Items #1, #2, #3, and #4 … find the equivalent fraction in ...
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|Packaging BROWNIE CAKES -- Multiple-Choice Items |
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|Open-top boxes can be made from cardboard layouts by folding on the dotted lines. (see sketch… at right) |
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|Sally’s box height is 4½ inches. The bottom length is 6 inches and the width is 4 inches. |
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|Ben made a similar box that had exactly the same height. However, the bottom of Ben’s box has different dimensions. The length is 8 inches and the |
|width is 3 inches. |
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|A single brownie cake to fit into these boxes has a height of 1½ inches, a length of 3 inches, and a width of 2 inches. |
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|Warm-up items: |
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|Draw a sketch of Sally’s completed box and label the dimensions. |
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|How many layers of 1½ inch high cakes can fit in each of the boxes? |
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|a) 1 b) 2 c) 3 d) 6 |
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|How many cakes are on a single layer of Sally’s box? |
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|a) 2 b) 4 c) 10 d) 24 |
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|Sketch the layout of one layer of cakes in Sally’s box … (at right). |
|Number the cakes in your sketch. |
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|Which of the following is true? |
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|A. The volume of Sally’s box is greater, so her box will hold more cakes than Ben’s box. |
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|B. The volume of Ben’s box is greater, so his box will hold more cakes than Sally’s box. |
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|C. The box volumes are the same and an equal number of cakes can fit in both boxes. |
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|D. Both boxes have the same volume, but different numbers of cakes fit in the boxes. |
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|PLAYGROUND TWIRLINGS -- Multiple-Choice Items |
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|Sam and Carlin are swinging their home-made bird models in the same playground area. (see sketch) |
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|Sam’s string is 8 feet long. Carlin’s string is 12 feet long. |
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|The playground is a rectangle that measures 40 feet long and 25 feet wide. |
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|Warm-up items: |
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|What is the area, in square feet, of the playground? |
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|a) 65 b) 115 c) 130 d) 1000 |
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|How many times larger is Carlin’s swinging area as compared with Sam’s swinging area? |
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|a) 2 b) 1 ½ c) 2 ¼ d) 4 |
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|What length, in feet, does the playground need to be so both Sam and Carlin can swing their bird models without ever crashing? |
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|a) 41 b) 40 c) 24 d) 20 |
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|If Sam swung his bird model standing at the corner of the playground, what fractional part of his bird’s circular path would lie beyond the |
|playground boundary? |
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|a) ¼ b) ½ c) ¾ d) 1 ¼ |
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|Which of the following is true? |
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|A. The total area needed by Carlin when swinging her bird model is one and a half times the area needed by Sam when swinging his bird model. |
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|B. The playground area is too small for Carlin to swing her bird model. |
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|C. If Sam and Carlin are both swinging their bird models in the playground at the same time, their models might crash into each other. |
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|D. The total playground area is 16 times greater than the area of the circle Sam needs to swing his bird model. |
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|SIDEWALK LEMONADE STAND -- Multiple-Choice Items |
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|Raul and Julia have a lemonade stand. Full cup servings sell for 25¢. Their cost to make one serving is 8¢. |
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|The mayor of the town wants each lemonade stand to pay a daily fee of $7. |
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|Raul and Julia’s sign is 2.5 feet high and 4.5 feet wide. Signs less than 12 square feet pay no fee. Larger signs pay a fee of 25¢ per square foot|
|per day for any extra area over 12 square feet. |
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|Their sign hangs between two 8-foot poles. (see sketch) |
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|Warm-up items: |
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|At 25¢ per drink, how many cups do they have to sell to pay the mayor’s lemonade stand fee? |
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|a) 17 b) 28 c) 36 d) 42 |
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|Raul and Julia want to make a daily profit of at least $17 after paying fees. How many cups per day need to be sold? |
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|a) 142 b) 120 c) 117 d) 97 |
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|The 8-foot signpost has wires 6 feet away from the bottom. How long, in feet, are those wires? |
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|a) 8.6 b) 9.8 c) 10 d) 10.5 |
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|What would be the extra daily fee, if their sign measured 6 feet by 3 feet? |
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|a) $0.72 b) $1.50 c) $2.16 d) $2.64 |
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|Which of the following is true? |
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|A. If Raul and Julia sell 90 cups of lemonade in 8 hours, they each make $2.00 per hour. |
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|B. If Raul and Julia sold 40 cups of lemonade, their profit is enough to pay the lemonade stand fee. |
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|C. Raul and Julia do not have to pay a fee for their sign. |
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|D. Each 8-foot pole is secured by 2 wires 6 feet from the bottom. The wires are 12 feet long. |
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|FRIENDS ACROSS TOWN -- Multiple-Choice Items |
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|Maria and Sandra are best friends at school. They live on opposite sides of a river with two bridges. |
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|The speed limit is 25 miles per hour [mph] on all roads and bridges. The distances between their two houses are shown in the note. (see right)|
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|On weekends (Sat. and Sun.) the bridge at the dam is closed to car traffic. On weekdays (Mon. – Fri.), the river bridge and the dam bridge are |
|both open for car traffic. |
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|However, bicycle traffic is allowed on the both bridges every day. When they ride bicycles between houses, their average bicycle speed is 6 miles |
|per hour. |
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|Warm-up items: Note: speeds (below) are average speeds (as given above) unless otherwise stated. |
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|What is the difference, in miles, between the two possible routes on weekdays? |
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|a) 3 b) 4 c) 6 d) 30 |
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|What is the difference, in minutes, between the two routes on a weekday, when driving at an average speed of 25 miles per hour? |
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|a) 65 b) 43.2 c) 28.8 d) 14.4 |
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|At an average speed of only 18 miles per hour, how many minutes does it take to drive between the houses using the dam bridge route? |
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|a) 40 b) 54 c) 60 d) 64 |
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|What is the difference between the two routes, in minutes, when bicycling on weekdays? |
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|a) 30 b) 60 c) 120 d) 180 |
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|Approximately how much less time, in minutes, does it take Maria or Sandra to drive at the speed limit between houses on weekend days, as compared |
|with riding a bicycle over the dam bridge? |
|A. 41 B. 43 C. 76.8 D. 12 |
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Fold on the solid lines and tape the vertical edges to make a box for the cakes.
40 feet
25 feet
PLAYGROUND -- showing Carlin’s circle
[pic]
Note: The dam bridge is closed both weekend days.
Distances between the two houses are as follows:
River bridge route = 18 mi.
Dam bridge route = 12 mi.
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