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Understanding Math Test Items: Similarities, Differences, and Problem Solving Techniques

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This comprehensive guide explores the similarities and differences between various math test items. It includes practical examples such as calculating areas of geometric shapes (e.g., triangle ADE, rectangle ABCD) and understanding ratios of areas. The content also addresses real-world scenarios like measuring gasoline in a container and determining fabric requirements for a pillow cover. Additionally, it covers the development of calculator usage protocols in Smarter Balanced Math Assessments from grades 6 to high school, emphasizing the gradual introduction of calculators as students advance.

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Understanding Math Test Items: Similarities, Differences, and Problem Solving Techniques

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  1. How are the test items different? How are the test items similar? THEN NOW

  2. ADE is inside ABCD. Point E is halfway between points B and C on the rectangle. • Side AB is 8 cm and side AD is 7 cm. • Part A: What is the area of ADE? • Part B: What is the ratio of the area of ABE to the area • of ABC? • Part C: What is the ratio of the area of DCE to the area of • ABCD?

  3. A 20-gallon container is filled with 6 gallons of gasoline. What fraction of the container is filled with gasoline? .

  4. Which equation is represented by the graph? 2y + x = 10 y - 2x = -5 -2y = 10x – 4 2y = - 4x - 10

  5. Three Linear Functions Are Represented in Different Ways Xf(x) -3 -9 33 6 9 2y + 3 = 3x (I) (II) (III) Which function has the greatest rate of change? Does any pair of functions have the same rate of change? Justify your answer.

  6. Chris Wants to Cover this Pillow with Fabric • What is the total surface area of the pillow? • Round your answer to the nearest hundredth. • Show your work: • Answer _________ square inches • If Chris shortens the length of the pillow to 12 in, how much less fabric will she need? • Round your answer to the nearest hundredth. • Show your work: • Answer _________ square inches

  7. Calculator Use on the Smarter Balanced Math Assessments How will Smarter Balanced determine protocol for calculator usage?

  8. Grades 6-HS • Calculators are available for a small proportion of grade 6 items and gradually increase in availability as students progress toward high school. • Calculators will be available for most or all of the high school math items.

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