2/2/2016 1 Comment Segment Addition Postulate
I prepped this by cutting a bunch of straws all in the same place. That way, I could just swap out colored sets so that each table had this:
For something this quick, I like to keep it as a full-class guided inquiry. Just say "Without measuring, I can tell you you may assume that both of these new "straws" are the same length. Now what if I told you that the yellow and blue pieces are also the same length? What could you conclude about the green and pink pieces. Why?"
Give some time. Allow them to discuss with a partner. Yes, it's obvious, but require each pair to come up with a very clear explanation of WHY. Then, have them write it out (just in a notebook or on scrap paper for something like this). It only takes a minute, and does not require a formal worksheet. When students think they have a great explanation, allow them to share it out loud with the class. This is a great opportunity to zero in on properties and vocabulary. I'm a big stickler on this. It is so crucial that students do not write that the pink piece is "equal to" the green one. I also do not allow explanations that say "the yellow piece plus the pink piece." Students must say that "the length of the yellow piece plus the length of the pink..." I always feel like I cannot possibly over-reinforce the fact that measurements can be equal, whereas segments are congruent. Otherwise, when we lead into proof writing, I see angles being added instead of angle MEASURES being added. I like to show this slide to clarify that over and over! (Check out proof writing in more detail here.)
Once they really tweak and perfect the explanations, develop an official postulate together and clarify that now they can use this new "Segment Addition Postulate" to justify steps.
The key to the guided inquiry process is that the students have noticed the properties that are at play here, and they explore it enough to write their own postulate. It's hard to hold back, but don't be tempted to feed the postulate to them. They'll get there eventually as you slowly help them revise their "explanations." Next phase: Tell a story! I like to tell the students stories about real-life projects, so for this one I chose to use a bench that my husband and I just built. Feel free to steal my story (I stretched the facts to make the math situation work anyway, but I willingly admit it). And project or display my bench pictures as your sample if you want! "We were assembling this lovely bench at my parents' house, 3 hours away, because that's where all the good tools were. So it was sitting there on the garage floor covered in wet paint until our next road trip to go pick it up. I wanted to put it in my daughter's room when we brought it back home. I was getting all the furniture moved around in her room, and making space for it. I was wondering if I could fit it under the window, when suddenly I realized I had forgotten to measure it! We did not follow any particular plan to know the exact dimensions! However, I had taken a photo of our hard work, and I knew that we had used 2x4s for the legs. (Explain that 2x4s are actually only 3.5 inches wide.) I remembered cutting the bottom front faces to 14 inches each. Can I figure out how long the whole bench is?"
Of course, they will be able to handle this math. They could have answered the problem in 4th grade. Make sure to then lead into variables and replace each 3.5 with an x, and each 14 with a y. Then show the next picture, and ask them to write an equation that's more complicated. Try taking out different missing pieces of information. Ask them if they knew the full length, how could they find one piece? This will lead into sample problems. Have students set up an equation for only AD, then for AE, etc.
Wrap it up by going back to the straws. Now, give them measurements for each segment (as expressions with variables!) and ask them to write an expression representing the length of all 4 of the pieces lined up as one long segment.
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Doing this effectively is going to be really easy, because we have done all the work for you! The "Spiral Studies" team is a group of 4 teachers from different subject areas working together to integrate curriculum seamlessly (Read more about the team below).
We think that one of the most important tips is to keep a focus on why you are incorporating a team building day or lesson into your curriculum. The goals listed here are what we feel are most important in each individual subject during a team building lesson. WHY
The goal of any community-building activity in the middle grades should be more than just getting to know one another. In fact, it should even go beyond trusting and respecting one another. Trust and teamwork is obviously important, but there is so much more that you can do with this type of activity.
Make your team-building exercise a learning experience that sets expectations for all cooperative learning for the rest of the year! Our team decided to target an essential question across the 4 major subject areas: "What does a team player look like in______ class?" We incorporated the most important skills that we want kids to have within each specific classroom. Collaboration in math class has a different look than collaboration in English class, and we wanted our team building day to reflect that. As a math teacher, I want my students to know how to describe and discuss a problem solving approach. I want them to be able to reach out to another group when they get stuck. I want them to be able to explain their own strategies and try to understand a classmate's strategy. I want them to keep going when a problem seems impossible. I don't want them to give up when they get stuck. A Science teacher wants different results. In a lab, it is important for each team member to know their own lab role. We broke it all down and came up with the following "WHY" goals for the reason behind a solid team building day in each class: HOW
It is amazing to be able to meet all these goals in just one class period for each subject area! Here are some key tips for how we make it happen:
Here's the Best Part!
We created the full lessons for each subject area, including student printables and lesson plans. Each has one version of the bookmark, which requires students with different versions to work together to fill in the blanks! The entire integrated project has been built for your teaching team to try!
And it's all completely FREE! Click the images to download all four lessons. Meet the Team
Click the links to visit the blogs and learn more about the "Spiral Studies" team:
We hope that your students love these lessons, and that they help you teach the guidelines for collaboration that will work well in your classroom.
This set of activities is great for the first day of school, and also works really well on those weird last days before a break. You can really insert this in anywhere you want throughout the school year. Please let us know what you think! You may also like...
I also find that sometimes students (or math clubs) are interested in this type of thing just for fun!
There are just so many uses for a good article that feels relevant to teens. Just have them read and summarize for a quick no-prep assignment. Choose a few that are appropriate for your students - I've included a few notes about what level each article is, so you do not have to browse through every one. The Math Equations that Determine the Fate of Refugees
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I hope your students enjoy these! I have so much fun collecting links like this, and am always looking for more. Feel free to share additional articles that you have found in the comments, so we can keep our collection growing!
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