I tried a new tact with systems of equations this year. I started with a card trick. Students choose two cards, then add and subtract the numbers. I quickly tell them which cards they have. We progress to larger numbers and even negative numbers before I explain the magic trick. For example, x + y = 12 and x - y = 2. Some students are able to use guess and check to solve which is fine for the simpler systems.
I borrowed an idea from the progressions documents and wrote 10 = 10 on the board. Below it I wrote 2 = 2. Then I had students think about adding the left sides and right sides of the equation to see if the value remained true. So, 12 = 12 is true. Students discovered it was true for addition, subtraction, multiplication, and division.
We took this idea and applied to x + y = 12 and x - y = 2. Students saw x + y + x - y = 12 + 2 or 2x = 14. So, x = 7 and substitution shows y = 5. We repeated this several times with systems using larger integers for x and y so students could not simply guess and check.
Then I borrowed a lesson from Yummy Math called Souvenirs and Concessions. I focused mainly on writing equations for the situations. This activity made it extremely easy for students to see how elimination with multiplication would work. For example, if 1 hat and 1 poster is $25, and 4 hats and 2 posters is $88, then the system can be written as 1h + 1p = 25 and 4h + 2p = 88. Students can try subtracting one equation but both variables remain. We think a bit and then realize that if 1 hat plus 1 poster is $25, then 2 hats plus 2 posters is $50. The students rewrite the equation and solve the system. Students seemed to have an easier time accepting that each term of an equation can be multiplied by any number and the value of the variables remain the same.
Then I used Scott Keltner's activity using Little Debbie's Oatmeal Creme Pies as inspiration and wrote my own activity using Oreos.
So, select this link (answer key now provided) to find everything you need to write a system using regular Oreos and the Triple Double Oreos. Yes, it is quite necessary to have enough Oreos to go around! It did help to have the Triple Doubles in the class for comparison so students could see the regulars had 2 wafers and 1 filling while the Triple Doubles had 3 wafers and 2 fillings.
I borrowed an idea from the progressions documents and wrote 10 = 10 on the board. Below it I wrote 2 = 2. Then I had students think about adding the left sides and right sides of the equation to see if the value remained true. So, 12 = 12 is true. Students discovered it was true for addition, subtraction, multiplication, and division.
We took this idea and applied to x + y = 12 and x - y = 2. Students saw x + y + x - y = 12 + 2 or 2x = 14. So, x = 7 and substitution shows y = 5. We repeated this several times with systems using larger integers for x and y so students could not simply guess and check.
Then I borrowed a lesson from Yummy Math called Souvenirs and Concessions. I focused mainly on writing equations for the situations. This activity made it extremely easy for students to see how elimination with multiplication would work. For example, if 1 hat and 1 poster is $25, and 4 hats and 2 posters is $88, then the system can be written as 1h + 1p = 25 and 4h + 2p = 88. Students can try subtracting one equation but both variables remain. We think a bit and then realize that if 1 hat plus 1 poster is $25, then 2 hats plus 2 posters is $50. The students rewrite the equation and solve the system. Students seemed to have an easier time accepting that each term of an equation can be multiplied by any number and the value of the variables remain the same.
Then I used Scott Keltner's activity using Little Debbie's Oatmeal Creme Pies as inspiration and wrote my own activity using Oreos.
So, select this link (answer key now provided) to find everything you need to write a system using regular Oreos and the Triple Double Oreos. Yes, it is quite necessary to have enough Oreos to go around! It did help to have the Triple Doubles in the class for comparison so students could see the regulars had 2 wafers and 1 filling while the Triple Doubles had 3 wafers and 2 fillings.
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