STEM 8 Math

Learning Intentions

Math

• Learn terminology related to naming triangles and angles
• Learn how to calculate percent error
  
• Learn how to measure angles with a protractor
  

Applied Skills

• Learn how to cut straight lines in paper with a boxcutter
• Learn how to measure angles with a protractor
  

Background Research

In this activity, we are going to be learning about the angles of a triangle, and associated terminology.

Please find the definition of the following terms:

• Acute angle
• Obtuse angle
• Right angle
• Extending: Reflex angle
• Isosceles triangle
• Equilateral triangle
• Scalene triangle
  

Equipment

• Boxcutter
• Hardboard cutting board
• Metal ruler
• Protractor
• White 8.5" x 11" printer paper
  
• Pencil
  

Instructions

Read through these instructions entirely before beginning so that you can lay out your paper properly.

On a single sheet of 8.5" x 11" white printer paper, using a straight edge, draw triangles matching the following descriptions:

1. 3 acute angles
2. 1 right angle and 2 acute angles
   
3. 1 obtuse angle and 2 acute angles

For an extension, also draw the following 3 triangles:

1. 3 equal acute angles
2. 1 right angle and 2 equal acute angles
3. 1 obtuse angle and 2 equal acute angles
   

On each of your triangles, draw a capital letter inside each angle. On the opposite side, draw the same lower-case letter. Every angle/side should have a unique letter.

Measure every angle and every side. Write the measurements in a list somewhere on the page with your triangles.

Take a picture of your page.

Using a metal straight edge, a boxcutter, and a sheet of hardboard (also known as high density fibreboard, or HDF), cut out each triangle.

Take a picture of the triangles.

Rip each triangle into 3 parts, such that each part contains 1 angle and half of 2 sides.

Lay out the angles on a line to show that the sum of the angles of a triangle is 180 degrees.

Take a picture of the angles.

When you are done taking your pictures, you can throw your paper in the recycling bin, and return your tools to their places.

To Submit

1. Your 3 pictures
2. What is the sum of the angles of each triangle, as measured using the protractor?
3. How much measurement error was there in the sums calculated in the previous question?
   
   
   
   

   	=	percent error
   	=	actual value observed
   	=	expected value

   
   
4. Look at the triangle with 1 obtuse angle and 2 acute angles. What relationship do you notice between the size of ∠x ("angle x") and the length of side X?
5. You are helping a grade 4 kid with their geometry homework, and they are having trouble with triangles. Please explain, at a 9-year-old-level, why it is impossible to make a triangle with:
1. 2 obtuse angles
2. 1 right angle and 1 obtuse angle
3. 2 right angles
6. Extension: You are using a thermometer to measure the temperature at which distilled water freezes, at 1 atm (atmosphere) of pressure and 20 °C. You observe that the thermometer reads -1.5 °C when the water begins to freeze. What percent measurement error is there in your temperature reading? How could you find the percent error?
   

Learn Some Science and Some Vancouver History

Temperature and pressure are very important when determining the state of matter (solid, liquid, gas, plasma, Bose-Einstein condensate, etc.). As a result, water boils at a lower temperature at the top of a mountain than it does at sea level. In Vancouver, there are 2 tall peaks that were originally named the Twin Sisters by Indigenous people in the area. The peaks are 1,646 m and 1,606 m above sea level, which means that water boils at around 95 °C at their peak.

Around 1890, John Hamilton Gray (a "Father of Confederation" who was forced to move to BC to become a judge) petitioned to have the Government of Canada officially refer to the Twin Sisters as The Lions, a decision influenced by the lion couchant of European heraldry and the lion statues erected in Trafalgar Square in 1863.

Triple Point of Water (1:54)

Assessment

	Pictures Submitted, Angles Measured	Measurement Error Calculated Properly	Easy-to-Understand Answers	Extension Questions
1. Beginning	✓	Some
2. Developing	✓	Most
3. Applying	✓	✓	Most	Some
4. Extending	✓	✓	✓	✓