options: Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
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


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