## Symmetry Made Accessible

**Tagged**axis of symmetry, Maria, Priovolou, reflect, reflection, symmetrical, symmetry, task analysis, Topmarks

Graphing linear functions and the underlying concept are challenging for many students. The video below shows a scaffolded approach to teaching how to graph. This approach also addresses the concept of the graph as a visual representation of all possible solutions (see photo above). Students often do not realize that the line is actually comprised of an infinite set of points which represent all the solutions. Here is a link to the document used in the video.

A Kahoot is an online and app quiz game that allows students to answer questions using a personal device (e.g. simulated phone in photo above). The teacher can create the questions (e.g. example question I created in photo above).

My approach is to use a Kahoot to scaffold learning. In this post I use plotting points as an example.

- I start with simple questions, e.g. identify the letter and number coordinates for the dog and chick below. Notice in the top photo below that I provide the actual coordinates in question 1 (“for the dog C4”) as a scaffold to show the students what to do.
- Then I show numeric coordinates for a point, but only with positive numbers.
- Eventually I present problems that address all 4 quadrants and ask questions about the parts of the coordinate plane (photo bottom one, below).
- Notice that the questions have times (in seconds). This indicates the time allotted to answer each question (teacher sets this). For students with special needs I print a hard copy to allow them more time to read the question. If necessary, they can respond by circling the answer on the handout.

This can be a game changer for students with special needs who struggle with math. The Desmos graphic calculator allows students to interact with math equations through multiple representations. It is far superior to graphing calculators in terms of quality and ease of use and is free. The app for Smartphones is outstanding.

Here are features that make this calculator user-friendly and an outstanding instructional strategy.

- Students can click on dots and the ordered pair will appear (see top photo below).
- Students can change features of the equation and immediately see how the graph changes.
- Students can collect data and create a graph and convert the data into “mathy” representations like equations (see top photo below).

Here’s a common word problem used for linear functions and equations (y=mx+b):

There are 6 inches of snow on the ground. Snow is falling at a rate of 2 inches per hour. Write a linear equation showing total snow as a function of time (in hours). The equation would be y=2x + 6.

Often the word problems like this are presented on a sheet of paper in isolation as an attempt to make the math relevant and to develop conceptual understanding. For students who have trouble with conceptual understanding, words on paper are likely too abstract or symbolic to allow applications like the one above to be meaningful.

The real life application is useful if presented more effectively. Here’s an approach to use the same scenario but in a more relevant and meaningful presentation. The photo above shows the current amount of snow – call it 6 inches. Students can be shown the photo to allow for a discussion about accumulation and for their estimates of the amount of snow shown. The photo below shows an excerpt from a storm warning. Showing this warning and a snow fall video can allow for a discussion about rate of snow fall and the purpose for storm warnings. Combined, this approach can lead into the above word problem.

Once the application is presented students can be asked to compute snow levels after 1 hour, 2 hours etc. Then they can be asked to determine how long it would take for the accumulation to reach 18 inches (the prediction for the day this post was composed). After computing the answers WITHOUT the equation the students can be shown how to use the equation – the “mathy way.”

Technology is often used as a support simply for the sake of using technology. Its use should be strategic. In the photo above is a do now/warm up/bell ringer for a 7th grade class that involves creating a bar graph. One student with autism struggled with the fine motor skills needed to draw graphs by hand (see a student artifact in the upper right corner of the photo). I taught him how to graph on Excel and he had a standing directive to use the classroom computer as necessary.

When he entered class and saw the warm up in the photo above he immediately went to the computer and created the graph seen in the photo below. The technology allowed him to access content he other wise would not access. (He also developed an important skill.) The technology served a strategic purpose.

My 5 year old son using Dragon Box to solve a proportion

Dragon Box (link to website here) presents solving equations, proportions (and fractions and expressions) using an alternative representation and in a highly engaging game format (different platforms!).

In the photo above, the goal is to get the treasure chest by itself. To do this, the fly looking thing and the snake have to be eliminated. First eliminate the snake with the black background (a night card) by placing the other snake card on top of it (a day card). The day card snake must be placed on the right side as well. The day and night card (representing positive and negative numbers) become a circulating hurricane looking card (which represents a zero).

I used it with my 5 year old son (video here) and he could solve 2 step equations (on the game) independently within a couple hours. This is a game changer in teaching kids algebra.

This is a screen shot from explorelearning’s Gizmos. This site has various simulations related to science and math. This one shows multiple reprsentations for a system of equations. The site has 5 minute test trials which can be used to present a topic in class. I used the one for photosynthesis for a 7th grader with asperger’s who was collecting data for his science fair project.

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