St. Patrick’s Day Shamrock with Graphs

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Link to the pdf and tns files

Link to the image that can be imported into a TI-84 CE

Shamrock_on_Nspire

How can this shamrock be drawn with graphs? Proceed to see one possible solution

 

page1.PNG

 

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 What this looks like on a TI-84 CE:

shamrock_on_84CE.jpg

 Link to the image that can be imported into a TI-84 CE

 

 

Pi Day Activity for TI-Nspire

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Link to TI-Nspire files for handheld and computer

Link to the video: Why Pi?

Link to website with more Pi activities and Einstein information

Nspire activity on one page

 

Pi Day Activity for TI-83/84

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Link to All Content: student version, teacher version, data

Link to more Pi day activities and Albert Einstein information

Link to short video explaining the activity

The student version is shown below. The teacher version has solutions and teaching hints.

01A02

 

 

 

My Heart is in Pieces

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For Valentines’s Day, February 14, I have created a series of graphs that outline the shape of a traditional heart.

If you are using a TI-83/84 or a TI-84 CE, I have created programs that when executed, will sketch out the shape of a heart. On the TI-84 CE it will be in color.

If you are using TI-Nspire, I have created a file that will not only sketch out the shape of a heart, but the file will also show the student (teacher) how this was accomplished.

Link to the files using the TI-83/84

Link to the files using the TI-84CE (color)

Link to the files using TI-Nspire

                                TI-Nspire “heart”                                        

TI-Nspire_heart

                                TI-84CE “heart”

TI-84CE_heart

Lines of code for the programs for the TI-83/84 and the TI-84CE are listed below. The actual programs can be downloaded from the links.

TI-83/84 version:

TI-8384_heart_program_lines_of_code

TI-84CE (color) version:

TI-84CE_heart_lines_of_code.PNG

Link to a 2 minute video explaining the activity.

Link to a video showing how this was done using TI-Nspire with regression equations and limited domains.

If you have questions, comments or suggestions, contact me: tom@tomreardon.com

 

Groundhog Day February 2

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This activity can be used at grade 7 or beyond. It can be done with a scientific or graphing calculator.

Below are links to a word document of the activity, a pdf of the activity, a pdf of the answer key, a TI-Nspire file of the activity, and a zip file with all these files.

Link to my dropbox with all files.

photo of phil  Phil

According to folklore:

If it is cloudy when a groundhog emerges from its burrow on February 2, then spring will come early.

If it is sunny, the groundhog will supposedly see its shadow and retreat back into its burrow, and the winter weather will persist for six more weeks.

There are several celebrations of Groundhog Day throughout the world, but the largest and most popular takes place in Punxsutawney, Pennsylvania, at Gobbler’s Knob, where crowds as large as 40,000 have attended the ceremony (about 90 miles northeast of Pittsburgh).

The German-based tradition began in the U.S in 1887.

photo of gobblers knob

A groundhog is also known as a woodchuck, a member of the squirrel family. Naturally they eat green plants such as grasses, clover and dandelions. Punxsutawney Phil, however, thrives on dog food and ice cream in his climate-controlled home at the Punxsutawney Library.       

Up on Gobbler’s Knob, Phil is placed in a heated burrow underneath a simulated tree stump on stage before being pulled out at 7:25 a.m. to make his prediction.

Here is a summary of whether or not Phil has seen has shadow from 1887 through 2015:

Shadow         107

NO shadow     12

no record          9

1 – 5. Please round all answers to the nearest percent or nearest whole number.

1.What percent of the time that records were kept, did Phil see his shadow?

2.What percent of the time that records were kept, did Phil not see his shadow?

3. What percent of the time since 1887, was there no record of what Phil saw?

4. Assume that records will be kept from now on. If the pattern above continues and you know that Phil has seen his shadow 150 times at some date in the future, how many times would he NOT have seen his shadow at that time? Explain.

5. How often has Phil been correct? Take a guess. Since 1887, when records were kept, what percent of the time do you think Phil was correct?

C 2016 Reardon Gifts, Inc   tom@tomreardon.com

Super Bowl 50 Scores

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This activity can be used at grade 7 or beyond. It can be done with either a TI-83/84 or the TI-Nspire. There are two links below – one for doing the activity with a TI-83/84, and one for doing the activity with TI-Nspire.

Each link contains the student version, the teacher notes, the answer key and other files.

Link to my dropbox with all files to use with a TI-83/84.

Link to my dropbox with all files to use with TI-Nspire.

