Mathematics · Grade 9 · Algebra 1

Compare Linear and Exponential Models

Translate additive and multiplicative changes into function rules. Evaluate and compare models with a stated domain. Explain model structure and limits on real-world prediction.

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Interpret functions in context →Compare linear & exponential models →

Learning goals

Translate additive and multiplicative changes into function rules.
Evaluate and compare models with a stated domain.
Explain model structure and limits on real-world prediction.

Before you begin

Use the prerequisite representations before moving to independent work.

Age and grade do not measure readiness. Adjust reading or adult support to preserve the intended learning goal.

Follow the sequence

Complete practice

Compare Linear and Exponential Models

Add each step or multiply each step

For nonnegative whole-number steps n, Model L starts at 2 and adds 3 each step. Model E starts at 2 and doubles each step. These are illustrative models, not forecasts.

Worked example: Starting at 1 and adding 2 gives 1, 3, 5; starting at 1 and tripling gives 1, 3, 9. The first few matches do not make the rules identical. Use the material to work through each task. Show the requested response.

1.Write L(n).

Practice preview

Grade 9

Key

Compare Linear and Exponential Models

Practice · Independent · 30 min

Translate additive and multiplicative changes into function rules. Evaluate and compare models with a stated domain. Explain model structure and limits on real-world prediction. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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1. Explore

Compare Linear and Exponential Models: Explore and Explain

Add each step or multiply each step

For nonnegative whole-number steps n, Model L starts at 2 and adds 3 each step. Model E starts at 2 and doubles each step. These are illustrative models, not forecasts.

Worked example: Starting at 1 and adding 2 gives 1, 3, 5; starting at 1 and tripling gives 1, 3, 9. The first few matches do not make the rules identical. Explore the material. Talk through your reasoning with suitable support.

1.Write L(n).

Practice preview

Grade 9

Key

Compare Linear and Exponential Models: Explore and Explain

Explore · Independent · 10 min

Translate additive and multiplicative changes into function rules. Evaluate and compare models with a stated domain. Explain model structure and limits on real-world prediction. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

2. Practice

Practice preview

Grade 9

Key

Compare Linear and Exponential Models: Practice Independently

Practice · Independent · 15 min

Translate additive and multiplicative changes into function rules. Evaluate and compare models with a stated domain. Explain model structure and limits on real-world prediction. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

3. Apply

Compare Linear and Exponential Models: Apply and Create

Add each step or multiply each step

For nonnegative whole-number steps n, Model L starts at 2 and adds 3 each step. Model E starts at 2 and doubles each step. These are illustrative models, not forecasts.

Use what you learned to explain, construct or apply an idea.

1.Explain how consecutive differences in L and consecutive ratios in E identify their structures.

Practice preview

Grade 9

Key

Compare Linear and Exponential Models: Apply and Create

Apply · Independent · 20 min

Translate additive and multiplicative changes into function rules. Evaluate and compare models with a stated domain. Explain model structure and limits on real-world prediction. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Teaching and response guide

Begin with: Write L(n).
Connect the response to: Calculate L(4) and E(4).
Ask students to apply the idea: Explain how consecutive differences in L and consecutive ratios in E identify their structures.

Watch for: Check the meaning of each quantity, the operation and the units; a numerical answer alone does not show the full reasoning.

Check the answer criteria for each task. A supported explanation may have more than one acceptable response. These activities offer evidence to discuss; completing a sheet alone does not establish mastery.