Posts Tagged ‘mathematics’

Brief note: a time-out from art-related items to post an assignment for a Coursera class for assessment by peers.

Unit: Exponential Relationships

click for link to image

9th grade, but 8th graders are welcome!

Investigation 1: Exponential Growth

Welcome to our new unit in Connected Math, Exponential Relationships! We have five different investigations, and you will find yourself doing a lot of comparisons of exponential relationships with linear relationships. (Told you linear would never go away!) You can see an overview of the unit by clicking on the link above to see the parent information letter. DO NOT WAIT TO GET YOUR NEW UNIT BOOK from your district office – you don’t want to get behind!!

Here are two key pieces we will focus on:

• * Is the relationship between variables an example of exponential growth or decay? Why?
• • How can this relationship be detected in a table, graph, or equation? What is the growth factor?
• • What table, graph, or equation would model the data or the pattern in a graph relating the variables?
• • How could I answer questions about an exponential situation by studying a table, a graph, or an equation of the exponential relationship?
• • How does this exponential relationship compare to other relationships between variables I have studied?

(All of the above from Connected Math 2: Growing, Growing, Growing)

Stuck? Email: ***************@***************

Now to the fun stuff: Investigation 1

• You will need: scissors and a sheet of paper (regular paper is fine, and you might be happier with a blank sheet)
• Your journal for record-keeping, notes, and solving problems
• A new anchor chart for vocabulary on a separate page in your journal – use a stickie tab on the page for easy reference to it.
• [Reference for peer readers on anchor charts – http://www.julieballew.com/A_Literate_Life/Photos/Pages/Anchor_Charts.html. Students will have other samples, since what I use I cannot share publicly (only in a classroom/online teaching setting) because of proprietary agreement with past employer)].

(Students have experience with anchor charts, and throughout the online lessons, I will have links to the unit anchor charts.)

1. Read on page 5, 1.1 Making Ballots and complete the short experiment.

2. Answer questions in your journal from page 6. Remember to indicate the investigation, number of the problem, and use complete sentences!

3. Upload your problem to the dropbox by ____________ for feedback from Mrs. Moran. (This should take no more than 1 day.)

4. Begin working on homework problems for this investigation: Practice problems on page 11 – 18: Everyone do #1-14, and then 3 others of your choice. Everyone do #33 – 38. (Due at the end of the week.)

Stuck? Email: ***************@***************

5. Read on page 6, 1.2 Requesting a Reward and add the new vocabulary to your anchor chart for this unit.

6. Complete the “Getting Ready” on page 6 in your journal.

7. Complete problem 1.2 on page 7 in your journal. Remember to indicate the investigation, number of the problem, and use complete sentences!

8. Upload your problem to the dropbox by ____________ for feedback from Mrs. Moran. (This should take no more than 1 day.)

9. Continue working on homework problems for this investigation: Practice problems on page 11 – 18: Everyone do #1-14, and then 3 others of your choice. Everyone do #33 – 38. (Due at the end of the week.)

Stuck? Email: ***************@***************

10. Read on page 8, 1.3 Making a New Offer and add the new vocabulary to your anchor chart for this unit.

11. Answer questions from page 9 in your journal.  Remember to indicate the investigation, number of the problem, and use complete sentences!

12. Upload your problem to the dropbox by ____________ for feedback from Mrs. Moran. (This should take no more than o1 day.)

13. Check out this video and try experimenting with values. Think about what you notice and try and make a connection between the video and the investigation.

Stuck? Email: ***************@***************

 

14. Continue working on homework problems for this investigation: Practice problems on page 11 – 18: Everyone do #1-14, and then 3 others of your choice. Everyone do #33 – 38. (Due at the end of the week.)

15. Log onto the class discussion forum (*******************address) and complete two responses. a) What are you discovering so far about exponential growth? and b) what differences do you notice between linear and exponential growth? (Due by the end of the week.) (Rubric http://www.mtsu.edu/ltanditc/docs/Discussion_Board_Rubrics.pdf)

16. Check out this video and see about exponential growth in real-world examples. You might get a few ideas for your Mathematical Reflection.

17. Start your draft of your mathematical reflection on page 19.

18. Read page 10, 1.4 Getting Costs in Line.

19. Answer questions from page 10 in your journal.  Remember to indicate the investigation, number of the problem, and use complete sentences!

20. Upload your problem to the dropbox by ____________ for feedback from Mrs. Moran. (This should take no more than 1 day.)

21. Upload your homework problems to the dropbox by ___________ for feedback from Mrs. Moran. (Due end of the week.)

Extra video – if you want to dig a little deeper and are interested in growth in businesses –

22. Complete your mathematical reflection on page 19. Use your word processor to complete the assignment. Use complete sentences – FOLLOW THE RUBRIC you already use for these! This is due by the end of the week – allow yourself two days for draft and final copy.

