testbank

Measurement Attributes and Measurement Systems

 * Have students determine sizes of playground space and equipment.**
 * After designing playground, they should see is equipment fits into space provided.**
 * Perimeter, volume, unit conversion**


 * When calculating budget, they should be able to convert units (cents and dollars)**

**Techniques and Tools**
Hands-on measuring of actual items to demonstrate derivations and application of measurement.
 * Measuring the size of the playground itself, the size of equipment, the relative size of equipment to children playing on it, and how items will into the design.**

Measurement Attributes and Measurement Systems
The width of a classroom door is indicated in the picture below. Which of the following is most likely the width of the door?


 * || A. || 0.1 kilometer ||
 * || B. || 10 meters ||
 * || C. || 100 centimeters ||
 * || D. || 10,000 millimeters ||

2011 Spring Release, Mathematics - Grade 8 Question 16: Short-Answer Reporting Category: Measurement Standard: 8.M.2 - Given the formulas, convert from one system of measurement to another. Use technology as appropriate.

The saguaro cactus can grow to a maximum height of 12 meters. What is the maximum height to the nearest foot of the saguaro cactus? (1 meter feet)

2011 Spring Release, Mathematics - Grade 3 Question 8: Multiple-Choice Reporting Category: Measurement Standard: 3.M.1 - Demonstrate an understanding of the attributes length, area, and weight, and select the appropriate type of unit for measuring each attribute using both the U.S. Customary (English) and metric systems.

Andre wants to measure the weight of his backpack when it is full of books.Which unit should Andre use?


 * || A. || pound ||
 * || B. || inch ||
 * || C. || foot ||
 * || D. || ton ||

2010 Spring Release, Mathematics - Grade 7 Question 19: Multiple-Choice Reporting Category: Measurement Standard: 7.M.1 - Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. //This standard is intentionally the same as standard 8.M.1.// Donnie has a spool that contains 18 yards of wire. What is the total number of inches of wire that the spool contains? || || A.
 * 162 ||
 * || B. || 216 ||
 * || C. || 540 ||
 * || D. || 648 ||

2010 Spring Release, Mathematics - Grade 3 Question 7: Open-Response Reporting Category: Measurement Standard: 3.M.1 - Demonstrate an understanding of the attributes length, area, and weight, and select the appropriate type of unit for measuring each attribute using both the U.S. Customary (English) and metric systems.

Jamie is measuring her pet mouse.
 * 1) Should Jamie measure her mouse’s length in inches, yards, or pounds? Explain how you know your answer is correct.
 * 2) Should Jamie measure her mouse’s weight in feet, ounces, or tons? Explain how you know your answer is correct.

2009 Spring Release, Mathematics - Grade 8 Question 15: Multiple-Choice Reporting Category: Measurement Standard: 8.M.1 - Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. Jessica has one piece of ribbon that is 62 3 yards long and one piece that is 51 3 yards long. What is the total length, in feet, of the two pieces of ribbon? || || A.
 * 332 3 feet ||
 * || B. || 34 feet ||
 * || C. || 341 2 feet ||
 * || D. || 36 feet ||

2009 Spring Release, Mathematics - Grade 8 Question 17: Multiple-Choice Reporting Category: Measurement Standard: 8.M.2 - Given the formulas, convert from one system of measurement to another. Use technology as appropriate. One of the largest statues of a cow in the United States is 38 feet tall. What is the height of the statue in meters, to the nearest tenth of a meter? (1 meter ≈ 3.28 feet) || || A.
 * 11.6 meters ||
 * || B. || 12.5 meters ||
 * || C. || 115.9 meters ||
 * || D. || 124.6 meters ||

2009 Spring Release, Mathematics - Grade 3 Question 4: Multiple-Choice Reporting Category: Measurement Standard: 3.M.2 - Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc. //This standard is intentionally the same as standard 4.M.2.// Mr. Jones used the three coupons shown below. What is the total amount of money that Mr. Jones saved by using the three coupons? || || A.
 * $0.15 ||
 * || B. || $1.50 ||
 * || C. || $15.00 ||
 * || D. || $150.00 ||

Which of the following measures could

be 432 square inches?


