Math

[|assistments link] [|video link] @Problem-solving strategies

• How will you organize your work to find the answer? (strategy) • How will you know that your answer is correct? • How will you know that it is the only possible answer? • If there is more than one answer, how will you know you have them all? • What if...?

Monday, August 15

A 9-inch square cake serves 9 people. How many people would a 12-inch square cake (of the same thickness) serve? (Hint: it's not 12!) //Suggested strategy: Draw a useful diagram.//

1. How many equivalent servings would a 9" x 12" cake have?

2. How many equivalent servings would a 8" x 14" cake have?

3. How many equivalent servings would a 10" round cake have? A 2-layer 10" round cake? A three-layer 10" round cake? (Assume each layer would be the same thickness of the original cake.)

Thursday, August 11

F=1.8C + 32 is a formula that relates temperatures in degrees Celsius to degrees Fahrenheit. F stands for the temperature in Fahrenheit and C stands for the temperature in Celsius. The Fahrenheit scale is used in the United States, but Celsius is used everywhere else. 1. What is the Fahrenheit equivalent to 16 degrees Celsius? Would it be appropriate to wear a sweater or sweatshirt?

2. What is the Fahrenheit equivalent to 30 degrees Celsius? What would be appropriate clothing for that temperature?

3. What temperature in Celsius would be equivalent to 16 degrees Fahrenheit? What would be appropriate clothing for that temperature?

Show your strategy for each problem above.

Wednesday, August 10

Asa is throwing darts randomly at a round bulls-eye that measures 14 inches in diameter. It consists of black and white concentric circles. The innermost circle has diameter 2 inches, and is painted black. The next circle is white, and has diameter 6 inches. The next circle is black and has diameter 10 inches. The outermost circle is white and 14 inches in diameter. Draw and label radii for a bull's eye that matches this description.

What is the area that is painted black? What is the area painted white? What is the ratio of black area to white area (as a lowest-terms fraction)? Click here for a hint

Extension Question: Write and answer one other question that could be answered from the given information.

Tuesday, August 9

Baseball players' batting averages are usually given as a decimal with three places (thousandths). So for example, a player with 37 hits out of 200 at-bats would have an average of 37/200 or 0.185 (nearest thousandth). A baseball player has 60 hits so far, and his average is .333 (to the nearest thousandth). How many hits will he need to improve his average to .500? Show your strategy.

Monday, August 8

Wheels

A wheel measures 20 inches in diameter. How many revolutions will the wheel complete when it travels 100 yards? (Circumference of a circle = diameter x pi)

Follow-up: 18" wheels vs. 19" wheels? How far will 1000 revolutions of an 18" wheel go? How far will 1000 revolutions of a 19" wheel go? How many revolutions will it take for an 18" wheel to go 100 miles? for a 19" wheel to go 100 miles?

Thursday, August 4

Danielle is stitching together a triangular mat made of identical circles. She measures a circle and finds that it is 18 cm in circumference. Once all 21 circles are connected, what will be the perimeter of the entire mat?

drawing of Danielle's triangular mat

Wednesday, August 3

Kira is making labels from a large sheet of poster paper. The labels are all 1" x 3" rectangles. The poster paper is 1' x 2'. How many labels can she make from one sheet of this paper?

<span style="color: #2f7930; font-family: 'Comic Sans MS',cursive; font-size: 20px;">Tuesday, August 2 Next week the Littleton Food Co-op is starting a Local Food Challenge for its employees, members, and shoppers. If Mrs. Snyder accepts the challenge, she can only eat food grown/produced within 100 miles. Which of the following cities and towns are within a 100-mile radius of Littleton? St. Johnsbury, VT Concord, NH Montpelier, VT Portland, ME Orleans, VT Sherbrooke, QUE Rumford, ME Newport, VT Burlington, VT Plattsburgh, NY Saratoga Springs, NY Boston, MA Augusta, ME Find at least 10 other towns or cities that are within a 100-mile radius from Littleton. (Bonus for towns or cities that neither Mrs. Glidden nor Mrs. Snyder have visited, and double bonus if you can show that there is at least one commercial farm currently in the town.)

Find the total area of the circle of the Local Food Challenge.

Estimate the number of cities and towns within the Local Food Challenge circle.

<span style="color: #2f7930; font-family: 'Comic Sans MS',cursive; font-size: 20px;">Monday, August 1 How many Friday the 13ths are there in 2011?

<span style="color: #2f7930; font-family: 'Comic Sans MS',cursive; font-size: 20px;">Thursday, July 28 Mrs. Snyder picked some cherries while in Michigan. She is bringing them home in a cooler that measures 18" x 18" x 24" and has walls that are all 2" thick. What is the interior volume of the cooler?

Extensions: What is the volume of the walls?

What percent of the space taken up by the cooler is actually usable for storing the cherries?

How would the answers to the above questions change if the walls of the cooler were 1 inch thick? 1.5 inches thick?

<span style="color: #2f7930; font-family: 'Comic Sans MS',cursive; font-size: 20px;">Wednesday, July 27 How many different squares are on an 8x8 chess board? (They can be different in position and/or different in size.)

<span style="color: #2f7930; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Tuesday, July 26

Use the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 to form two three-digit numbers that add to a third, three digit number. __(Use each digit only once)__

<span style="color: #2f7930; font-family: 'Comic Sans MS',cursive; font-size: 20px;">Monday, July 25 - __<span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Rectangle Perimeters __

<span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">On a sheet of graph paper, draw as many rectangles as you can that have a perimeter of 20 units. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">What are the dimensions of these rectangles? <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Make a table to list your results. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Create a graph that shows the relationship between length and width. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Describe this relationship in words. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">//__Extensions__//: <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Add a column to your table that lists the areas of the rectangles. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Create another graph that shows the relationship between length and area. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Describe this relationship in word. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Repeat this problem with a different given perimeter. <span style="font-family: 'Comic Sans MS',cursive; font-size: 17px;">Repeat this problem with a given area, such as 24 square units, and find possible lengths, widths, and perimeters.