Take Me Out to the Ballgame

A pitcher's Earned Run Average (ERA) is the mean (average) number of runs he gives up per nine innings pitched, which is a full game of baseball. For example, if he's pitched six innings and given up four runs, that's an average of two runs per three innings. Extending that to nine innings, he'd give up six runs, so his ERA would be 6.00 at that point.

As the season goes on and he pitches more games, his ERA will constantly change in value, but it always represents the average number of runs he would give up over nine innings of pitching. If he's given up 11 runs after pitching a total of 18 innings, his ERA would be 5.50.

I recently attended a Red Sox game, and one pitcher had an ERA of 13.50 when he came into the game. After he got one batter out, his ERA dropped to 13.00. Note that since there are three outs in an inning, one out represents a third of an inning pitched.

How many innings had that pitcher pitched before he came into the game I saw?

Send your answer to  eric_lass@psbma.org

Solution

The linear equation for the music stores is y = -3.317 x + 69.8 The linear equation for the other stores is y = 2.17 x +18.5 2. The predicted percentage value of the music stores for 2000 is 36.5%, for the other stores 40.5%.  The equation for other stores is more accurate.

Here's the new POW:

At Least This Many

How does the National Basketball Association (NBA) determine which player is its best field-goal shooter?

The NBA cannot rank strictly on the basis of shooting percentage without running the risk of comparing apples and oranges. If John Doe plays only a few minutes in one game, attempts only one shot, makes it, and then sits on the bench for the rest of the game, it doesn't seem fair to conclude he is a "better" shooter than Jay Public, who attempted ten shots, and hit eight of them - even though Doe's average of 100% tops Public's average of 80%. Therefore, a player qualifies for the "league lead" only after he appears in a minimum number of games and sinks a minimum number of shots.

To qualify for rankings after appearing in 10 games, a player must make 41 shots. Later on in the season, after appearing in 40 games, he must make 168 shots.

These two data "points" allow you to form a linear equation; in slope-intercept form,    y = mx + b, where the independent variable "x" represents the number of games in which a player must have appeared; and where the dependent variable "y" represents the number of field goals that must have been made.

Your task for this Problem of the Week is:

1. to find that equation, stating the values for m and b in common fractional form; 


2. to use it to predict the number of shots made so that a player qualifies for the rankings after appearing in 20 games, and then also for 30 games (rounding results to nearest whole number)

Solution

Chuck will get the most cola by using the vending machine. He will get 84 oz of cola. This is not the best buy. The best buy is the jug at the grocery store on a per oz basis.

Here's this week's POW:

Buy This Tune!

Where do you buy your music these days? You used to say, "At a music store!" but after the year 1990 there was a definite shift as to where music was purchased.

So it's clear that music stores are not the overwhelming choice it used to be.

Your tasks are to:

·      Determine the linear equation for each type of store for 1990 and 1996.

·      Use those equations to 'predict' the percentage values for 2000.

·      State which equation (Music or Online) was the better predictor for the actual sales in 2000.

Have a nice weekend!

Buying Cola

Chuck is buying some cola for his friends. He can go to the vending machine and get 12 oz. cans for $.60 per can, he can go to the corner store and get 20 oz. bottles for $.95 per bottle, or he can go to the grocery store and get 32 oz. jugs for $1.45 per jug.

He has $4.25 to spend.

At which place can he get the most cola?

Is this the best buy?

Monday is a holiday, so no new work until Wednesday, have a nice long weekend!

Teeter Troop

A seesaw can balance with four weights on it. The product of each weight and its distance from the fulcrum contributes to the balancing. If the sum of those products on one side equals the sum of the products on the other side, balance is achieved.

Four animals are balancing on a seesaw as shown below. All of the distances are measured in feet.

Use the diagram and the following clues to determine the weight of each animal.

·      The sum of their four weights is 40 pounds.

·      The rabbit weighs 2 pounds more than the ferret.

·      The cat weighs 8 pounds less than the dog.

