DOK 3 Practice

Explaining, comparing, and choosing strategies

This challenge set emphasizes justification, error analysis, representation choice, and interpretation while keeping all arithmetic manageable by hand.

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Practice Questions

10 calculator-inactive questions

Work each one by hand, choose an answer, then check or reveal the explanation.

Question 1

Initial value

Which representation has the greatest initial value?

Question 2

Quadratic reasoning

A student says x^2 + 8x + 15 has zeros at x = -3 and x = -5. Is the student correct?

Question 3

Strategy selection

Which strategy is most efficient for solving 2x + y = 13 and y = x + 1?

Question 4

Pattern type

The table has y-values 5, 10, 20, 40 for x = 0, 1, 2, 3. What type of model fits best?

Question 5

Function comparison

At x = 3, which function has the greater value: A: y = 4x + 1 or B: y = x^2 + 1?

Question 6

Error analysis

A student solves -3(x - 2) = 12 by writing -3x - 6 = 12. What is the error?

Question 7

Equivalent expressions

Which expression is equivalent to (x + 4)^2 - 16?

Question 8

Interpret intercepts

A tank has 12 gallons and drains linearly to 0 gallons after 3 hours. What does the x-intercept represent?

Question 9

Systems reasoning

Which system has no solution?

Question 10

Model choice

A savings account starts with $50 and increases by $15 each week. Which model best represents the balance after x weeks?

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