Math Teachers at Play is a monthly blog carnival that compiles posts from several blogs under the theme of teaching math in unique and innovative ways. We’re thrilled to partner with them this edition and couldn’t help ourselves from including some interesting trivia and riddles centered on our edition number – Happy Number 86!
Happy Numbers are numbers whose digits are such that – when squared and added iteratively, the number 1 is reached. For example,
82 + 62 = 100
12 + 02 + 02 = 1
So 86 is a happy number!
Image Credit: Chris, Creative Commons License
An 86 Riddle
The Seattle Resident Painters Association has been hired to paint the numbers 1 through 86 on 86 apartments, how many times will they paint the number 8? How many times will they paint the number 6?
Pre-K and Elementary
A deck of cards offers endless possibilities of math play for the pre-K age group. Zeno’s (@Zeno_Math) contribution – the Number Staircase – is a great example of using cards to build number sense. In this game, move up the staircase by rearranging the cards in hand to get the largest possible number.
Learning to make the best use of the numbers at hand is a life skill. Zeno’s second contribution is a math game with an interesting title that encourages strategy and mental addition. In PIG, all that is required is a pair of dice and the attached game board and practicing mental addition is as easy as child’s play!
Fan Tan (Sevens)
Denise Gaskins over at Let’s Play Math (@letsplaymath) has shared a card game that builds math skills and offers fun for the whole family. Fan Tan is a folk game that is played around the world with several different variations. In one variation, make a ‘fan’ on either side of 7, and add to the cards in counting down order. First one to play all the cards in their hand wins!
“When was the last time you paused to appreciate the beauty and simplicity of our number system?” asks Mathematical Mom Alexandra Fradkin (@aofradkin). With an eye-opening discussion on what life would be like without a number system, Alexandra introduced her students to the ancient numeral system of cuneiform numbers, with the class writing their cuneiform calculations in clay!
Image Credit: Tom Magileri, Creative Commons License
Middle, High School and Beyond…
Using Pattern Blocks to Reason and Prove
Mike Jacobs (@msbjacobs) aka The Math Guy shares a hands-on activity to reinforce geometry principles in the 6th Grade classroom. The class estimated angles of pattern blocks, without using protractors, but with the use of reasoning skills. While the students got a hands-on feel for spatial geometry, Mike himself was reminded of the teaching philosophy – “Teach Less, Learn More.”
A given set of 7 numbers (2, 3, 12, 14, 15, 20 and 21) may be divided into two sets such that the product of each set is the same. What is that equal product? “Go on, have a go at it yourself” encourages Stephen Cavadino from cavmaths and when you’re ready, see his solution to the equal products puzzle.
Games about Viruses
We discovered this interesting article by Matthew Farber (@MatthewFarber) on MindShift that combines knowledge of current health scares – such as Ebola – with an emerging tool in the classroom – games – to teach students about the mathematics of communicable diseases. Predicting and estimating the rate of diseases that spread at exponential rates is critical to help prevent and stop its spread. Matthew discusses three games about viruses that have math at their core, but interconnect principles from economics and social health awareness.
Before you slice that grapefruit for breakfast, try to find its roots of unity! “On a whim, I decided to figure out the area of a spherical triangle using grapefruits and hair elastics in my geometry/topology class this semester rather than just walking through someone else’s version of the proof, ” shares Evelyn Lamb (@evelynjlamb). Her junior year math majors most certainly benefited from this creative exploration, and Evelyn states that the activity can be adapted to other age groups as well.
Image Credit: Steve Chihos, Creative Commons License
Factoid: 86 is equal to the sum of the numbers formed in calculating its multiplicative persistence, which is multiplying the digits, repeating with a product until a single digit is left. So for 86,
86 = (8 x 6 = 48) + (4 x 8 = 32) + (3 x 2 = 6).
General Math Education
Mathematical Habits of the Mind
Problem solving is the core of math. We found this article by Cindy Bryant (@learnbop), significant to all of us in the field of mathematics. She states that the preformed pathways of the mind can either hinder or help the way we solve problems. These habits “separate the “experienced” from the “inexperienced” problem solver.” Being aware of the way we approach problems can help both ourselves and our students to be effective problem solvers.
We believe that the most important skill every student needs is perseverance. We found this activity from Meg (@fourthgrstudio) who guides her students toward effective and independent problem solving, while holding true to the underlying principle of math perseverance. Regardless of age, perseverance in problem solving pays off especially in mathematics!
Factoid: 86 is the largest known number which as an exponent of 2 contains NO zeros!
286 = 77,371,252,455,336,267,181,195,264 (26 digits)
On to the 87th Edition!
That’s a wrap for 86! Next month, the 87th Math Teachers at Play Carnival will be hosted between June 22-26 at cavmaths. For lists of past and future carnivals, instructions on submitting, and answers to frequently asked questions, see the main Math Teachers at Play Carnival site.
We hope you enjoyed this feast of math activities! Please share with us how you enjoyed these activities with the budding mathematicians in your life!