Pokémon Distance Challenge: Absolute Value Inequalities

Materials Needed

• Pencil and paper or a digital notebook
• Number line, ruler, or graphing tool
• Optional: Pokémon cards, figures, or a Pokémon-themed timer
• Optional: colored pencils or highlighters

Learning Target

I can solve real-world problems involving one-variable absolute value inequalities and represent the solutions algebraically and graphically.

Objectives

By the end of this 15-minute lesson, I can:

• Explain that an absolute value represents distance from zero or from a number.
• Write and solve absolute value inequalities from Pokémon-themed situations.
• Graph solutions on a number line and explain what the graph means.

Success Criteria

• I identify whether the inequality uses less than or greater than.
• I correctly solve the inequality, including reversing the inequality for “greater than” situations.
• I use an open circle for < or > and a closed circle for ≤ or ≥.
• I explain my answer using the context of the problem.

Introduction and Bell Work: Pokémon Warm-Up — 2 Minutes

Directions: Solve each problem. Then check your answers using substitution.

1. A Poké Ball costs 8 PokéDollars. If you buy x Poké Balls and spend 40 PokéDollars, write an equation and solve for x.
2. Solve: 3x + 2 > 11.
3. On a number line, what does |x| < 4 mean: numbers close to 0 or numbers far from 0?

Answers: 1. 8x = 40, so x = 5. 2. x > 3. 3. Numbers close to 0.

Hook: A Pokémon trainer can safely catch a rare Pokémon only when the Pokémon’s level is within a certain distance of the trainer’s target level. How could we describe all possible levels using one inequality?

Body: I Do, We Do, You Do — 10 Minutes

I Do: Teacher or Parent Models — 3 Minutes

Explain that an absolute value inequality describes a distance.

Example 1: Within a distance

A Pikachu’s level must be within 4 levels of level 20 to join a training challenge.

Let x represent Pikachu’s level.

|x − 20| ≤ 4

This means the distance between x and 20 is no more than 4. Rewrite it as a compound inequality:

−4 ≤ x − 20 ≤ 4

Add 20 to all three parts:

16 ≤ x ≤ 24

Solution: Pikachu can be any level from 16 through 24.

Graph: Place closed circles at 16 and 24 and shade between them.

Example 2: More than a distance

A Pokémon trainer earns a badge when their score is more than 5 points away from 30.

|x − 30| > 5

“More than 5 away” means the score is either less than 25 or greater than 35:

x − 30 < −5 or x − 30 > 5

x < 25 or x > 35

Graph: Use open circles at 25 and 35, then shade left of 25 and right of 35.

Important rule:

• |x − a| < b means between two values.
• |x − a| > b means outside two values.
• Use a closed circle for ≤ or ≥ and an open circle for < or >.

We Do: Solve Together — 4 Minutes

Work through each problem aloud. The learner may draw a number line, use a digital graphing tool, or act out the distance with Pokémon cards or markers.

Problem A: Eevee’s Training Zone

Eevee can train in a zone when its power level is within 3 points of 12.

1. Write an absolute value inequality.
2. Solve it.
3. Describe or draw the graph.

Solution:

|x − 12| ≤ 3

−3 ≤ x − 12 ≤ 3

9 ≤ x ≤ 15

Graph closed circles at 9 and 15 and shade between them.

Problem B: Gym Challenge

A trainer qualifies for a special gym challenge when their score is at least 7 points away from 50.

1. Write an absolute value inequality.
2. Predict whether the graph will be between two values or outside two values.
3. Solve it.

Solution:

|x − 50| ≥ 7

Because the score is at least 7 away, the graph is outside two values.

x − 50 ≤ −7 or x − 50 ≥ 7

x ≤ 43 or x ≥ 57

Graph closed circles at 43 and 57; shade left of 43 and right of 57.

Quick Check: Ask, “Why does Problem A use one connected section while Problem B uses two separate sections?”

You Do: Independent Pokémon Mission — 3 Minutes

Choose one mission. Show your inequality, solution, graph, and a sentence explaining your answer.

1. Pokédex Mission: A trainer’s Pokédex must contain fewer than 6 entries away from 25 entries to earn a reward.
   Write and solve an absolute value inequality. Graph the solution.
2. Battle Mission: A Pokémon’s battle score must be more than 8 points away from 40 to enter a special battle.
   Write and solve an absolute value inequality. Graph the solution.

Possible answers:

• Pokédex Mission: |x − 25| < 6, so 19 < x < 31. Use open circles at 19 and 31 and shade between.
• Battle Mission: |x − 40| > 8, so x < 32 or x > 48. Use open circles at 32 and 48 and shade outside.

Conclusion and Exit Ticket — 3 Minutes

Recap

Complete these statements aloud or in writing:

• An absolute value inequality represents a distance from __________.
• A “within” or “less than” situation usually gives a solution __________ two values.
• A “more than” or “greater than” distance situation gives solutions __________ two values.
• A closed circle means __________, and an open circle means __________.

Exit Ticket

A Charmander can participate in a contest when its level is no more than 2 levels away from level 10.

1. Write an absolute value inequality.
2. Solve the inequality.
3. Describe the graph.
4. Write one sentence explaining what the solution means for Charmander.

Answer: |x − 10| ≤ 2, so 8 ≤ x ≤ 12. Use closed circles at 8 and 12 and shade between them. Charmander can participate at levels 8 through 12.

Assessment

• Formative: Check bell work, listen to explanations during “We Do,” and ask the learner to justify the graph.
• Summative: Evaluate the independent Pokémon Mission and exit ticket.
• Feedback: Give one specific praise and one next step, such as “Your graph correctly shows the solution between the endpoints. Next, double-check whether the endpoints should be open or closed.”

Differentiation and Choice

• Support: Provide a number-line template, highlight keywords such as “within,” “no more than,” and “more than,” and use the sentence frame: “The distance from ___ is ___, so |x − ___| ___ ___.”
• Additional support: Begin with numerical examples such as |x − 5| ≤ 2 before applying the Pokémon context.
• Extension: Create a Pokémon problem with a solution of x < 18 or x > 30. Write the absolute value inequality and graph it.
• Creative choice: The learner may present the solution as a written explanation, a labeled drawing, a digital graph, or a short verbal explanation.