Answers to Problems of the Week - October 11 to October 17

Rewards for Problems of the week:

5 stars for the correct answer at your level; 10 stars for the next level; 20 stars for 2+ levels up.

Lower Elementary: 

Question: Would you rather have one half of a chocolate bar that weighs 10 ounces or one half of a chocolate bar that weighs 16 ounces? Draw a picture of the candy bars to show why.

Answer:  Answers vary.

Solution:  Half of 16 ounces is 8 ounces, and half of 10 ounces is 5 ounces.

A student might want the 8 ounce piece of chocolate because it’s bigger or the 5 ounce piece because it’s smaller.

Upper Elementary:

Question: You can find the approximate temperature in Celsius by subtracting 32 from the temperature in  Fahrenheit, then dividing that number by 2. A recipe for pecan brittle needs to be heated to 300°F, but your candy thermometer only measures in Celsius. Find the temperature in Celsius to which you should heat the candy.

Answer:  134°C

Solution:  Three hundred degrees Fahrenheit, minus 32 is 268. We can mentally calculate half of 268 by finding half of each place value because each place value has an even digit. Half of 268 is 100 + 30 + 4 = 134°C.

Middle School: 

Question: Polly is selling candy bars for a fund raiser. She sells caramel chocolate bars for $3 and peanut butter chocolate bars for $4. If she sells twice as many peanut butter chocolate bars as caramel chocolate bars and gets $44 in total, how many of each kind of candy bar did she sell? Solve this problem by using the portioning strategy.

Answer:  4 caramel chocolate bars

8 peanut butter chocolate bars

Solution:  Since Polly sold twice as many peanut butter chocolate bars as caramel chocolate bars, we need a number of $3 bars and twice as many $4 bars to make a total of $44 worth of chocolate bars.

Two $4 bars and one $3 are worth $11 altogether. Since $11 × 4 = $44, two peanut butter chocolate bars and one caramel chocolate bar are a quarter portion of the total chocolate bars. Polly sold 2 × 4 = 8 peanut butter chocolate bars and 1 × 4 = 4 caramel chocolate bars.

Algebra and Up: 

Question: A cylindrical chocolate peppermint cookie has a layer of dark chocolate cookie, a layer of peppermint creme on top, and layer of dark chocolate all over the whole thing. The cookie layer is 2mm thick, the peppermint creme layer is 3mm thick, and the chocolate layer is 1mm thick on all sides. If the whole cookie is 52mm across, then what is the volume of the chocolate peppermint cookie?

Answer:  4,732π mm³

Solution:  The volume of a cylinder the area of its base multiplied by its height: π × r² × h. So, the volume of the whole cookie is π × 26² × (2 + 3 + 2) = 4,732π mm³. Note that since the chocolate layer is 1mm thick on all sides, it adds 2mm to the height.

Challenge problem to take home. 5 stars for the correct answer. 

Nalani and Violet are treating themselves to ice cream at their favorite Jen & Berry's. First, they choose one of the 3 sizes — small (one flavor), medium (two flavors), and large (three flavors). Then they pick from these 3 flavors — strawberry, vanilla, and chocolate.

For both girls, the order of flavors matters. But while Nalani doesn't mind repeated flavors, Violet doesn't want more than one scoop of each.

How many more options does Nalani have compared to Violet?

Answer: Nalani has 24 more options than Violet