Is a Square a Rectangle?

We started another mini geometry unit today: square and rectangles.

First, we investigated characteristics of square and rectangles.  We decided:

Rectangles

• have four 90° angles
• opposite sides are the same length
• opposite sides are parallel

Squares

• have four 90° angles
• all four sides are the same length
• opposite sides are parallel (from which we deduced that the lines must be straight)
• is a rectangle

This last feature about squares brought this question forth:

The students discussed this and came up with some very valid answers.  They should good critical thinking skills and through debate and discussion were able to decipher that this statement is true and why it is so.

Using Tools to Make Perpendicular Lines

Yesterday students learned about parallel and perpendicular lines, and how to draw them.  The tool we chose to start with was a triangular ruler, that has a 90° angle incorporated in its structure.  This led us to today's goal:

With a bag of different measuring tools in front of them, students first choose the one we know and demonstrated how to use it to create perpendicular lines.  Then, from the remaining tools left on their desks they needed to choose on that they thought they could use to create perpendicular lines.

After some discussion, and trying out one tool which we deemed would not work to accurately create a perpendicular line, they decided that we could use a protractor to help us in this endeavour.  Through a class demonstration, the students agreed that indeed this would work.  So then we set out to practice creating perpendicular lines alternating between the two measuring tools.

Making Lines

Using triangle rulers, students practiced making parallel and perpendicular lines today.  It's nice to start with graph paper to help ensure that our lines are straight and that we do create 90° angles.  When we leave the graph paper, our triangle rulers will definitely help as will using a protractor.  It's amazing how previous unit concepts return to be applied again. ;)

Protractor Fun

Students are learning how to use a protractor to measure angles.  This can be a very tricky tool to use as it's important to place it on the angle you are measuring properly in order to get an accurate measurement.  Also, angles can be measured from the right or the left, hence a protractor has two sets of numbers.  We have to be very aware of which numbers to use, therefore applying our math thinking and knowledge of kinds of angles.

We are using protractors to both draw and measure angles.  Once we've gotten it, it doesn't seem so tricky anymore. :)  Thankfully Singapore Math has some wonderful online resources for us to use in the classroom.

Angles

Students were learning how to name angles today.  First we reviewed the different types of angles (right, obtuse, straight and acute) and then looked at how to name them using letters.  It's a tricky process, especially when we are looking at naming angles that are part of closed shapes, but the students have a good start!