Minds On

Notice and wonder

Explore the following circles:

  • What do you notice about the circles? How are they divided?
  • What do you notice happens to the angles inside the circles?

There are 6 circles. The first circle is not divided by any lines. The next circle has been divided evenly in half. The line goes from the top of the circle to the bottom. The third circle is divided into thirds (three equal pieces). The fourth circle is divided into quarters (four equal pieces). The fifth circle is divided into fifths (five equal pieces). The last circle is divided into sixths (six equal pieces). As the circle is divided into more and more pieces, the pieces become smaller in size. Other than circle one and circle two, the other circles all have a central point where each piece meets.

Action

Benchmark angles

There are many important angles in math. We will study four of those important angles in this activity. These important angles are sometimes called benchmark angles.

  • An acute angle is an angle that is less than or smaller than a right angle (less than 90°).
  • A right angle resembles the corner of a square or rectangle and measures 90°.
  • A straight angle resembles a straight line and measures 180°.
  • An obtuse angle is larger than a right angle but smaller than a straight angle.

To think of it another way, an acute angle is less than 90°, a right angle is 90°, an obtuse angle is between 90° and 180°, and a straight angle is 180°.

4 different angles: an acute angle, a right angle, an obtuse angle, and straight angle

Task 1: Practice identifying angles

Using what we just learned about the four types of benchmark angles (acute angles, right angles, obtuse angles, and straight angles), answer the questions about the seven following angles. Record your answers using a method of your choice.

7 angles; Angle 1 is 180 degrees, Angle 2 is 90 degrees, Angle 3 is 25 degrees, Angle 4 is 105 degrees, Angle 5 is 30 degrees, Angle 6 is 135 degrees, and Angle 7 is 45 degrees.

Task 2: Estimating angles

Using the benchmark angles, we can estimate the measure of an angle. We will practice this skill with the following angles. Record your answers using a method of your choice.

Using a right angle as a benchmark, estimate the measure of this obtuse angle. An obtuse angle that is slightly larger than a 90 degree angle.

Press ‘Answer’ to reveal a possible solution.

Possible solution: If we were to draw a right angle on top of this one, we notice that this angle is just a little bit larger than the right angle. A good estimate for this angle might be anything between 95° and 105°.

Using a right angle as a benchmark, estimate the measure of this acute angle. An acute angle that is about half the size of a right angle.

Press ‘Answer’ to reveal a possible solution.

Possible solution: If we were to draw a right angle on top of this one, we notice that this angle is a fair bit smaller than the right angle. It almost looks like this angle is about half of a right angle. So, if we take 90° and divide it by 2 we would get 45°. A good estimate for this angle would be around 45°.

Using a straight angle as a benchmark, estimate the measure of this obtuse angle. An obtuse angle that is approximately halfway between a straight angle and right angle.

Press ‘Answer’ to reveal a possible solution.

Possible solution: If we were to draw a straight angle along the bottom line of this angle, we notice that this angle is a fair bit smaller than the straight angle. It almost looks like this angle is about halfway between a right angle and a straight angle. The difference between a straight and a right angle is 90°, so if we go halfway between 90° and 180°, we would be going 45° past 90°. A good estimate for this angle would be around 90° + 45° or around 135°.

Consolidation

Task 1: Independent practice

Match the correct size angle with the image and description. Record your answers in your notebook or a method of your choice.

Task 2: Which benchmark is it closest to?

Complete Angle Benchmark and Estimate in your notebook or using the following fillable and printable document. You can also use another method of your choice.

Decide which benchmark angle each of the following is best represented by: acute, right, obtuse, or straight. Then make an estimate of what you think the angle is.

Angle Benchmark and Estimate

Angle A

A pair of line segments that form an angle. The angle is not more than 90° and greater than 89°.

Benchmark: (Blank)

Estimate: (Blank)

Angle B

A pair of line segments that form an angle. The angle is greater than 90° and less than 180°.

Benchmark: (Blank)

Estimate: (Blank)

Angle C

A pair of line segments that form an angle. The angle is more than 0° and less than 90°.

Benchmark: (Blank)

Estimate: (Blank)

Angle D

A line segment that forms an angle. The angle is more than 90° and not less than 180°.

Benchmark: (Blank)

Estimate: (Blank)

Angle E

A pair of line segments that form an angle. The angle is more than 0° and less than 90°.

Benchmark: (Blank)

Estimate: (Blank)

Angle F

A line segment that forms an angle. The angle is more than 90° and not less than 180°.

Benchmark: (Blank)

Estimate: (Blank)

Press the ‘Activity’ button to access the Angle Benchmark and Estimate.

Once you have decided which benchmarks are most appropriate for each angle you may use the following Fill-in-the-Blanks to check your answers.

For each of the angles in the previous task, choose what size you think the angle is closest to. You may use the chart that was provided in task 2 to record your answers or a method of your choice

Once you have tried estimating the angle size on your own, you may use the following multiple choice activity to check your answers.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel…

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.