{"id":300,"date":"2016-09-22T01:37:06","date_gmt":"2016-09-22T01:37:06","guid":{"rendered":"http:\/\/newblog.primefactorisation.com\/2016\/09\/22\/zero\/"},"modified":"2024-11-02T15:02:43","modified_gmt":"2024-11-02T20:02:43","slug":"zero","status":"publish","type":"post","link":"https:\/\/www.primefactorisation.com\/blog\/2016\/09\/22\/zero\/","title":{"rendered":"ZERO!"},"content":{"rendered":"

I invented a new game for factoring quadratic trinomials over the summer break. After waiting to get to quadratics, I’m excited that this week I was finally able to play it with my Algebra 2 classes.<\/p>\n

As I was planning, I was thinking about how to motivate teaching factoring. In particular, I was inspired by Dan Meyer’s thoughts<\/a>, where he mentioned that locating zeroes is the key problem that factoring helps solve. I decided to find a way to make finding those zeroes the focus of how I introduced this topic.<\/p>\n

This game, which I’m calling “ZERO!” is about evaluating expressions and finding zeroes. Students are in groups of four, and each group receives a set of 36 cards with a range of expressions on them. Most are quadratic trinomials, but there are some linear expressions, quadratic binomials and a handful of factored quadratics.<\/p>\n

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As a warm-up, I had students each choose a card, which I required to be a quadratic trinomial. I gave them a value for x, and they evaluated their expression with that value on dry erase boards. They then checked their answers with a calculator. My students are only just getting to grips with the TI-84, so I showed them how to store the value in x to evaluate the expression. Then I gave them a couple more values for x, which they also evaluated with the same card and checked with their calculator.<\/p>\n

I asked if anyone got zero for any of the values of x, and a few students put their hands up. I revealed that this is the aim of the game – to get a card that evaluates to zero. The game works like this:<\/p>\n

    \n
  1. Each group turns all of their cards face up so everyone can see all the expressions. <\/li>\n
  2. Everyone chooses a card to place in front of themselves. <\/li>\n
  3. The teacher chooses a number randomly between -5 and 6 (inclusive). <\/li>\n
  4. Each student evaluates their expression with that number. I let them use their calculators so the game would go as quickly as possible, but I can see the benefits of having them do it by hand. <\/li>\n
  5. If a student gets zero, they shout “ZERO!”* and turn their card face down, scoring one point in the process. If multiple students in a team get zero, they still only get one point. <\/li>\n
  6. If a student scored, they replace their card for the next round. Other students can swap their card too, if they wish. <\/li>\n
  7. Most points win. I went with first to ten points, before revising it to six, but a time limit isn’t a bad idea either.<\/li>\n<\/ol>\n

    As we worked through the game, I started prompting students with questions about which cards are the best ones to choose, and which cards are easiest to evaluate. I was also asking kids which numbers they needed to come up for them to get zero.<\/p>\n

    Students started realizing that the quadratics were better than linears, because they have two different zeroes – mostly. There are a few quadratic cards with only one zero. I decided against choosing any expressions that couldn’t be factored, because I didn’t want a student to be stuck with a card they couldn’t get zero from.<\/p>\n

    They also slowly realized that it was best to have different zeroes for their cards than the rest of their team (which is why I only allow one point per team each round). Four cards means eight possible zeroes, which is a better than even chance when there are twelve possible values for x. Of course, knowing what those zeroes are is easier said than done.<\/p>\n

    Well, until they know how to factor, that is. \ud83d\ude09<\/p>\n

    To play this game, you’ll need the following:<\/p>\n