Equation Modeling Today

Overview

Students will learn to create equations from verbal and graphical descriptions and then solve them to answer a realistic question. The lesson focuses on translating relationships into mathematical form, aligning with Algebra 1 skills for creating one- and two-variable equations.

Learning intentions

Students will be able to:

• Create a linear equation in one variable to model a number or relationship.
• Create a two-variable equation to represent a relationship between quantities and graph it.
• Solve equations and interpret solutions as valid or nonviable in context.
• Rearrange a formula to highlight a quantity of interest.

Success criteria

I can…

• Write an equation that matches a verbal description and identify the variable correctly.
• Solve the equation using appropriate methods and check the solution in context.
• Graph a two-variable equation with labeled axes and a reasonable scale.
• Decide whether a solution makes sense for the situation described.

Curriculum links

• Create equations and inequalities in one variable and solve problems, including equations arising from linear and quadratic functions (CCSS.MATH.CONTENT.HSA-CED.A.1).
• Create equations in two or more variables to represent relationships, and graph equations on coordinate axes with labels and scales (CCSS.MATH.CONTENT.HSA-CED.A.2).
• Represent constraints by equations/inequalities and interpret solutions as viable or nonviable options in a modeling context (CCSS.MATH.CONTENT.HSA-CED.A.3).
• Rearrange formulas to highlight a quantity of interest (CCSS.MATH.CONTENT.HSA-CED.A.4).

Lesson structure (50 minutes)

1. 0–5 min · Warm-up (Quick Model). Teacher displays: “A number increased by 7 equals 25.” Students write an equation using a variable of their choice and circle the variable.

2. 5–15 min · Direct teach (Creating equations). Teacher models a step-by-step process: define the variable, translate key phrases (“increased by,” “twice,” “difference,” “equals”), and form the equation; then solves a short example and checks by substitution. Students follow along and complete a second “fill-in-the-blank equation” slide: “3 less than x equals 14” → equation ___, solve for x.

3. 15–27 min · Guided practice (One-variable equation in context). Teacher gives a problem: “Tickets cost $8 each. The total cost is $56. How many tickets were sold?” Students, in pairs, write an equation, solve, and write one sentence interpreting the answer (viable and makes sense).

4. 27–37 min · Two-variable relationship (Equation to graph). Teacher introduces a second situation on the board: “A phone plan charges a fixed fee plus $0.12 per text. Let x be texts and y be total cost. Total cost follows y = 0.12x + 15.” Teacher graphs a few points with the class, then shows how the equation generates a line. Students complete a quick graph on their own: choose at least 3 x-values (within a reasonable range given on the prompt), compute y, plot points, and draw the line.

5. 37–45 min · Check constraints and interpret. Teacher asks: “The company allows at most 100 texts in one billing cycle. What values of y are possible?” Students find y for x = 0, 100, and at least one value between; they state whether any larger y would be nonviable based on the constraint. Teacher emphasizes interpreting solutions/options in modeling contexts.

6. 45–50 min · Exit ticket (Create, solve, interpret). Students answer one prompt independently: “Maria has some money. She spends $5 plus $2 per snack and ends with $21. Let x be the number of snacks. Create an equation, solve for x, and state whether the result makes sense for the situation.”

Resources

• Printed one-page practice set (4 short modeling items, one graphing task, one exit ticket)
• Coordinate graph paper or graphing template
• Pair work scratch paper
• Calculator access as needed (optional)
• Colored pencils/markers for plotting points

Assessment

• Circulate during warm-up and guided practice to check equation formation and variable choice.
• Collect pair-work equations/solutions to verify correct translation and interpretation.
• Use the exit ticket to assess: equation creation, solving, and contextual viability statement.

Differentiation

• Support: Provide sentence starters for equation writing (e.g., “Let x represent…”, “The phrase ‘increased by’ means…”).
• Support: Offer a “translation word bank” for common algebra phrases and a checklist for modeling steps (variable → equation → solve → check).
• Extension: For the guided constraint question, ask students to explain how changes in the maximum texts would change the possible y-values (qualitative reasoning).
• EAL/SEN: Allow an additional example for practice and permit verbal explanation before writing final answers; emphasize the meaning of variables and “check in context.”