In this activity, students cut out nets and form three square pyramids. When taped together properly, these three square pyramids can be folded up to make a cube. The purpose of this activity is to illustrate that the volume of a pyramid is one-third the volume of the corresponding prism.
Nets and explanation in Word format: Pyramid Folding Activity
A great introduction to systems of measurement is to have students create their own. Ask students to create referents for measuring small things (like dimes), medium things (like the width of their desk), and large things (like the distance to the next town over). Students will likely use body parts as these referents, which is great, because they carry those referents with them wherever they go. It might be handy for them to know that the width of their finger is about 1 cm, the length of their leg is about 1 m, and so on.
You can give the students a sheet to track their invented system and compare it to SI and Imperial, which is likely where you are headed next in this unit. This is an example of such a sheet, in Word format. Referent Chart
David Cox created a GeoGebra applet to help students learn about x and y intercepts and posted it on his blog, calling it the un-lecture. Students work through a series of randomly generated equations of lines, and learn how to find x and y intercepts on their own.
His post describes the applet, includes a pre- and post-test great formative assessment tools), and explains what his applet is all about.
As an aside, I took David’s applet, and with a lot of his support was able to build my own that is similar, but says slightly different things. I learned a lot about scripting in GeoGebra by going through that. Here’s the one I built. John’s Variation.
This is a lesson I built as a demo during my travels. In it, I attempt to have students learn from each other, rather than from me writing everything on the board. The technique I am using is activating students as instructional resources. Right after I used this lesson, I described it in great detail on my blog.
Everything you need is in this word document: Multiplying Radicals Lesson
Have the students work through it in pairs. At various points, they are instructed to check in with other pairs. They will eventually create their own notes, and it concludes with an exit slip so you can see if they learned what they were supposed to learn.
This technique comes from Dylan Wiliam’s book “Embedded Formative Assessment“. I describe it it much more detail on my own blog.
I use this technique frequently in high school math classes. I plan and structure lessons in such a manner that students learn from each other, rather than from me. There are times when I have to step in, and then I step right back out and let them go.
Sometimes I print these lessons on worksheet-type things that the students work through. Sometimes I manage their learning without worksheets. In every case, though, I consciously plan opportunities for students to talk to each other and learn from each other.
Complete list of activities that activate students as instructional resources available on this blog.
The “row game” technique is explained in this post.
The link below will take you to a row game that Kate Nowak created for radical operations. It makes a great review, check for understanding, practice exercise, and formative assessment tool.
Radicals Row Game
Complete list of row games available on this site.
I first encountered row games on Kate Nowak’s blog. She later posted row games galore, where she collected even more of them from other sources in a box.com folder. Kate describes them as follows:
Make a worksheet of problems organized in two columns. Column A and column B. The tricky part is the pair of problems in each row has to have the same answer. Obviously some topics are more suited to this than others. (Solving linear systems, easy. SOHCAHTOA, easy. Graphing inequalities, hard.)
Pair up the kids. Decide who is A and who is B. Tell the kids to only do the problems in their column. When done, compare answers to each question number with their partner. And if they don’t get the same answer, work together to find the error. That last step is where the magic happens. I know how well I taught the topic by how busy I am while they are row gaming it up. (Sipping coffee: go, me. Running around like lettuce with its head cut off: self-recrimination time.)
This activity is much better than traditional worksheets and homework assignments for a number of reasons.
- Kids actually do it because they are accountable to each other.
- It’s great formative assessment. Notice where Kate mentions the data she gathers above.
- It can be differentiated by making one column slightly easier, and making sure your strugglers get that one.