Learning Session 1 -Matchstick patterns Using matchsticks to create ...

Learning Session 1 -Matchstick patternsUsing matchsticks to create patterns, we can represent the pattern mathematically in differentways.How can we prove that the pattern we see in the matchsticks represents all possible matchstickshapes in that pattern? How you could prove to someone else that the pattern you see is thepattern that is there?1. The pattern of aliens:alien number 1 2 3number ofmatchsticks ______ ______ _______What relationship links the alien number to the number of matchsticks needed for that alien?How many ways could you represent that relationship?How could you convince someone that your representation represents all possible match aliens inthat pattern?One way of proving a pattern to exist is to look at the structure of the situation, by separating thediagram into the parts that are the same for every pattern and the parts that change as the patternnumber changes.We could draw the aliens like this:alien number 1 2 3The picture above shows that the alien head of five matchsticks stays the same for each alien, whilethe number of 3 matchstick body parts is the same as the alien number, so the pattern can berepresented by the equation Matchsticks = 3 × Alien number + 5 (using algebra we write m = 3 × a+ 5, where m represents the number of matchsticks and a represents the alien number). Is there adifferent equation we could use to represent the same pattern?2. Draw the matchstick patterns below in a way that shows the structure, and write an equation torepresent relationship between the pattern number and the number of matchsticks:Page 1

a.b.3. Draw pictures of a pentagon row pattern like the patterns above. Colour the pattern to showthe structure of the relationship between the pattern number and the number of matchsticks.Describe that relationship. Do the same for hexagons and heptagons.4. What if we wanted to describe the pattern for rows of any polygon? Can you write a generaldescription that will work for any polygon? You could use sides or s as a shortcut instead ofsaying “the number of sides in the polygon”.5. Colour the patterns below to show the structure of the relationship and describe therelationship between the pattern number and the number of matchsticks used.6. Make up your own matchstick pattern. Colour it to show the structure. Describe therelationship between the pattern number and the number of matchsticks used.7. Can you draw a matchstick pattern that uses subtraction instead of addition? What problemsmight you run into? In mathematics, you can indicate the pattern numbers that won’t work bysetting limits on the pattern numbers you can use for that pattern.Page 2