 * || A. || the width of a car ||
 * || B. || the area of a doormat ||
 * || C. || the volume of a suitcase ||
 * || D. || the perimeter of a classroom ||

2008 Spring Release, Mathematics - Grade 7 Question 28: Open-Response Reporting Category: Measurement Standard: 7.M.1 - Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. //This standard is intentionally the same as standard 8.M.1.// A park near Jon's house has a jogging trail that is 2640 yards long.
 * 1) What is the length, in feet, of the jogging trail? Show or explain how you got your answer.
 * 2) Using your answer from part (a), determine the length, in miles, of the jogging trail. Show or explain how you got your answer. (1 mile=5280 feet)
 * 3) The jogging trail starts at the entrance to the park and ends at a pond. The trail starts with a sign, ends with a sign, and has a sign posted along the trail every [[image:http://www.doe.mass.edu/mcas/images/db/frac1_4.gif width="15" height="30" caption="one quarter"]] mile. What is the total number of signs along the trail from the beginning to the end? Show or explain how you got your answer.

2008 Spring Release, Mathematics - Grade 3 Question 23: Open-Response Reporting Category: Measurement Standard: 3.M.1 - Demonstrate an understanding of the attributes length, area, and weight, and select the appropriate type of unit for measuring each attribute using both the U.S. Customary (English) and metric systems. || Morgan made the drawing below to show the area of the library. || ||
 * 1) What is the area, in square yards, of the library?
 * The area of Morgan's classroom is 36 square yards.
 * 1) On the grid below, draw a rectangle with an area of 36 square yards.

2008 Spring Release, Mathematics - Grade 3 Question 29: Short-Answer Reporting Category: Measurement Standard: 3.M.2 - Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc. //This standard is intentionally the same as standard 4.M.2.// Cathy’s classroom is 9 yards long.

How many feet long is Cathy’s classroom? (1 yard = 3 feet)

Write your answer in the Answer Box below.

2007 Spring Release, Mathematics - Grade 4 Question 15: Multiple-Choice Reporting Category: Measurement Standard: 4.M.1 - Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute. Elin has centimeter blocks like the one shown below.

She also has a box with the length, width, and height shown below.

Which of the following is best represented by Elin filling the box with centimeter blocks?

|| || A.
 * the area of the box ||
 * || B. || the perimeter of the box ||
 * || C. || the weight of the box ||
 * || D. || the volume of the box ||

Measurement **Techniques and Tools**
2011 Spring Release, Mathematics - Grade 10 Question 16: Short-Answer Reporting Category: Measurement Standard: 10.M.2 - Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area. The diagram below shows a right square pyramid. Based on the dimensions in the diagram, what is the lateral surface area, in square centimeters, of the pyramid?

Abby drew and, as shown in the diagram below. The figure in the diagram has the following properties: What is the area of the shaded triangle, ? || || A.
 * Point H lies on [[image:http://www.doe.mass.edu/mcas/images/2011/224629_block_2.png caption="line segment GJ"]].
 * The length of [[image:http://www.doe.mass.edu/mcas/images/2011/224629_block_3.png caption="line segment FG"]] is 8 inches.
 * The length of [[image:http://www.doe.mass.edu/mcas/images/2011/224629_block_4.png caption="line segment HJ"]] is 10 inches.
 * 80 sq. in. ||
 * || B. || 64 sq. in. ||
 * || C. || 48 sq. in. ||
 * || D. || 40 sq. in. ||

2011 Spring Release, Mathematics - Grade 10 Question 36: Multiple-Choice Reporting Category: Measurement Standard: 10.M.1 - Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles. A stage floor is composed of a rectangle and an isosceles trapezoid. The diagram below shows the stage floor and some of its dimensions. What is the perimeter of the stage floor? || || A. || || ||  ||



2011 Spring Release, Mathematics - Grade 8 Question 2: Multiple-Choice Reporting Category: Measurement Standard: 8.M.3 - Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. A box is in the shape of a rectangular prism and has a volume of 360 cubic inches. The box has a width of 6 inches and a length of 10 inches.What is the height of the box?
 * || A. ||  || 110 ft. ||
 * || B. ||  || 145 ft. ||
 * || C. ||  || 1000 ft. ||
 * || D. ||  || 1375 ft. ||
 * 6 inches ||
 * || B. || 10 inches ||
 * || C. || 23 inches ||
 * || D. || 36 inches ||

