Best+Practices

media type="custom" key="18531846"
 * Type of Activity**: Product Claim Verification
 * Concepts/Skills Addressed**: Graph Reading, Investigation, Experiment Design, Laws of Cooling
 * Materials Needed**: Nspire Calculator, Vernier Temperature Probe, Thermal Coffee Mug, Hot Water (and video camera if you can't/don't want to heat up water in class).
 * Time Required**: 1 - 2 class periods, and time for data collection (at least 6 hours).
 * Submitted by**: Tony Alteparmakian
 * Adapted from**: Me...I'm a coffee junkie. :) I found the link to the Joulies from a coffee website I visit.


 * Extension**: Which method works better? Are the Joulies (see video below) really worth the money, especially compared to the coffee mug? This would be a great activity to do in conunction with a science teacher who could do an activity explaining how the heat transfer principles work.
 * Concepts/Skills**: Same as above
 * Materials Needed**: Joulies ($50)
 * Time Required**: Additional 1 class period.

media type="custom" key="18851658"


 * Description of Activity**: Show the students the picture of the mug along with the price and the video of the Joulies along with the price. Ask them what questions come to mind. Allow them to make guesses about the answers to their questions. Then, ask them to figure out how they can answer the questions for themselves. Let them design an experiement and guide them throug the process. Work in small groups here is preferred. Some considerations might be how many data points do we collect, how do we collect it, what is the definition of "hot" and "cold."


 * Type of Activity**: Intro to Systems of Equations
 * Concept/Skills Addressed**: Solving systems of equations (graphically and algebraically), scatter plots, regression lines
 * Materials Needed**: Article and graphs (links found below), digital projector.
 * Time Required**: At least two class periods.
 * Submitted by**: Tony Alteparmakian
 * Adapted from:** Me. I found the article on [|www.cultofmac.com]

[|The Web Is Dead - Wired Magazine Article]

[|Apps Set to Outsell Songs - CultofMac Article] [|(Original Article Link from Asymco)]

[|Apps Sales Pass Songs - CultofMac Article]

More Resources on my webpage

I typically start this activity by showing them the article, The Web is Dead, where the author claims that the internet is being accessed more and more by mobile devices/apps and less by desktop/computer browsers. I then show them "proof" found in the second article (referencing yet a third article) where a business analyst states that the revenue generated by apps will outpace the revenue generated by songs sold in iTunes within three years. The graph is perfect! it cuts off the intersection so students have to figure out why the analyst can figure that out from the graph. Following the link to my webpage provides you with the data courtesy of the author of the article. How far you want to take this depends on you and your students. You can enter the data in a spreadsheet, graph the scatter plot, take a guess at what the line of best fit might be, perform a linear regression using a calculator, talk about minimizing the sum of squares, and answer questions like, what does the slope mean here? what does the y-intercept mean?
 * Description of Activity**:

media type="custom" key="18531426"
 * Type of Activity**: Counting Sandwich Options (and helping their Marketing team)
 * Concepts/Skills Addressed**: Counting Options, Investigation, Pattern Creation and Recognition
 * Materials Needed**: Picture below, projector to display picture (optional).
 * Time Required**: 1 - 2 class periods.
 * Submitted by**: Tony Alteparmakian
 * Adapted from:** 101qs.com


 * Description of Activity**: I found this great picture on a website called 101qs.com, where users post mathematically thought provoking pictures and videos. I can picture a marketing team sitting together trying to figure out how many unique sandwiches that customers can order, but frustrated, they finally throw in the towel and insert the phrase.."and as you can see...a number of possibilities." So, let's help them out. How many sandwiches can you make? Let the students figure out the mathematical methods by starting small (2 cheeses, 3 meats, etc.), working their way up and looking for patterns.

Intro to Probability (with Binomial Distribution mixed in)
 * Submitted by**: Tony Alteparmakian
 * Adapted from:** Saw this idea at a workshop I attended a few years back. I don't remember the presenter's name.

media type="custom" key="18531458"
 * Type of Activity**: NFL Draft Sweepstakes!
 * Concepts/Skills Addressed**: Permutations, Counting, Probability, Expected Value, Number Sense, Pattern Finding
 * Materials Needed**: Digital projector, picture below, calculator.
 * Time Required**: 1 - 2 class periods.
 * Submitted by**: Tony Alteparmakian
 * Adapted from**: Me. I found it in an ESPN Magazine.
 * Description of Activity**: One of my favorite topics is probability and it seems as though students are naturally curious about how likely they are to win the lottery or other prizes. So I use a lot of activities like this that lets students explore possible answers and then be amazed when they find out just how difficult it is to win this prize, and why the backers of the sweepstakes probably aren't sweating a winner. Students with knowledge of the NFL (by the way, this is best suited for around the time of the draft which is in April) will likely start talking about who they think will go first, second, etc. They usually can't go further than pick 3 because of all of the possibilities. More than likely, a few students will offer different names. Ask the class how many different scenarios or sweepstakes tickets we could fill out. What would be the chance of getting it right if we guessed? Now let them find the answer by starting small (i.e. 5 people in the draft with 5 teams picking) and getting bigger, looking for patterns along the way that they can extend to 32 teams. Of course, there are more like 50 people that are good enough to get picked in the first round. How many more possibilities does that create? Have them develop the pattern for that scenario as well.