23. Breath Deeply and congratulations! You’ve made a major start in understanding a very practical application of algebra!!!!

Deadlines:

Investigation 1.1 should be completed within a day.

Investigation 1.2 should be completed within a day

Investigation 1.3 should be completed within a day.

Investigation 1.4 should be completed within a day.

Homework Problems due  end of the first week.

Discussion forum responses due the end of the first week.

Mathematical Reflection due the end of the first week.

STATE STANDARDS:

• HS.F-LE.A.1a. Distinguish between situations that can be modeled with linear functions and with exponential functions.
• HS.F-LE.A.1b. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Mathematical Practice Standards:

• 1. Make sense of problems and persevere in solving them.
• 2. Reason abstractly and quantitatively.
• 3. Construct viable arguments and critique the reasoning of others.
• 4.Model with mathematics.
• 5.Use appropriate tools strategically.
• 6.Attend to precision.
• 7.Look for and make use of structure.
• 8.Look for and express regularity in repeated reasoning.

Copyright notice: all links are public domain and links are included by clicking on pictures. This unit is directly from Connected Math 2, published by Pearson. The conversion to an online format is the work of the instructor, Linda Moran, and cannot be reproduced without permission of the instructor.

Lots of items bookmarked and ready to show you. I so love all the things you can learn online – and all the places you can go!

First up, The Trouble with Bright Girls – being one, as well as teaching many of them, I can relate to this article. We need to be so careful of the messages we send.

“Researchers have uncovered the reason for this difference in how difficulty is interpreted, and it is simply this: more often than not, bright girls believe that their abilities are innate and unchangeable, while bright boys believe that they can develop ability through effort and practice.”

Animals playing around – gotta watch!

The art of Jim Dingilian – filling a bottle with smoke and creating art!

I’m always looking at business sites and mentoring opportunities for my own marketing. Came across Gary’s site and am thinking about buying the book as gifts for two friends looking to start small businesses. Check out Gary Bizzo – www.garybizzo.com.

Also in marketing, a new site I found on line for printing – looks like quality work, and they’re in Canada, which is great when I move to Vermont! PrintingPeach at http://printingpeach.com.

Absolutely LOVE this close-up of the creation of a Dior bag – amazing!

This next poster is really cool, even if you don’t understand all of it! Science and art together!!

10 Mathematical Equations that Changed the World – fascinating, again even if you don’t understand all the math.

You know I love math – The Magic of Fibonacci!

Once again, science, art and math – Dance on the Circle.

Till next time, enjoy the web!!

So I am not a video gamer. Couldn’t even master Pac-Man, and I hurt my wrist trying Frogger. Plus, I hate the amount of violence in video games. This week I discovered an article about a gun-free video game. Who knew? Called the Unfinished Swan, it has lots of elements of art within it. Fascinating.

“Ian Dallas was a comedy writer who cut his teeth at the Yale Record, then The Onion, before moving into TV and working on Comedy Central’s Drawn Together. But his plan was always to make video games. So he went to grad school and created a prototype for an unusual game wherein players are confronted with a white void of a world to which they give form by splattering paint around to reveal the objects and environment around them. ”

I’m finally working through all the cool things from Cool Hunting. Here’s a neat item from Vermont: Battenkill Brittle, gluten-free energy bars, and they look yummy.

Here’s a wonder of the world a lot of people don’t know about: The amazing Bay of Fundy in time-lapse.

Have trouble with deciding what colors look good together? Check out Design Seeds – a collection of pictures that have identified the color palette within. Lots of inspiration here.

From Origami Joel comes another very interesting paper artist, Matt Shlian. Absolutely beautiful!

The Biological Advantage of Being Awestruck – beautiful video from my friend Amethyst, who minored in the philosophy of science. It sounds like she did some incredibly interesting reading in those classes! I could take those classes now…..

This is an interesting blog from the Surface Design Association on feng shui for your studio. I need to reread this at lenght, and I also think I will investigate the books she mentions efore I look at repurposing the garage into a wet dye studio.

Jamie Ridler guides artists to authentic creative living. Here’s a post about learning from the Olympics that has some really good thoughts in it. Olympic Lessons for Non-Athletes – Or What I Learned from the Olympic Games.

If you are running a small business, hopefully you know about Handmadeology – an online collection of articles on all aspects of marketing. Some really great stuff here….and I say that even though I write a regular blog for them!

Finally, for all my math friends – Prime Number Patterns. I can SO see a bunch of quilts from this!!

Have a great week! Let me know what cool things you find on line.