Although we're trying to get through quite a bit of material before our state testing, we took some time today to explore triangles. I'm sure many of you may have done this exploration, but it was quick and fun, so I thought I'd share:) We explored the idea that the sum of the two smaller sides of a triangle must be greater than the longest side. I cut straws of three different lengths, and asked students (in groups) to use the straws to make a triangle.
In my first math class, I used straws that were cut to 2 inches, 3 inches, and 5 inches. These lengths, using straws, made it almost possible to make a triangle, even though it shouldn't have been possible. So, I had to insist that their straw ends be lined up perfectly. I wanted to use 3, 5 and 2 inches to show that even these dimensions won't make a triangle, because the sum is equal to the longest side, not longer than it. So, after understanding how precise they had to be and that they couldn't leave segment parts sticking out of the end of the triangle, they came to the conclusion that it couldn't be done. Next I gave the groups a new set of straws that were cut to 3 inches, 3 inches, 5 inches. In this case, they were excited to make their triangles in about 30 seconds! We then discussed why the 3, 2, 5 didn't work and worked our way to "creating" the rule.
For my next classes, I trimmed the 3 inch straws to 2 inches, so that my next classes would have more difficulty getting the ends to meet. It was so funny to hear their comments  "This doesn't work," "Is this a trick question?" "This is impossible!" And then, their excitement when they made the 3, 3, 5 triangle  "We did it first!"
For my next classes, I trimmed the 3 inch straws to 2 inches, so that my next classes would have more difficulty getting the ends to meet. It was so funny to hear their comments  "This doesn't work," "Is this a trick question?" "This is impossible!" And then, their excitement when they made the 3, 3, 5 triangle  "We did it first!" I think (hope!) that they understood the concept....we'll see tomorrow when we go over their homework:)
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As I was thinking about school today, I was thinking about one of our next topics: equivalent expressions.
(CCSS.6.EE.A3: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.) Last year, I worked this concept in through the use of my daily math warmups, which brought the idea back time and again, and the students did well with it. This year, even though we will spend more time with direct instruction, I was thinking about other ways to use equivalent expressions, and I thought of using them for partnering cards! Using the Partnering Cards They're very easy to use  determine the number of pairs of needed for the number of students you have and pass out that number of cards. Give students to a few minutes to factor or distribute to find an expression equivalent to the one on their card, and then set them loose to find their partner for your activity. My students did a great job with them when we used them:) The cards can be used many times throughout the year as partnering cards, for a quick, random reinforcement, so laminating them is a great idea. You can also use them for a quick matching activity. Grab for Free You can download these for free, if you'd like. There are 6 pages, with 3 sets on each page, giving you 18 sets (36 students). The set is in the download twice  once with a background and once without. I hope you can use them!
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