Geometry Concepts: 2-D Shapes October 18, 2013

Shape and Space is one of the four strands of mathematics that is part of the BC curriculum (indeed, part of the WNCP curriculum in Canada as well). In today’s session with grade 6 teachers in SD#60, we talked about using a set of 2-D shapes in lessons involving lines, angles, etc. I first came across the shape set in a text by John Van de Walle. After printing the shapes on coloured card stock, cutting them out, laminating them, and cutting them out again, I found they could be used over and over for a variety of activities at different grade levels. Note that when doing the activities students may have a full set of shapes or a partial set. (I had personally printed full sets of the shapes in four different colours and found that to be adequate for the activities that I did).

Ideas for using the set(s) of 2-D include (but are not limited to)…

• Have students randomly chose a shape and then describe it using as many mathematical words as they can (e.g., name the shape if it has a specific name, name kinds of angles, kinds of lines, number of vertices, etc)
• Have students each select any two shapes then tell what is the same and what is different about them.
• Have students place 4 of 5 shapes in a group, all having something in common. Other try to guess the “common rule”.
• Have students randomly pick three shapes and try to find something that is the same/different for all three.
• Sort the shapes using a single rule (e.g., those with/without an acute angle; those with/without a curve ; those that are/are not regular, etc.)
• Create a large two circle Venn diagram and sort the shapes according to two rules (e.g. sort by having parallel lines and having an obtuse angle)
• Ask students to find and hold up a shape with a particular feature that you name (e.g., an obtuse angle, two pairs of parallel lines; exactly one pair of parallel lines, etc.)
• Ask students to find and hold up a shape with two particular features that you name (e.g., a right triangle, a pentagon with three obtuse angles, etc.)
• Ask students to find all shapes that have two particular features
• Students play “Shape Find” by picking one shape that is in their set to be the mystery shape (it remains on the table); then other players must ask yes/no questions to eliminate all the other shapes until only the chosen one remains.

I hope you will print off one or more of the shape sets (as needed) and try some of these activities. And please, if you have other ideas to add to the list, I’d love it if you would share those with us.

Download the shape set template here.

Mathematically yours,

Carollee

PS: Thanks to all the grade 6 teachers who participated in today’s session here in SD#60. There was such a lot of positive math talk going on all afternoon!

Pi Day Approaches! March 12, 2012

Mathematicians tend to celebrate 3/14 as Pi Day in honour of the important relationship that exists between the circumference and diameter of any circle. Historians note that at least 2000 BC humans had noticed the constant ratio between these two parts of any circle, but it was not until 1706 that the notation using the Greek letter π was introduced by a man named William Jones.

This site http://www.educationworld.com/a_lesson/lesson/lesson335.shtml offers a whole host of ideas for exploring and celebrating Pi Day with students. Try singing this song (to the tune of Oh Christmas Tree) written by LaVern Christianson:

 

Oh Number PI

Oh, number Pi
Oh, number Pi
Your digits are unending,
Oh, number Pi
Oh, number Pi
No pattern are you sending.
You’re three point one four one five nine,
And even more if we had time,
Oh, number Pi
Oh, number Pi
For circle lengths unbending.

Oh, number Pi
Oh, number Pi
You are a number very sweet,
Oh, number Pi
Oh, number Pi
Your uses are so very neat.
There’s 2 Pi r and Pi r squared,
A half a circle and you’re there,
Oh, number Pi
Oh, number Pi
We know that Pi’s a tasty treat.

And here’s a quick video showing several approximations of pi: http://video.google.com/videoplay?docid=-6200593424291031420&hl=en

Have fun, and enjoy a slice of Pi!
Mathematically yours,
Carollee

Happy Pi Day! March 14, 2011

Math lovers note that March 14 (or 3/14) can be linked to the approximation for pi, which is 3.1415926535897… Pi is the ratio between the circumference of a circle and its diameter. This is true for any circle, any size, anywhere! It is a consistent ratio.

Helping students come to an understanding of this ratio can be done by collecting a number of items that are cylinders (cans of different sizes work great), and then measuring 1] across the top at the widest part (going through what would be the centre of the circle lid) and 2] around the circumference of the cylinder. A flexible measuring tape works best for the latter, but if you do not have one on hand, use a piece of string to mark the distance around the circle and then measure the length of string.

The various measurements can be recorded on a chart, and once the measuring is done, the dividing can begin. Each time the circumference measurement for a particular can is divided by its respective diameter measurement, the answer should be 3 and a bit (if not, recheck your measurements).

Using this information, the circumference of a circle can be found by multiplying the diameter times pi. If the radius of the circle is known, we double this to get the diameter, then multiply by pi. So another way to state the circumference of a circle is “pi times 2 times radius”. The length of a semicircle can be found by multiplying pi times the radius.
So, C = d x pi and C = 2r x pi.

Pi turns up regularly when we are measuring circles, and area is no exception. Students are often given the formula A=(pi)(r)(r) or “pi times radius squared” but we seldom stop to help them visualize what that might look like.

I am attaching a clip I found on the web that illustrates an activity that can be done with students to help them visualize the formula for the area of a circle. I have done this activity numerous times in the classroom, all to good effect! So get a paper circle, some scissors, a pencil, and have some fun with it!

Mathematically yours,
Carollee