options: Rewrite rational expressions.

Represent and solve equations and inequalities graphically.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Use polynomial identities to solve problems.

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Multiply and divide within 100.

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

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

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

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

Solve systems of equations.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

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

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

Generate and analyze patterns.

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

Solve equations and inequalities in one variable.

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

Write expressions in equivalent forms to solve problems.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

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

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

Perform arithmetic operations on polynomials.
problem_activity: Optional activity
This activity is optional due to time considerations. The purpose of this activity is for students to reason about whether given values make an inequality true and justify their answers using inequality statements and graphs (MP3). Students explored this concept in the previous activity, so they should work to articulate how they check if a number is a solution to an inequality statement and an inequality on a number line.
Students will play a game to practice this skill. The game’s goal is for one student to guess a mystery number using as few inequalities as possible. To create a class competition, keep track of how many inequalities each group uses for each number and display scores after each round. The winning group is the group with the lowest score.
Launch
Arrange students in groups of 4. As students read the game instructions with their group, give each group 1 set of inequalities and 1 set of numbers, pre-cut from the blackline master. Review the game instructions as a whole class. Students will play 1 round and then pause to reflect and plan strategies for the next rounds. Allow students 10 minutes of game time followed by a whole-class discussion.
Once student groups have completed one round of game play, pause the game and ask groups to reflect on their strategies. Groups should make a plan before continuing to the second round of the game. Post or ask these questions to guide a short discussion:
“Clue givers, how did you decide which inequalities would be the most helpful for your detective?”
“Clue givers, did you work together to decide which 3 clues to give or did you decide independently?”
“Detective, were some inequalities more helpful than others as you tried to guess the mystery number? If so, what made an inequality more helpful?”
Action and Expression: Internalize Executive Functions.
Begin with a small-group or whole-class demonstration of how to play the game. Check for understanding by inviting students to rephrase directions in their own words.
Supports accessibility for: Memory; Conceptual processing
Student Facing
Your teacher will give your group two sets of cards—one set shows inequalities and the other shows numbers. Place the inequality cards face up where everyone can see them. Shuffle the number cards and stack them face down.
To play:
One person in your group is the detective. The other people will give clues.
Pick one number card from the stack and show it to everyone except the detective.
The people giving clues each choose an inequality that will help the detective identify the unknown number.
The detective studies the inequalities and makes three guesses.
If the detective does not guess the right number, each person chooses another inequality to help.
When the detective does guess the right number, a new person becomes the detective.
Repeat the game until everyone has had a turn being the detective.
Student Response
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Anticipated Misconceptions
Some groups may misunderstand the directions, thinking that each person giving clues is supposed to take a different number card from the stack. Explain to them that there is only one unknown number per round and everyone gives clues about this same number. When a new person becomes the detective, that is when a new number card is drawn.
Activity Synthesis
Once all students have had a turn as the detective, start a whole-class discussion. Ask groups to share their most successful strategies for choosing helpful clue inequalities as well as strategies for using those clues to guess the mystery number. Emphasize how students can check that a value is or is not a solution to an inequality: both symbolic statements (substitute the value and check that the resulting statement is true) and on the number line (plot the value to test and make sure that it falls within a shaded region).
Speaking: MLR8 Discussion Supports.
To support all students to participate in the discussion, provide students with sentence frames, such as “One strategy I used to choose a clue was _____” or “One way that I checked that a value was a solution to the inequality (number line representation) was to _____.” Ask them to complete one of the sentences in writing or share a completed response verbally with a partner.
Design Principle(s): Maximize meta-awareness


correct_option_index: 15