Good day my young math scholars,

1) Go to student.desmos.com

2) Sign in with your real name, no nicknames please

3) 7th grade code:   VFWB2K

    8th grade code:   JZK4QA

Good day my young math scholars,

Solution to Last Week's POW

a=2, b=3, c=5

Dinner at Pepe's

Cynthia, Annie, and Suz went to Pepe's Pizza Palace for dinner after band practice. They shared a large pizza and each girl ordered a soda. When the bill came, they talked about how to split it up fairly.

"Annie, you had three slices and a medium soda so you should pay one-third of the bill," said Suz.

"Well, I'll chip in a dollar more than that," replied Annie. Annie replied to Suz, "And since you only had two slices and also ordered a small soda, you should only pay 20% of the bill."

"That seems fair," said Cynthia. "I ate three slices and had a large soda, so I should pay the most. I'll pay the remaining $8.80."

1. How much was the total bill for the pizza and the three sodas, and how much did each girl pay?

2. At Pepe's, a medium soda costs 25 cents more than a small, and a large soda costs 25 cents more than a medium. The cost of the sodas made up one-fifth of the total bill.  Figure out the actual cost of each girl's meal. Whose estimated cost was the closest to her actual cost?

1) Go to student.desmos.com

2) Sign in with your real name, no nicknames please

3) 7th grade code:    FWK29Q

    8th grade code:    EUE6PC

Good day my young math scholars,

For those of you who shared your work with me through your Google Drive, I've been able to look at all of it, so go check your documents for comments.

Today's task is on Desmos, so

1) Go to student.desmos.com

2) Sign in with your real name, no nicknames please

3) 7th grade code:    B8CNGS

    8th grade code:    5TPVBK

If you have any questions, I'll have a Google Meet Up on Tuesday, 1:00pm for 7th graders and 2:00pm for 8th graders.

Date of Message: Friday, March 27

Good day my young math scholars,

Adrienne's Axel 

The new program will have 1 double Salchow, 2 Axels, and 2 Lutz-Loop- Loop combinations. 

Let s = # of double Salchows, a = # of Axels, and c = # of combinations. Then Mandy's statements give 3 equations: There are 9 jumps: s + a + 3c = 9 (remember a combination is 3 jumps) There are 11 rotations: 2s + 1.5a +3c = 11 There are 2 combinations: c = 2 Substituting c=2 in the first 2 equations and rearranging we get s + a + 6 = 9 or s + a = 3 2s + 1.5s + 6 = 11 or 2s + 1.5a = 5 These two equations in two unknowns may be solved by any standard method, such as substitution or linear combinations. For example, using substitution, s = 3-a, so 2(3-a) + 1.5a = 5, so 1 = 0.5 a, so a = 2. Thus s = 3-2 = 1. So the program has one double Salchow, 2 Axels, and 2 Lutz-Loop-Loop combinations. Bonus: No. Without any information about combinations, we have s + a +3c = 9 2s + 1.5a +3c = 11 But remember that the solutions must be whole numbers (you can't do half an Axel or a negative double Salchow, for example). Thus 1.5a < 11, so a < 11/1.5 = 22/3, i.e., a < 7. But the number of Axels must be even, because we have no half-jumps in this program, and an Axel is 1.5 rotations. With a = 6, from the first equation, s=0 and c=1 or s=3 and c=0, neither of which work in the second equation. With a = 4, from the first equation, s=2 and c=1 or s=5 and c=0, neither of which work in the second equation. With a = 0, from the first equation, s=6 and c=1 or s=3 and c=2 or s=0 and c=3, none of which work in the second equation. Thus a=2 is the only possible number of axels. Then s + 3c = 7 and 2s + 3c = 8, so s = 1 and c = 2.  

Here's the new POW:

The ABCs of Exponents

Given the following three equations, solve for a, b, and c:

Show your work and email me your solutions by next Friday at:

eric_lass@psbma.org

Date of Message: Thursday, March 26

Good day my young math scholars,

If you've shared a document with me, please take a look at them as I've been able to read and comment on everything.