2011 Spring Release, Mathematics - Grade 7 Question 3: Multiple-Choice Reporting Category: Measurement Standard: 7.M.3 - Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms and cylinders. Use technology as appropriate. Samantha drew a square and a parallelogram. The parallelogram and one of its dimensions are shown below. What is the value of x ? || || A. || || ||  ||
 * The square has a side length of 8 centimeters.
 * The perimeter of the square is the same as the perimeter of the parallelogram.
 * || 22 ||
 * || B. ||  || 12 ||
 * || C. ||  || 11 ||
 * || D. ||  || 6 ||



2011 Spring Release, Mathematics - Grade 6 Question 10: Open-Response Reporting Category: Measurement Standard: 6.M.1 - Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate. Kelsey has a rug in the center of her bedroom floor. Both the floor and the rug are in the shape of a rectangle. The rug, the floor, and some of their dimensions are shown in the diagram below.
 * 1) What is the area, in square feet, of the entire floor? Show or explain how you got your answer.
 * 2) What is the perimeter, in feet, of the rug ? Show or explain how you got your answer.
 * 3) What is the area, in square feet, of the part of the floor that is not covered by the rug? Show or explain how you got your answer.

2011 Spring Release, Mathematics - Grade 5 Question 8: Open-Response Reporting Category: Measurement Standard: 5.M.1 - Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate. Kiesha is decorating her bedroom. She wants to put ribbon around the picture shown below. The picture is in the shape of an equilateral triangle. Kiesha plans to cover one wall of her bedroom with wallpaper. The wall is in the shape of a rectangle. The dimensions of the wall are 13 feet by 9 feet. Kiesha plans to carpet the floor of her bedroom. A diagram of the floor is shown below.
 * 1) What is the perimeter, in inches, of the picture? Show or explain how you got your answer.
 * 1) What is the <span class="bold_text">area, in square feet, of the wall? Show or explain how you got your answer.
 * 1) What is the area, in square feet, of the floor? Show or explain how you got your answer.

2011 Spring Release, Mathematics - Grade 4 Question 18: Open-Response Reporting Category: Measurement Standard: 4.M.4 - Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring. A diagram of John’s garden and the length of one side are shown on the grid below. <span class="para_left">John’s sister, Kara, also has a garden. The diagram below shows Kara’s garden.
 * 1) What is the <span class="bold_text">perimeter, in units, of John’s garden? Show your work or explain how you got your answer.
 * 1) What is the <span class="bold_text">area, in square units, of Kara’s garden? Show your work or explain how you got your answer.
 * 2) Whose garden has a bigger <span class="bold_text">area ? Explain how you know your answer is correct.

2010 Spring Release, Mathematics - Grade 8 Question 18: Open-Response Reporting Category: Measurement Standard: 8.M.3 - Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. A cafeteria has a recycling container for cans. The recycling container has a lid that is in the shape of a circle with an opening in the center that is also in the shape of a circle. The lid and some of its dimensions are shown in the diagram below. <span class="para_left">The shaded part of the diagram represents the opening in the lid.
 * 1) What is the circumference, in inches, of the lid of the recycling container? Show or explain how you got your answer. (Use 3.14 for π.)
 * 2) What is the area, in square inches, of the lid, <span class="bold_text">including the opening? Show or explain how you got your answer. (Use 3.14 for π.)
 * 3) What is the area, in square inches, of the lid, <span class="bold_text">not including the opening? Show or explain how you got your answer. (Use 3.14 for π.)

Models

 * direct connection to models -- deciding on scale and making accurate representation**

2011 Spring Release, Mathematics - Grade 10 Question 37: Multiple-Choice Reporting Category: Patterns, Relations, and Algebra Standard: 10.P.7 - Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. (AI.P.11) A model of a skyscraper is 15 inches tall. The model uses the scale shown below. Which of the following proportions can be used to find <span class="italic_text">x, the height in yards of the actual skyscraper? || || A.
 * [[image:http://www.doe.mass.edu/mcas/images/2011/224669_block_0.png caption="fifteen over twelve equals zero point five over x"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224669_block_1.png caption="fifteen over x equals zero point five over twelve"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224669_block_2.png caption="zero point five over fifteen equals x over twelve"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224669_block_3.png caption="zero point five over twelve equals x over fifteen"]] ||

**use in connection to determining how long it will take to build playground**

2011 Spring Release, Mathematics - Grade 8 Question 3: Multiple-Choice Reporting Category: Patterns, Relations, and Algebra Standard: 8.P.4 - Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.

