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Building the Score Engine

Dev intern Leo writes the scoring code. The distributive property, exponents, and like terms keep the formulas correct and efficient.

Enrichment Reading + Math Distributive Property, Exponents, Like Terms 6.EE.1–4 Challenge Level
Part 1 — Exponents in the Formula

Leo's combo bonus uses an exponent: 2Âŗ + 4. "Exponents come first in the order of operations," he reminded himself, "before adding."

2Âŗ + 4 = (2 × 2 × 2) + 4 = 8 + 4 = 12.

Analyze — Q1

Why does Leo compute 2Âŗ before adding 4?

Solve It — #1

Evaluate 3² + 5.

Part 2 — The Distributive Property

A multiplier rule read 3(x + 4). Leo used the distributive property to rewrite it as an equivalent expression — multiply the 3 by each term inside.

3(x + 4) = 3¡x + 3¡4 = 3x + 12. (Check: at x = 5, both give 27.)

Solve It — #2

Use the distributive property to expand 4(n + 2). (Write it like 4n+8, no spaces.)

Analyze — Q2

Why are 3(x + 4) and 3x + 12 called equivalent expressions?

Part 3 — Evaluating with a Variable

A power score used the expression 2x² + 1. Leo evaluated it at x = 3, being careful to square before multiplying.

2x² + 1 at x = 3: first 3² = 9, then 2¡9 = 18, then 18 + 1 = 19.

Solve It — #3

Evaluate 3x² when x = 2.

Part 4 — Combining Like Terms

Leo found two score parts: 2x + 3x. "These are like terms — same variable — so I can combine them into one," he said. A simpler expression runs faster.

2x + 3x = 5x. (At x = 4, that is 5 × 4 = 20.)

Solve It — #4

Evaluate the score expression 5x + 2 when x = 6.

Analyze — Q3

Why can Leo combine 2x and 3x but not 2x and 3?

After You Read — Analytical Writing

Make a Mathematical Argument

Prompt A — Prove equivalence. Show that 3(x + 4) and 3x + 12 are equivalent by evaluating both at two different x-values. Explain what "equivalent" means using your results.
Prompt B — Explain efficiency. Explain why combining like terms (2x + 3x = 5x) makes an expression simpler, and why the order of operations is essential when an exponent is involved. Use an example from the story.

Optional academic frame: "Because ______, the expressions are ______; this matters because ______."

Challenge Extension

Think Further

Leo writes 2(x + 3) + 4x. Expand and combine like terms into a single simplified expression, then evaluate it at x = 5. Explain each step. (Try it, then check with your teacher.)

How You Are Scored

Rubric

Category4 — Advanced3 — Proficient2 — Developing
Comprehension & inferenceAll analysis questions correct; explains equivalence & like terms2 of 3 correct1 correct
Multi-step mathAll 4 Solve-It answers correct (exponent+order, distributive, evaluate x², evaluate)3 correct2 correct
Mathematical argumentProves/explains with specific values; clear reasoningClaim with some evidenceLittle evidence
🔑 Teacher Answer Key (click to expand)
  1. Q1 — Order of operations does exponents before addition.
  2. Solve It #1 — 14 (3² + 5).
  3. Solve It #2 — 4n + 8 (distributive).
  4. Q2 — They give the same value for every value of x.
  5. Solve It #3 — 12 (3·2²).
  6. Solve It #4 — 32 (5·6 + 2).
  7. Q3 — 2x and 3x are like terms; 3 has no variable.
  8. Extension — 2(x+3) + 4x = 2x + 6 + 4x = 6x + 6; at x = 5, 6·5 + 6 = 36.

Grading accepts 4n+8 with or without spaces; numeric answers in common formats.

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