Even More Counting media type="custom" key="18531924"media type="custom" key="18531942"
 * Submitted by**: Tony Alteparmakian
 * Adapted from**: Dan Meyer (blog.mrmeyer.com)

Penny Pyramid (Patterns, Cubic, Law of Finite Differences, Summation, Quadratic) media type="custom" key="18531656"
 * Submitted by**: Tony Alteparmakian
 * Adapted from:** Dan Meyer (blog.mrmeyer.com)

Skeleton Tower (Patterns, Quadratic, Linear, Law of Finite Differences, Summation/Gauss) media type="custom" key="18531694"
 * Submitted by**: Tony Alteparmakian
 * Adapted from:** Me**.** I saw this problem for the first time in high school.


 * Type of Activity**: Cylinder Origami (Paper Folding)
 * Concepts/Skills Addressed**: Volume, Surface Area, Pattern Finding
 * Materials Needed**: Construction Paper, dried beans or rice
 * Time Required**: 20 mins - 1 class period.
 * Submitted by**: Tricia Neville
 * Adapted from:** Unknown

This activity is to teach the student how to calculate volume and surface area of a cylinder. This activity can be linked to history by discussing how the ancients may have measured volume.

Procedure:
 * Show students a piece of 8 ½” x 11” construction paper. Roll the piece of paper into a tall cylinder, then tape it. Roll a different piece of the same size construction paper into a shorter, wider cylinder. Ask the students which they think would hold more.


 * After breaking students into groups, give each group 2 pieces of construction paper of the same size. Have students measure the length and width of the construction paper to figure the surface area of the cylinder (excluding tops and bottoms). Ask students what we would need to add to get the complete surface area of a cylinder (what is missing from our constructions?)


 * Have each group make 2 cylinders from their construction papers; one tall and narrow and the other short and wide


 * Again, ask the students to think which of their 2 cylinders will hold more. Give some sort of dry good (such as beans or rice) to measure how many “cups” fit into each cylinder.


 * Have each group calculate the volumes of their cylinders (talk about what needs to be done to figure out the volume…V = Bh with B = Area of Base).


 * Ask students why one of the cylinders holds more even though the paper is the same.


 * Type of Activity**: Measuring Circles (Understanding Pi)
 * Concepts/Skills Addressed**: Measurement, pattern finding, circumference and diameter
 * Materials Needed**: Several round objects, measuring tape
 * Time Required**: 20 mins - 1 class period.
 * Submitted by**: Tricia Neville
 * Adapted from:** Unknown

Through this activity, students will be able to understand where the number pi came from.


 * Students will need to be in groups of 2. Each group will need a measuring tape, piece of paper, pencil, and hands. You may need to review how to use a measuring tape and how to get an accurate measurement from the tape


 * Teacher will need to bring in several different sized round objects to measure. I usually bring in candle holders, plastic lids or dishes that have a round edge. Students may also use anything they have in their backpacks that are round


 * Students are to measure 5 round objects. I have them set up the following chart as a guide”
 * Object || Circumference || diameter || Circumference/diameter ||


 * At the end of the activity, I have the students write down anything they notice about their chart…any similarities or differences or patterns they see.


 * They should notice that the last column’s numbers are around 3.14…which is pi.


 * Conclusion…pi = circumference/diameter. Now they should have a better understanding of the number pi

**Concepts/Skills Addressed**: critical thinking, word problem, analysis, comparing and contrasting Story: Penny Pincher saves money all the time. In other words, she is real careful with her spending. She finds a special bank account where it will **double** her money everyday. She deposits a “penny” (1 cent). Now her Uncle Buck does not trust banks. So he puts his money under his mattress. Uncle Buck is a gambler so everyday upon his return (his a successful gambler) he puts $1,000 under his mattress. These two have an argument as to who can save the most money in 30 days. Students: 1. Guess who will save the most money. 2. Compute what each person saves. 3. Are you surprised with the results? 4. How many days was it before Penny had more money than Buck? (Day 23) 5. What would Uncle Buck need to save each day to have the same amount as Penny? ($178,956.97) Present questions 1 and 2 first. Then questions 3, 4, and 5. Try this without a calculator (until it gets frustrating). This lesson is from a CPM course that was taught at one time in the district. This is a fun activity for Foundation or Algebra students.
 * Type of Activity**: Penny Pincher and Uncle Buck
 * Materials**: Calculator (optional)
 * Time Required**: 1 day
 * Submitted by**: Diane Lunsford
 * Adapted from**: CPM

**Concepts/Skills Addressed**: Order of Operations, Factorials, Radicals
 * Type of Activity**: Four Fours
 * Materials**: Calculator (optional)
 * Time Required**: Multiple Days (Warmups?)
 * Submitted by**: Diane Lunsford
 * Adapted from**: Historical Connections in Mathematics

My lesson is called “Four Fours.” Using exactly 4-fours create, the numbers from 1-50. You can add, subtract, multiply, divide, use square roots, use factorial, and grouping symbols. The only ones that I have been unable to do are the numbers 31, 33, 37, 39, 41. Example: 3 = (4 + 4 + 4) ÷ 4 35 = 44 ÷ 4 + 4! (some leeway with this number) This lesson is an extension of an activity found in Historical Connections in Mathematics. Order of Operations is the concept. Discussion is needed on radicals and factorials. Have the students fold a piece of notebook paper (Hot Dog style) and number 1-25 on the left side and 26-50 on the right side. The students can start wherever they would like. Give them a few examples, give them the rules (only 4’s and exactly 4-fours), discuss square roots and factorial. Work on it in class and then continue this assignment for homework.

**Concepts/Skills Addressed**: Graphing, Statistical Regression
 * Type of Activity**: Usain Bolt - 100m Race Analysis
 * Materials**: Graphing Calculator
 * Time Required**: 1 - 2 days
 * Submitted by**: Doina Apperti
 * Adapted from**: International Baccalaureate Math