Link to a 3:30 video that explains the activity

Idea: the scores of the first 49 Super Bowl football games will be placed into lists on the calculator. On the TI-83/84, the data is easily placed into the proper lists with the ease of running a supplied program. On the TI-Nspire, the data is already in the tns file. The students are then asked questions about the data and will need to perform either 1 Variable Statistics to answer them, or to create a box plot to answer them. We encourage the use of groups of 4 to do the activity in class. See the Teacher Notes for either calculator.

The Teacher Notes also contains 10 fun trivia facts about the Super Bowl, including how it got its name. Enjoy…

Super Bowl Scores Activity 2016   Student Activity

TI-83/84: Have the program “SUPRBOWL” put onto your calculator.  This program will clear all your lists and place the following data into your lists:  L1  Game Number     L2 Winning Score    L3 Losing Score
TI-Nspire: The data is already in the activity.
Use the data to answer the following questions:
  1. a. What is the largest winning score?     b. What is the smallest losing score?     c. What is the winning score that occurred the most often?     d. What is the mean of the winning scores?     e. What is the median of the winning scores?
  2. a. What is the smallest losing score?     b. What is the largest losing score?     c. What is the losing score that occurred most often?     d. What is the mean of the losing scores?     e. What is the median of the losing scores?
  3. a. What is the largest number of total points scored by both teams?     b. What is the smallest number of total points scored by both teams?     c. What is the number of total points that occurred most often?     d. What is the mean of the total points scored?     e. What is the median of the total points scored?
  4. a. What is the largest point difference of the scores?     b. What is the smallest point difference of the scores?     c. What is the point difference that occurred most often?     d. What is the mean of the point differences?     e. What is the median of the point differences?
  5. Based on your analysis of the data, if you had to pick a final score to the Super Bowl, what score would you pick? And why? Explain.
All answers and step-by-step screen shots of the solutions are supplied in the files in my dropbox (see links above).
10 Questions to ask as class openers (answers supplied in the dropbox links above:
1. What is the average price of a Super Bowl 50 ticket? (compared to the most expensive ticket in 1967)
2. How much does a 30-second commercial cost for the Super Bowl? (compared to 1970)
3. How much money does each player of the winning team win? (losing team?)
4. How many pounds of guacamole will probably be consumed on Super Sunday?
5. How many chicken wings will be consumed on Super Sunday?
6. What Super Bowl had the most TV views?
7. Of the top ten individual television broadcasts ever, all but one are Super Bowls. What was that one TV event?
8. With what numbers have Super Bowls been referred to?
9. There are 4 NFL teams that have never played in a Super Bowl. Who are they?
10. How did the name Super Bowl come about?
See the dropbox links above for the answers. Enjoy…
tom@tomreardon.com

Prius versus Corolla – which car to purchase? An innovative math activity for middle or high school.

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Link to dropbox folder with all the files

Link to video with an overview of the activity.

The Toyota Prius gets 48 mpg on the highway and 51 mpg in the city and has a sticker price of $25,235. The Toyota Corolla gets 40 mpg on the highway and 30 mpg in the city and has a sticker price of $23,495. If we consider only the cost of the car and the cost of the fuel, which car will cost less?

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We supplied this information using a TI-Nspire document:

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Step 1. Pass back the pictures of the cars, stickers, and mpg information on a word document or in the TI-Nspire file. Or display that information on your screen or interactive white board. With the students in groups, have each of them generate at least one question about the numbers that they see. Here are some of the questions that I heard from students:

  • How was the ‘Annual Fuel Cost’ calculated?
  • How was it calculated that you would save $6250 in fuel costs over 5 years?
  • Why does the Prius get better gas mileage in the city than on the highway?
  • The Prius costs more, but uses less gas, so how long before it is cheaper to have a Prius?

Have them discuss those questions in their groups and then discuss them as a whole class. The 4th question listed above, was the one that caused the most interest (and it was the one that I had hoped that they would generate). We made that the focus.

Step 2.  One student brought up the idea about having to finance the car and that we should include the interest paid on the loan as part of the cost of the car. We discussed down payments, interest rates, and other related finance issues. We decided that the down payment for each car would be the tax and title and that we would finance the car based upon the sticker price, although car buyers normally negotiate that sticker price. We used the Finance app on the TI-Nspire, which is also on the TI-83/84 family, to calculate the monthly payment and the total interest paid over the duration of the loan. We decided on a 4 year loan, paying monthly, at 3.9% APR. Here are some screen shots from students:

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I used Navigator to assess what each student was doing, to see which students were successful and which students needed assistance. Fortunately, most of the students were successful, and all of them were trying.