<span class="para_left">Jeff completed a hiking trail in <span class="italic_text">t <span class="para_left"> hours. Michelle completed the trail in half the time it took Jeff to complete it.Which of the following expressions represents the time it took Michelle to complete the hiking trail?


 * || A. || [[image:http://www.doe.mass.edu/mcas/images/2011/224271_block_0.png caption="two multiplication dot t"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224271_block_1.png caption="two division sign t"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224271_block_2.png caption="t minus sign two"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224271_block_3.png caption="t division sign two"]] ||

**use in connection to determining how steep slides should be**

2011 Spring Release, Mathematics - Grade 8 Question 10: Multiple-Choice Reporting Category: Patterns, Relations, and Algebra Standard: 8.P.5 - Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems. Which graph has the line with the greatest slope? || || A.
 * [[image:http://www.doe.mass.edu/mcas/images/2011/224480_CMH043_slopes_opt_a01.png width="157" height="162" caption="a grid with a horizontal line drawn on it"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224480_CMH043_slopes_opt_b01.png width="157" height="162" caption="a grid with a line drawn on it"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224480_CMH043_slopes_opt_c01.png width="157" height="162" caption="a grid with a line drawn on it"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224480_CMH043_slopes_opt_d01.png width="157" height="162" caption="a grid with a line drawn on it"]] ||

**determining overall cost and apportionment of equipment and supplies** **use in connection to determining how long it will take to build playground**

2011 Spring Release, Mathematics - Grade 6 Question 1: Multiple-Choice Reporting Category: Patterns, Relations, and Algebra Standard: 6.P.6 - Produce and interpret graphs that represent the relationship between two variables in everyday situations.

Bruce is moving bags of concrete. Each bag weighs the same amount. The graph below shows the relationship between different numbers of bags and the total weight, in pounds, of the bags. Bruce will move a total of 100 bags. Based on the graph, what is the total weight of 100 bags of concrete?


 * || A. || 1,800 pounds ||
 * || B. || 6,000 pounds ||
 * || C. || 15,000 pounds ||
 * || D. || 30,000 pounds ||

**fun with see-saws**

2011 Spring Release, Mathematics - Grade 4 Question 20: Multiple-Choice Reporting Category: Patterns, Relations, and Algebra Standard: 4.P.4 - Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships.

The diagram below shows a scale that is balanced. Each has the same weight, and each  has the same weight. Based on the diagram, which of the following is true?


 * || A. || [[image:http://www.doe.mass.edu/mcas/images/2011/224454_EBH1860_scale_opt_a01.png width="232" height="20" caption="three cubes plus one ball equals one cube plus six balls"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224454_EBH1860_scale_opt_b01.png width="232" height="20" caption="three cubes plus one ball is greater than one cube plus six balls"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224454_EBH1860_scale_opt_c01.png width="226" height="20" caption="three cubes plus one ball equals four cubes plus two balls"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224454_EBH1860_scale_opt_d01.png width="226" height="20" caption="three cubes plus one ball is greater than four cubes plus two balls"]] ||

**fun with see-saws**

2010 Spring Release, Mathematics - Grade 6 Question 9: Multiple-Choice Reporting Category: Patterns, Relations, and Algebra Standard: 6.P.5 - Solve linear equations using concrete models, tables, graphs, and paper-pencil methods.

The scale shown below is balanced. Which of the following will balance one ?


 * || A. || [[image:http://www.doe.mass.edu/mcas/images/2010/183577_AL661217_scale_opt_a01.png width="13" height="13" caption="1 ball"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2010/183577_AL661217_scale_opt_b01.png width="28" height="13" caption="2 balls"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2010/183577_AL661217_scale_opt_c01.png width="56" height="13" caption="4 balls"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2010/183577_AL661217_scale_opt_d01.png width="85" height="13" caption="6 balls"]] ||

**pricing and ordering equipment and supplies**

2010 Spring Release, Mathematics - Grade 10 Question 17: Open-Response Reporting Category: Patterns, Relations, and Algebra Standard: 10.P.7 - Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. (AI.P.11) <span class="para_left">When Nuri buys an item from a catalog, the total amount he pays is made up of the following three amounts of money: <span class="para_left">Nuri bought a game with a price of $100 from the catalog.
 * the price of the item
 * sales tax of 5% of the price of the item
 * a fixed shipping fee that is always the same regardless of the cost or size of the order
 * 1) What was the sales tax, in dollars, that Nuri paid on the game? Show or explain how you got your answer.
 * 2) The total amount, including the sales tax and the shipping fee, that Nuri paid for the game was $120. What was the shipping fee, in dollars? Show or explain how you got your answer.
 * 3) Nuri bought an item with a price of $400 from the catalog. What is the total amount he paid, in dollars, including the sales tax and the shipping fee? Show or explain how you got your answer.
 * 4) Write an equation that expresses the relationship between <span class="italic_text">y, the total amount paid for an item from the catalog including the sales tax and shipping fee, and <span class="italic_text">x , the price of the item. Show or explain how you got your equation.