I'd like to have another meet up today to talk math, books, movies, or anything else on your minds. Let's try Zoom this time:

7th graders - Thursday from 1:00 - 1:30pm

8th graders - Thursday from 2:00 - 2:30pm

To access the video conference:

1) log onto  www.zoom.us    (PLEASE NOTE THE  .US)

2) you can download the zoom app if you haven't done so yet, but leave some time         as it takes a little while for them to send you a confirmation email

3) I've been told there's also a way to jump on a conference without the app if you scroll down the zoom website

4) enter the appropriate code:

        7th graders:  370 745 582

        8th graders:  165 450 458  

Date of Message: Wednesday, March 25

Good day my young math scholars,

Thanks to those of you who joined in to chat yesterday, it was great to see you all!

Sorry if it was a bit chaotic, if you have math questions please email me and I'll either respond or we can set up a 1:1 or small group conference.

For those of you who shared your work with me, I've been able to look at all of it, so go check your documents for comments.

Today's task is on Desmos, so

1) Go to student.desmos.com

2) Sign in with your real name, no nicknames please

3) 7th grade code:    2F3FX4

    8th grade code:    TBSZ7Y

I'll post Thursday's office hours and codes tomorrow morning. I think we'll try Zoom this time.

Date of Message: Tuesday, March 24

Good day my young math scholars,

If you didn't see my message from yesterday, please scroll down and give one of the problems I've posted a try.  I plan to post something new to do on Wednesday.

For today (Tuesday), I'm going to try to vault myself into the 2020s by holding a video conference meet up.  If you have any questions on the math problems I assigned or are looking for an alternative that might be easier, or maybe just want to check in and say hello, please join me!

7th graders - Tuesday from 1:00 - 1:45pm

8th graders - Tuesday from 2:00 - 2:45pm

To access the video conference:

1) go to your PSBMA account

2) click on the "waffle" in the upper right hand corner of your screen

3) choose "Meet"

4) enter the appropriate code:

        7th graders     hvn-ogoy-gqf

        8th graders     dkj-dxzr-mvr

There's a small chance that the technology (or more likely Mr. Lass) will encounter a problem, so I apologize in advance if this goes less than smoothly.  We'll get better at it by Thursday.

Best regards,

Mr. Lass

Date of Message: Monday, March 23

Hello my young math scholars,

First off, I miss seeing you all and hope you and your families are healthy and keeping busy!

I'm going to start offering work for you on Mondays and Wednesdays as well as a new Problem Of the Week on Fridays (see below for POWs and solutions). 

I'm also trying to figure out a way for you to check in if you need help (or just want to say hello) on Tuesdays and Thursdays. Maybe Google hangout, but stay tuned...

Please click here to access your Big Problem for Monday, March 23rd:

https://sites.google.com/site/lassmath/my-forms

Each file contains three problems. They range from easier to more difficult. Read all three and choose ONE problem that seems like the most difficult you might be able to solve. You may type your solution or write it out and take a photo. As always, SHOW YOUR WORK!  Your finished product should include the math you used as well as a paragraph or two explaining what you did.  This should take you 30-60 minutes over the next couple of days.

Share your solution with me on Google Drive or email it to me (whichever is easiest for you) at:   

eric_lass@psbma.org     

7th graders, if you'd like a bigger challenge, try an 8th grade problem instead of the 7th grade list. 8th graders, if you're having trouble, feel free to try a 7th grade problem.

Here's a template to help any and all with answering the Big Problem:

https://docs.google.com/document/d/1yspRDX6KjjnwuMrVwk7yT915bDvy27e_hy7JDYydRoY/edit

I also included an additional challenge problem if you're looking for something even bigger!

If you have questions, feel free to email me.

My other assignment is for you to try to do something nice for a friend or family member each day. This is a difficult time for everyone and it can be hard to be stuck at home with the same people every day, even if they're the people you love most. If we all can do something nice for each other, it will make life more pleasant all around.

I hope we can see each other again soon!

Best regards,

Mr. Lass