Nav_screen_shots01

STEP 2 a (optional): Create an amortization schedule for 2 or 3 months so that students can see first hand how interest is used. Then have the students create an amortization schedule using either a spreadsheet like Excel, or the spreadsheet app on TI-Nspire. This will allow the students to see how the first payments go more towards interest than the last payments do. And to see that the car loan is, in fact, paid off in 48 months. This also allows students to see the power of generalization and the power of spreadsheets.

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Notice the formulas for the calculation of interest on the left and the end_balance on the right.

Step 3.  Questions to answer: How long do we need to keep the Prius before the total cost of the car plus the gas costs is cheaper for the Prius than for the Corolla? Where is the “break even” point? Instead of just giving the students the data that they need to know to answer these questions and solve the problem, I highly suggest that you have the students generate a list of questions that they need to know in order to solve the problem. Have them discuss in groups and then come together as a class and list them — good and not so good. Then give them the answers to their questions and ask them to solve the problem. If there are too many questions, they should ignore that data and if they didn’t ask the right questions, they will get stuck and then ask.

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They will decide that they need to calculate the cost for one year of gas for each car. Here are some of the questions that they generated:

  • How many miles are driven per year?
  • How many of those miles are highway? … city?
  • What is the cost per gallon of gas that we should use?
  • What is the size of the gas tank?
  • How often do we fill the tank?

Those questions (and others) were placed on the board and I gave them the answers. NOTE: the first 3 questions above are necessary and the other two are not. It is very important that the students decide what numbers they need to know to solve this problem — not just give them the numbers. We decided to use 10,000 miles per year on the highway, 5,000 miles per year in the city, and $3.59 for a gallon of gas. We discussed why those numbers were used. Then the students were asked to calculate those yearly gas costs for each car. Here are some student screen shots:

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Prius gas cost for one year: $1099.88 ( some students will round differently).               Corolla gas cost for one year: $1495.83

Step 4.  Now how can we decide where the “break even” point will be? Allow students to discuss different ways to answer that question.Some possible ways to do this include i) guess ‘n check, ii) generate equations for each car that include the cost of the car and cost of gas per year and solve graphically, iii) use a spreadsheet.

i) Guess ‘n check. Here are some screen shots to illustrate:

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Notice that somewhere between the 4th and 5th years, the total cost for the Prius becomes less than that for the Corolla. By doing this guess ‘n check some students saw how we could generalize this. Let x represent the number of years, then the total cost, y, for each car could be described with an equation. A smooth transition to part ii.

ii) The equation for the total cost for the Prius is  y = 1099.88x + 27295.20. The equation for the total cost for the Corolla is y = 1496.83x + 25413.12.

This is a great opportunity for discussing what the y-intercepts are for each equation and what it means in the problem situation. Another great opportunity is to discuss what the slope is for each equation and what it means in the problem situation. Emphasize that 1099.88 means dollars for gas per year.

What to do with these two equations to solve the problem? Options: solve algebraically by setting each left side equal to one another. Or we could solve graphically. Let’s look at the graphical solution. Students will need to decide upon a good window and that requires them to think of domain and range (without using those actual words). Let them discuss and try different windows. Below is one possible window with both equations graphed:

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NOTE: Make sure the Graph Settings are set to Fix 2, otherwise the numbers will be in scientific notation.

Now find the intersection point. But more importantly, make sure the students can explain what the numbers in the ordered pair mean in terms of the problem situation.

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x = 4.75 means 4.75 years, that is, at 4 and 3/4 years, the cost of the car plus the gas costs will be the same, $32,523.29. Before that time, the Corolla is less expensive, and after that the Prius is less expensive. The longer we have the Prius after 4.75 years, the more money we save in gas costs.

iii)  Use a spreadsheet (optional). This is a good way to introduce the power of spreadsheets like Excel. (The TI-Nspire file will be included with all the materials.) A couple of screen shots are shown below with explanations of how they could be used.

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The top screen shot shows the data that is known. The bottom screen shot shows the calculations that were made. As you can see, the cost for the Prius is much more after one year. One of the powers of the spreadsheet is that it generalizes what we did so that if we wanted to compare other cars, we could easily do so. We can also quickly evaluate and compare each car at different numbers of years. See the screen shots for years 3, 4, and 5 below.

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Notice that in year 5, the cost of the Prius is less than that of the Corolla. Let’s look at 4.75 years:

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Notice that the cost for each car is not exactly equal. We would need to discuss why, that is, that the point of intersection was not exactly at x = 4.75, but that x is rounded to the nearest hundredth, and that is why the costs are about a dollar off from being equal.

Link to dropbox folder with all the files

Student work:

Student_work_TrentStudent_work_Sam

 

 

 

 

 

 

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