**Visualization and Models**
**translating 2-D design to 3-D model**

2011 Spring Release, Mathematics - Grade 8 Question 17: Multiple-Choice Reporting Category: Geometry Standard: 8.G.8 - Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings. Phyllis made the stack of blocks shown below. Which of the following figures shows the front view of the stack of blocks? || || A.
 * [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_a01.png width="91" height="48" caption="a row of four square blocks with a row of two square blocks above the third and fourth block from the left"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_b01.png width="91" height="48" caption="two rows of four square blocks"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_c01.png width="91" height="69" caption="two rows of four square blocks with a third row of two square blocks above the thrid and fourth block from the left"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_d01.png width="91" height="69" caption="two rows of four square blocks with a third row of one block above the third block from the left"]] ||

2011 Spring Release, Mathematics - Grade 8 Question 17: Multiple-Choice Reporting Category: Geometry Standard: 8.G.8 - Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings. Phyllis made the stack of blocks shown below. Which of the following figures shows the front view of the stack of blocks? || || A.
 * [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_a01.png width="91" height="48" caption="a row of four square blocks with a row of two square blocks above the third and fourth block from the left"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_b01.png width="91" height="48" caption="two rows of four square blocks"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_c01.png width="91" height="69" caption="two rows of four square blocks with a third row of two square blocks above the thrid and fourth block from the left"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224523_CMC313_blocks_opt_d01.png width="91" height="69" caption="two rows of four square blocks with a third row of one block above the third block from the left"]] ||

2010 Spring Release, Mathematics - Grade 10 Question 38: Multiple-Choice Reporting Category: Geometry Standard: 10.G.10 - Demonstrate the ability to visualize solid objects and recognize their projections and cross sections.

<span class="para_left">The diagrams below show the top view and the front view of a solid object. Which of the following could be a diagram of the solid object?


 * || A. || [[image:http://www.doe.mass.edu/mcas/images/2010/182806_CMC344_views_opt_a01.png width="56" height="72" caption="Four answer options. Each option is a solid object with the front labeled."]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2010/182806_CMC344_views_opt_b01.png width="59" height="86" caption="Four answer options. Each option is a solid object with the front labeled."]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2010/182806_CMC344_views_opt_c01.png width="65" height="79" caption="Four answer options. Each option is a solid object with the front labeled."]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2010/182806_CMC344_views_opt_d01.png width="65" height="98" caption="Four answer options. Each option is a solid object with the front labeled."]] ||

2008 Spring Release, Mathematics - Grade 8 Question 28: Open-Response Reporting Category: Geometry Standard: 8.G.8 - Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.

Michael stacked cubes to make the structure shown below. Michael used a total of 14 cubes to make his structure.
 * 1) Draw the right side view of Michael's structure. Be sure to label your drawing "right side view."
 * 1) Draw the front view of Michael's structure. Be sure to label your drawing "front view."
 * 2) Draw one possible top view for Michael's structure. Be sure to label your drawing "top view." Show or explain how you got your answer.

**manipulation of 3-D shapes**

2010 Spring Release, Mathematics - Grade 5 Question 11: Open-Response Reporting Category: Geometry Standard: 5.G.2 - Identify, describe, and compare special types of three-dimensional shapes (cubes, prisms, spheres, pyramids) based on their properties, such as edges and faces.

Felipe is studying three-dimensional shapes. His teacher gives him the four shapes shown below to sort into groups.
 * 1) Group A contains shapes that have <span class="bold_text">exactly 5 faces. Which shapes should Felipe sort into group A? Show or explain how you got your answer.
 * 2) Group B contains shapes that have <span class="bold_text">fewer than 10 edges. Which shapes should Felipe sort into group B? Show or explain how you got your answer.
 * 3) Felipe’s teacher gives him another pyramid. It has a base with 6 edges. What is the total number of edges of this pyramid? Show or explain how you got your answer.

