of expressions.

Work with addition and subtraction equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

Represent and solve problems involving multiplication and division.

Understand and apply properties of operations and the relationship between addition and subtraction.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write expressions in equivalent forms to solve problems.

Understand the connections between proportional relationships, lines, and linear equations.

Use polynomial identities to solve problems.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Analyze patterns and relationships.

Solve systems of equations.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Write and interpret numerical expressions.

Understand properties of multiplication and the relationship between multiplication and division.

Rewrite rational expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Multiply and divide within 100.

Work with radicals and integer exponents.
problem_activity: Activity
This activity is designed to give students opportunities to use their understandings from this unit to perform mathematical modeling.
The trail mix context is familiar from the previous activity, but students are challenged to choose quantities, determine how to represent them, interpret and reason about them, and use the model they create to make choices. It also enables students to reflect on their model and revise it as needed (MP4).
Students are likely to want to use graphing technology, as the nutritional information involves decimals and the inequalities written would be inconvenient to graph by hand. This is an opportunity for students to choose tools strategically (MP5).
No time estimate is given here because the time would depend on decisions about the research students do and on the expectations for collaboration and presentation.
Launch
Arrange students in groups of 2–4. Provide access to Desmos or other graphing technology.
Explain the expectations for researching nutritional values, for collaboration with group members, and for presentation of student work. (If each group is presenting one response, provide each group with tools for creating a visual display. If each student is presenting a response, give each student tools for creating a visual display.)
Engagement: Develop Effort and Persistence.
Provide prompts, reminders, guides, rubrics, or checklists that focus on increasing the length of on-task orientation in the face of distractions. For each question, allot a specific amount of work time and display expectations. Display a countdown timer, along with a bulleted list of what teams or individuals are to produce to complete a given step. For instance, during question 1, display a 5 minute countdown timer and the list: “You’re finished if you. . . (1) Have your two ingredients (2) Have the nutrition information ready.”
Supports accessibility for: Attention; Social-emotional skills
Student Facing
It's time to design your own trail mix!
Choose two ingredients that you like to eat. (You can choose from the ingredients in the previous activity, or you can look up nutrition information for other ingredients.)
Think about the constraints for your trail mix. What do you want to be true about its calories, protein, sugar, fat, or fiber?
Write inequalities to represent your constraints. Then, graph the inequalities.
[IMG]
Is it possible to make trail mix that meets all your constraints using your ingredients? If not, make changes to your constraints or your ingredients and record them here.
Write a possible combination of ingredients for your trail mix.
Pause here so your teacher can review your work and give further instructions for displaying your work.
Student Response
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Activity Synthesis
Select groups to share their visual displays. Encourage students to ask questions about the mathematical thinking or design approach that went into creating the display. Here are questions for discussion, if not already mentioned by students:
What constraints did every group use?
How do the graphs of the various mixes compare?
Did anyone have to revise or change their model in order to come up with a solution they could use?
How did you use the graph to choose a recipe for your mix?
Representing, Conversing: MLR7 Compare and Connect.
Use this routine to prepare students for the whole-class discussion. At the appropriate time, invite groups to create a visual display of their work. Students should consider what types of details (annotations, notes, diagrams, arrows, etc.) to include on their displays that will help communicate their reasoning. Begin the whole-class discussion by selecting and arranging 2–4 displays for all to see. Give students 2–3 minutes of quiet think time to interpret the displays before inviting the authors to present their work.
Design Principle(s): Optimize output; Cultivate conversation


correct_option_index: 6

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