Author Archives: Mr. Polack

April Blog Problem of the Month

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Example: It takes me 2 hours to cover the 120 miles to grandma’s house. So, I am traveling at 60 miles per hour.
120 (distance) = 60 (rate) X 2 (time)

 

D=RT

(Distance = rate X time)

If you could go anywhere in Howard County, in Maryland, in the United States, in the world, in the universe – where would it be? Why do you want to go there? Now, tell us how long it will take you to get there. You will need to figure out how far you are traveling and what speed you will be traveling. You can use the formula above to help you. (d= distance, r = rate, t = time). So let’s say I want to go to Deep Creek Lake from Rockburn Elementary School. Google maps tells me that is 174 miles (d – the distance) and that it will take me 2 hours 47 minutes (t – the time). But it doesn’t tell me how fast I need to go (r – rate). So I need to do a bit of seesaw math here.  To get the rate, I have to divide both sides by the time…

174 (distance) divided by 2.78333 (I converted the 47 minutes to 0.78333 hours using the don’t know method)…

Tells me my rate will average a little over 62.5 miles per hour. According to Google Maps, that means you are following the average posted speed limit. Now let’s pretend I have a magic vehicle which will allow me to safely and legally travel at much higher speeds. How fast would I have to travel to get there in 2 hours? (172 divided by 2) That would be an unsafe 87 miles per hour. OK, lets really have some fun. To get there in 1 hour, I’d have to travel 174 miles per hour. To get there is 30 minutes, 348 miles per hour.   

 I could do this all day. But I’ve decided I’d rather go to the moon! A little research on-line, tells me the moon is 238,855 miles away from earth. So let’s do this another way. If I could travel 5000 miles an hour, how long will it take me to get to the moon? A bit more seesaw math (238,855 – the distance, divided by 5000 – the rate) tells me I could get to the moon in just under two days (47.771 hours)! Now that is some magic vehicle!

Remember, tell us where you want to go and why. Then tell us how far away it is, the rate you will be traveling (I’ll lend you my magic vehicle if you like) and how long it will take you to get there. Now, play with either the rate or the time a few times and see how going faster or slower will affect how long it takes you to get there. Give us a few variations. Have fun!

March Blog Problem of the Month

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Favorite Mathy Things and or/ Real-World Math Stuff: [Pick one bullet per blog response. Answer as many as you like.]

  • In honor of π-Day this month: what is your favorite real world circle and why? Is it 2D or 3D? If it is 3D, is it a cylinder or a sphere? What is its circumference? What is its area? If it is 3D, what is its volume? [Example: Baseball because I love to play and watch baseball. V=4/3 πr (cubed)]
  • What is your favorite real world 2D shape and why? What is its perimeter? What is its area? [Example: A rectangle because most windows are rectangles and I like looking at nature. A=lw and P=2l+2w]
  • What is your favorite number and why? [Example: 24 – just think of all the Challenge 24 cards I have. For example, if my numbers were 6, 7, 1, and 2.  I could do (6+7-1)2=24]
  • What is your favorite number expression and why? Research to find out how the expression got started if you can. [Example: Baker’s Dozen – because who doesn’t want an extra doughnut? One explanation I found follows: During the reign of Henry III, bakers who were found to have shortchanged customers could be subject to severe punishment. To guard themselves from such punishments, they (bakers) would give 13 for the price of 12.]
  • What is your favorite recipe? How much of each ingredient do you need to make one batch or meal? How many people will that serve? How much of each ingredient would you need to make enough of your favorite recipe to serve 100 people?
    Example:

    RAGGEDY ANN COOKIES
    1 c. brown sugar, packed firmly
    1 c. shortening
    1 egg
    1 tsp. maple flavoring
    2 1/4 c. sifted all-purpose flour
    1/2 tsp. baking powder
    1/2 tsp. salt
    1 c. shredded coconut
    Granulated sugar

     

    Beat together brown sugar, shortening, egg and maple flavoring until fluffy. Add flour, baking powder and salt and mix well. Stir in coconut. Drop by spoonfuls 2 inches apart onto greased cookie sheet. Dip bottom of greased small glass into granulated sugar and press cookie flat. (Edge will be ragged.) Bake in 350 degree oven 10 to 12 minutes. Cool on rack. Yield: 5 dozen.
  • What is your favorite real world 3D shape and why? What are its dimensions? What is its volume? [Example: A Rubik’s Cube because I think they are so cool to play with and I love to watch people solve them fast. Cool link to a video showing how to solve a Rubik’s cube.]

 

February Blog Problem of the Month

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X     Y

3…..7

5…..11

8…..17

4…….?

6…….?

?…….21

?…….25

So what is going on here? Well it is time for a little Function Fun! If you look at my function table (ok – really can’t create the boxes here – but you get the idea), what numbers go in all the question marks? What is the function rule? Well beside the 4 would be a 9, so (4,9). Beside the 6 you would get a 13, so (6,13). The final two would be (10,21) and (12,25). By now I’m sure you figured out the function rule which is twice the X value plus one. I’ll write that as Y=2X+1. OK, I know what you are thinking. Good for you Mr. Polack, now what are we suppose to do? Well here is your challenge, during the month of Febreuary everyone gets to make as many Function Fun tables you like. Just as I did up top. You need to have at least three lines with both x and y values and then at least a few with missing x values and a few with missing y values. (Hint: Use seven periods between numbers.) DO NOT TELL PEOPLE THE RULE OR THE ANSWERS LIKE I DID! During the last week of February, I will go in and start approving answers to be posted. So you can try to solve each other’s Function Fun Tables but I won’t post any answers until the end of the month. Then in class, we will see who was able to figure out whose tables. Feel free to make as many as you like! On your mark… get set…FUNCTION AWAY!!!!!