2009 Spring Release, Mathematics - Grade 4 Question 2: Multiple-Choice Reporting Category: Geometry Standard: 4.G.1 - Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes. Calvin drew a shape that has the attributes listed below. Which of the following could be the shape that Calvin drew? ||  || A.
 * It has exactly 4 sides.
 * It has exactly 2 right angles.
 * [[image:http://www.doe.mass.edu/mcas/images/db/09math4q02a.gif caption="answer a"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/db/09math4q02b.gif caption="b"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/db/09math4q02c.gif caption="c"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/db/09math4q02d.gif caption="answer d"]] ||

Data Collection
2011 Spring Release, Mathematics - Grade 4 Question 9: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 4.D.1 - Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data. <span class="para_left">The manager of the Flower Market keeps a record of the number of flowers sold each day. <span class="para_left">The manager of the Flower Market wants to know how many daisies were sold on the three days.Which of the following should the manager use to figure out how many <span class="bold_text">daisies <span class="para_left"> were sold? ||  || A.
 * On Monday, 54 roses, 32 carnations, and 28 daisies were sold.
 * On Tuesday, 65 carnations, 27 daisies, and 17 roses were sold.
 * On Wednesday, 40 daisies, 34 roses, and 21 carnations were sold.
 * [[image:http://www.doe.mass.edu/mcas/images/2011/224366_block_0.png caption="twenty-eight plus twenty-seven plus forty"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224366_block_1.png caption="twenty-eight plus seventeen plus twenty-one"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224366_block_2.png caption="fifty-four plus thirty-two plus twenty-eight"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224366_block_3.png caption="fifty-four plus sixty-five plus forty"]] ||

2011 Spring Release, Mathematics - Grade 3 Question 10: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 3.D.3 - Construct and draw conclusions from representations of data sets in the forms of tables, line plots, pictographs, tallies, and bar graphs. The line plot below shows the number of buttons on the clothes worn by each student in a class one day. How many students had <span class="emphasis_text">fewer than 5 buttons on their clothes? ||  || A.
 * || 2 ||
 * || B. || || 9 ||
 * || C. || || 11 ||
 * || D. || || 18 ||
 * || C. || || 11 ||
 * || D. || || 18 ||
 * || D. || || 18 ||

2011 Spring Release, Mathematics - Grade 3 Question 13: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 3.D.2 - Match representations of a data set in the forms of tables, line plots, pictographs, tallies, or bar graphs with the actual data set. The line plot below shows the number of hours Ms. Jackson’s students practiced violin last week. Which of these pictographs shows the same data as the line plot? ||  || A.
 * [[image:http://www.doe.mass.edu/mcas/images/2011/224543_piano_line_plot_ER578_opt_a01.png width="175" height="197" caption="Pictograph with a key that shows each smiley face stands for two students. One and a half smiley faces next to three hours; two and a half smiley faces next to four hours; two smiley faces next to five hours"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2011/224543_piano_line_plot_ER578_opt_b01.png width="175" height="197" caption="Pictograph with a key that shows each smiley face stands for two students. One smiley face next to three hours; three smiley faces next to four hours; two smiley faces next to five hours"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2011/224543_piano_line_plot_ER578_opt_c01.png width="175" height="197" caption="Pictograph with a key that shows each smiley face stands for two students. One and a half smiley faces next to three hours; two smiley faces next to four hours; two and a half smiley faces next to five hours"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2011/224543_piano_line_plot_ER578_opt_d01.png width="175" height="197" caption="Pictograph with a key that shows each smiley face stands for two students. Three smiley faces next to three hours; five smiley faces next to four hours; four smiley faces next to five hours"]] ||

2010 Spring Release, Mathematics - Grade 8 Question 8: Short-Answer Reporting Category: Data Analysis, Statistics, and Probability Standard: 8.D.1 - Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling. <span class="para_left">Mr. Jamison is the principal at a new school with an enrollment of 430 students. He surveyed 10% of the students at his school to find out which colors they would like as the school colors.What is the number of students in the sample size of the principal’s survey?

