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°.
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.
Press ‘Answer’ to reveal a possible solution.
Press ‘Answer’ to reveal a possible solution.
Press ‘Answer’ to reveal a possible solution.
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 A Benchmark: (Blank) Estimate: (Blank) |
Angle B Benchmark: (Blank) Estimate: (Blank) |
Angle C Benchmark: (Blank) Estimate: (Blank) |
Angle D Benchmark: (Blank) Estimate: (Blank) |
Angle E Benchmark: (Blank) Estimate: (Blank) |
Angle F 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.