January Blog Problem of the Month

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Monica Meanless and Abraham Average are just regular kids from Statisticsville, Mathalopolis. They both love sports! All kinds of sports! But sometimes when they are talking to their friends about their favorite sports, it sounds like their friends are on another planet. They just don’t understand.

In baseball they wonder about batting averages, on-base percentages, winning percentages, and slugging average. In football they wonder about quarterback completion rate, quarterback rating, average yards per carry, average yards per touch and how offensive and defensive rankings are figured out. In basketball there is that whole free throw percentage thing. In hockey they wonder what “shots on goal” means. Please help Monica Meanless and Abraham Average enjoy even more the sports they love by explaining one of the above (or any other statistical item from any other sport – they really love sports) to them.

If someone else explains something, you can put it in your own words or add to the explanation.

 

December Blog Problem

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Mathematical Musings
(Answer one at a time. Answer as many times as you like.)

 On the twelfth day of Christmas, my true love sent to me ….
Twelve drummers drumming,
(What kind of drum? How big is it? What is the area of the top? What is the circumference? How many cubic inches of air are inside the drum?)
 Eleven pipers piping,
 (Bag pipes I presume? How much air from your lungs is needed to get sound out of the bag pipes?)
 Ten lords a-leaping,
(How high are they leaping? How many times do they leap? Will you measure that by the minute?
Do they leap all day? Do they sleep? Eat? Take a break?
What is the combined leap of the ten lords during the twelve days of Christmas?)
Nine ladies dancing,
(What kind of dancers? How long do they dance?
How many combined hours during the twelve days do they dance?)
Eight maids a-milking,
(Let’s assume each maid has her own cow to milk. How long per day can the average cow be milked?
How much milk does the average cow produce in one day?
What would it cost to buy the milk from the eight cows during the twelve days of Christmas?)
Seven swans a-swimming,
(So if they swim in a rectangular pool that is 40 ft long by 20 feet wide, with a shallow end 3 feet deep that is 15 ft long and a deep end 9 ft deep that is 15 ft long – the remaining 10 ft is a slope – what is the volume of the pool?
Hint: There are about 7.48 cubic ft in a gallon!)
Six geese a-laying,
(How many eggs do geese lay? Do they lay eggs every day?
Assuming these are all adult geese,
how many eggs would you expect these six geese to lay during the twelve days of Christmas?)
Five golden rings,
(How do you measure gold rings? [karats?] What does gold cost these days?
It can change daily. What might it cost to buy these five golden rings?)
Four calling birds,
(Sound is measured in decibels. How loud do you suppose four birds calling are?)
Three French hens,
(Make up your own for this one and post back to the blog for others to solve.)

Two turtle doves,
(Where are you going over the break? [city, town, state?]
How many combined miles would it be for these two turtle doves to fly round trip with you?)
And a partridge in a pear tree!
(The ratio of partridges here to pear trees is 1 to 1 [one partridge – one pear tree]. But what do you suppose the ratio is of partridges to pears? How many pears does an average pear tree have at any given time?)

November Blog Problem of the Month

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We have a big break coming up at the end of November! Many families will celebrate Thanksgiving. Just about everyone will get together with relatives and maybe some friends. Find out what your family is planning. Are you having a big celebration at your house on Thanksgiving? Are you going to a relative’s house on Thanksgiving? Are you going out to eat somewhere? Are you going to a friend’s house on Thanksgiving? Figure out (ask parents to help) how many people in total do you expect to be there. Make sure to include all brothers, sisters, parents, aunts, uncles, cousins, grandparents, friends of the family [FOF], and anyone else. How many of them are male? How many are female? How many are age 10 and under? How many are 11 and older? How many live in the state of Maryland? How many live outside the state of Maryland?

Record all the information below first as a fraction [11/20 for females would mean that 11 of the 20 people coming are female], then as a decimal [so 11/20 would = 0.55], then as a percent [11/20 = 55%]. Remember you can use keyboard shortcuts to copy the following and paste it into your answer. Then you just need to write the fractions, decimals and percents.

Males:

Females:

Brothers:

Sisters:

Parents:

Aunts:

Uncles:

Cousins:

Grandparents:

Friends of the family [FOF]:

Age 10 or under:

Age 11 or older:

Live in the state of Maryland:

Live outside the state of Maryland:

Bonus A:       

Add another category or two (or several) of your choice. Be creative [how many have x-box’s, iPads, been to Disney World – anything you can think of!]

Bonus B:

What is your highest fraction/decimal/percent? What is your lowest? What is the median fraction? What is the mean decimal? (Might want to use a calculator for that one.) What is the range of your fractions or decimals?

 

October Blog Problem of the Month

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Where do you keep your socks? Go to the drawer and carefully remove them and anything else that is in there. (Be neat! You will have to put them back neatly!) Now go get a ruler and measure your drawer. You need to measure the length, width, and height of the drawer in inches. Now you will need to do some estimating to answer as many of the following questions as you like. You can answer one each time you reply or do several all at one time.

 

·   What is the volume of your drawer?

·   Get your favorite book that you have in your house. Put it in your drawer. About how many books that size could fit into your drawer? Tell us how you figured that out. (Make sure to tell us the name of your favorite book!)

·   About how many pairs of socks can you fit in your drawer? Tell us how you figured that out?

·   Find a quarter somewhere.  Put it in your drawer. If your drawer was absolutely filled completely with quarters only, about how much money would there be in the drawer? Tell us how you figured that out.

·   Put your calculator in the drawer. About how many calculators like yours could fit in the drawer? (You might need a calculator to figure that one out. You might need a calculator to figure any of these out!) Tell us how you figured that out.

Now carefully and neatly replace your socks so nobody comes to yell at you for messing up your room!