2010 Spring Release, Mathematics - Grade 7 Question 13: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 7.D.1 - Select, create, interpret, and utilize the following tabular and graphical representations of data: circle graphs, Venn diagrams, stem-and-leaf plots, tables, and charts. The manager of a theater surveyed 500 people to determine their favorite type of play. Each person selected one type of play. The manager started to make the circle graph below to show the results of her survey. The percentage of people who selected drama was the same as the percentage of people who selected mystery. Based on the information in the circle graph, what was the total number of people who selected drama? ||  || A.
 * 100 ||
 * || B. || 125 ||
 * || C. || 150 ||
 * || D. || 200 ||

2010 Spring Release, Mathematics - Grade 5 Question 3: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 5.D.2 - Construct and interpret line plots, line graphs, and bar graphs. Interpret and label circle graphs. Jack counted the numbers of cardinals and sparrows he saw in his yard during one week. His results are displayed in the bar graph below.

What fraction of the birds were sparrows? ||  || A.
 * [[image:http://www.doe.mass.edu/mcas/images/2010/180984_block_0.png caption="ten-twenty-fourths"]] ||
 * || B. || [[image:http://www.doe.mass.edu/mcas/images/2010/180984_block_1.png caption="ten-fourteenths"]] ||
 * || C. || [[image:http://www.doe.mass.edu/mcas/images/2010/180984_block_2.png caption="fourteen-twenty-fourths"]] ||
 * || D. || [[image:http://www.doe.mass.edu/mcas/images/2010/180984_block_3.png caption="fourteen-tenths"]] ||

Statistical Methods
2011 Spring Release, Mathematics - Grade 10 Question 4: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 10.D.1 - Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. The bar graph below shows the one-year rate quotes Sanjay received from different car insurance companies. What is the mean one-year rate for the quotes Sanjay received? ||  || A.
 * $875 ||
 * || B. || $900 ||
 * || C. || $950 ||
 * || D. || $1025 ||

2011 Spring Release, Mathematics - Grade 10 Question 8: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 10.D.1 - Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. The table below shows the monthly rents charged for different apartments. What is the median monthly rent charged for the apartments? ||  || A.
 * $900 ||
 * || B. || $925 ||
 * || C. || $938 ||
 * || D. || $975 ||

2011 Spring Release, Mathematics - Grade 10 Question 13: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 10.D.1 - Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. The list in the box below shows the ticket prices for ten concerts scheduled at a stadium. A ticket price of $70 is added to the list. Which of the following measures of the data will change? ||  || A.
 * $32, $36, $65, $30, $46, $19, $46, $40, $70, $16 ||
 * range ||
 * || B. || median ||
 * || C. || maximum ||
 * || D. || minimum ||

2011 Spring Release, Mathematics - Grade 10 Question 23: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 10.D.1 - Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. The circle graph below shows information about the budget for a school party. <span class="para_left">The total budget for the party is $1500. What is the total dollar amount in the budget for entertainment? ||  || A.
 * $300 ||
 * || B. || $450 ||
 * || C. || $500 ||
 * || D. || $1050 ||

2011 Spring Release, Mathematics - Grade 8 Question 19: Multiple-Choice Reporting Category: Data Analysis, Statistics, and Probability Standard: 8.D.2 - Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts. Differentiate between continuous and discrete data and ways to represent them. A newspaper reporter surveyed 30 people after they cast their votes in a recent election. He created the stem-and-leaf plot below to display the ages of the voters surveyed. Which of the following is closest to the percent of the voters surveyed whose age was less than 41? ||  || A.
 * 40% ||
 * || B. || 47% ||
 * || C. || 53% ||
 * || D. || 60% ||

2010 Spring Release, Mathematics - Grade 10 Question 20: Open-Response Reporting Category: Data Analysis, Statistics, and Probability Standard: 10.D.1 - Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. The line plot below shows the number of skateboards owned by each of the 10 members of the Skateboard Club. <span class="para_left">Two people became new members of the Skateboard Club. However, the <span class="bold_text">median <span class="para_left"> number of skateboards owned by the 12 club members did not change.
 * 1) What is the range of the numbers of skateboards owned by the Skateboard Club members? Show or explain how you got your answer.
 * 2) What is the mode of the numbers of skateboards owned by the Skateboard Club members? Show or explain how you got your answer.
 * 3) What is the mean number of skateboards owned by the Skateboard Club members? Show or explain how you got your answer.
 * 4) What is the median number of skateboards owned by the Skateboard Club members? Show or explain how you got your answer.
 * 1) What could be the number of skateboards each of the two new club members owns? Explain your reasoning.