Warm-ups in the Math Class

My first question about warm-ups is why are they used primarily in math and not other subjects? I think they can be very effective to get your mind thinking in the mode of the class. Writing classes I think could benefit from this especially creative writing or poetry. In math it serves to get students to focus and think mathematically. It can also have a calming or focusing effect for students who are coming in from lunch or from other frantic activities. It can also be a sort of brainstorm activity instead of the common questions. A quick chat within small groups about yesterdays lesson serves to refresh the previous lesson. It can also be a recap by the teacher, specifically about the expectations you have of them or the direction your unit is headed. This would help keep students on track after maybe the third or fourth day on the same subject. They could also be used to take the "temperature" of the class and to determine if students are following along. Except for a very informal formative assessment I don't think this is very practical because you would have set aside grading time for each warm-up and track every piece of paper turned in. 

Middle School Geometry Standards

The standards from the three different organizations are fairly similar with a few being more specific and others being more general. For instance the Common Core Standards ask a student to be able to draw a geometric shape and the NCTM standards call on a student to be able to analyze characteristics of shapes. The three standards together, in my opinion, cover almost every aspect of geometry and bring it down to a middle school level. Connected Math goes further to requiring specific vocabulary that students would know. My favorite standard is from the CC standards, 7.G.6. involves solving real-world problems involving two and three dimensional objects. This goes to the very heart of why we teach math, so that our students can solve real-world problems. 

My matrix of middle school geometry standards.

Appropriate Use of Technology

• Task 2-2:  Standards, standards everywhere.    

http://www.khanacademy.org/video/similar-triangles?playlist=Geometry 

This lesson defiantly addresses some of the standards for 7th grade geometry. It shows how to draw triangles and the unique properties of triangles including sum of all angles will equal 180 degrees. It also describes sizes, orientations and transformations of triangles and the properties of similar triangles and how similar triangles may be different sizes due to scaling but the angles remain the same. It also touches on rotational symmetry.

I think this was effective for refreshing my memory about similar triangles and would be a good demonstration to begin a class with. However I think that a better lesson would be one where 7th graders could follow along with. Giving them a hands-on opportunity to see how similar triangles interact. It also would need to build on previous knowledge about the properties of triangles. He is very clear and concise which makes him easy to understand and follow.

This technology does offer a way for students to access lessons from home if they have computers. It also would be available to parents who are trying to help their children with homework.

It does lack some sort of hands on element that I think is essential to this kind of lesson. Maybe different size similar triangle blocks or paper cut outs. I also would include rotational symmetry in more depth. Showing how the same triangle can be resized or rotated and still have the same angles. 

I would include a hands on element to this lesson. Blocks, paper cutouts or an online application would help to reach students who have a hard time following along or are tactile learners. I would also include examples for the real world such as the Eiffel Tower or bridges that use triangles to increase strength. There are also some really cool resources out their to illustrate geometric properties like this one from Wolfram (http://demonstrations.wolfram.com/GoldilocksAndThe3SimilarTriangles/).

The standard share a few harmonious similarities but are in some cases vague and disconnected. The NCTM Standards seemed very concrete. They are worded in a more real world situation and I can see connecting them to real life situation easier.