The purpose of this Warm-up is to elicit ideas that show understanding of a solution to an inequality represented on a number line, which will be useful when students interpret and represent solutions to inequalities on the number line in the associated Algebra 1 lesson. While students may notice and wonder many things about these images, the meaning of the shading is the important discussion point.

This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is how the graphs of inequalities represent all of the possible solutions.

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the connections between the image and the given inequality do not come up during the conversation, ask students to discuss them. Point out the open circle if no student mentions it. Invite students to wonder about it.

Mention that this is a graph of all the solutions to the inequality.

Students sometimes struggle to decide on their own what values to test in a given inequality. In this activity, they are given specific options to consider and get to choose the value they most want to test. This provides an opportunity to talk about why certain values might be chosen. Students are also asked to think about which values will definitely satisfy and not satisfy the inequalities. This encourages them to analyze the structure of the expression and think about how its value will change when testing large numbers, negative numbers, zero, or other types of values. Students look for and express regularity in repeated reasoning when they generalize ideas about what numbers to use to test their solutions (MP8). This activity prepares students for work in the associated Algebra 1 lesson in which they find solutions to inequalities and compare the situations that the inequalities represent.

Monitor for students who use these different strategies:

• Choose to test zero

• Consider values that will result in whole numbers when divided by a whole number or multiplied by a fraction

• Strategically choose large numbers

• Strategically choose negative numbers

• Always choose the same number

The purpose of this activity is for students to practice applying their understanding of inequalities. They generate values that do and do not satisfy each inequality, and then match inequalities to a verbal description of the inequality. This will be useful in the associated Algebra 1 lesson when students identify possible ranges of values for situations and use various inequalities to represent them.

In this activity, students reason abstractly and quantitatively (MP2) as they match expressions containing inequalities to verbal descriptions.