In this Warm-up, students practice estimating a reasonable angle measurement, based on their knowledge of angles so far and their familiarity with clocks. Later in the unit, students will take a closer look at the angles in an analog clock and apply their understanding of angles to solve more sophisticated problems.
Launch
Groups of 2
Display the image.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
1 minute: partner discussion
Record responses.
Draw an arc to label the angle that measures and show the clockwise turn of the minute hand from the hour hand.
“Your estimate should show the size of this angle in degrees. If you need to, revise your estimate.”
As needed, record any revisions.
How many degrees is the angle formed by the long hand and the short hand of the clock?
Make an estimate that is:
too low
about right
too high
Student Response
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Advancing Student Thinking
Activity Synthesis
Consider asking:
“Is anyone’s estimate less than _____? Is anyone’s estimate greater than _____?”
“How did you go about making an estimate? How did you know that _____ must be too low and _____ must be too high?”
“Based on this discussion, does anyone want to revise their estimate?”
Consider revealing the actual measurement: .
Activity 1
Standards Alignment
Building On
Addressing
4.MD.C.6
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
In this activity, students follow directions for drawing lines, rays, and angles. To create angles precisely and as specified, students need to use a protractor and a ruler or straightedge (MP6).
Each step in the drawing process involves one or more decisions for students to make. In some cases, the resulting drawing will be the same.
For example, in the first question, students could use the protractors in different ways to create perpendicular lines.
Going from to
(outer set of numbers):
Going from to
(outer set of numbers):
Going from to
(inner set of numbers):
In other cases, the resulting drawings will vary, depending on the decisions made. For example, in the second question, students could choose to draw the first angle () above or below the given ray. When drawing the second angle (), they could choose to draw it inside the angle or adjacent to the angle (and choosing one side or the other)—in both cases, meeting the specifications. Similarly, when drawing the third angle (), students could choose to draw it adjacent to the other angles or with one or both of the other angles inside.
MLR8 Discussion Supports. Synthesis: Some students may benefit from the opportunity to rehearse with a partner what they will say before they share with the whole class. Advances: Speaking
Action and Expression: Develop Expression and Communication. Provide alternative options for expression. For example, invite students to work with a partner. One partner can draw as the other partner tells them what to do (for example, exactly how to move the protractor and where to draw points and lines). Supports accessibility for: Visual-Spatial Processing, Language, Fine Motor Skills
Launch
Groups of 2
Give each student a protractor and access to rulers or straightedges.
2 minutes: independent work time on the first question
Pause for class discussion. Ask 1–2 students to share how they drew their perpendicular lines.
Activity
5–6 minutes: independent work time on the remaining questions
2 minutes: partner discussion
Identify students with different-looking drawings to share later.
Draw a line that is neither vertical nor horizontal. Put a point somewhere on this line. Use your protractor to draw a perpendicular line through this point. Be as precise as possible. (No folding this time!)
Here is a ray that starts at point M.
Use a protractor to draw:
A ray starting at point M to create a angle.
Another ray starting at point M to create a angle.
One more ray starting at point M to create a angle. Label each angle with its measurement.
There is one angle that is not labeled with a measurement and is greater than . Label the angle with an arc. How many degrees is this angle? Explain how you know.
Activity Synthesis
Select students to share their drawings and their reasoning for the last question.
“What decisions did you have to make when creating the drawing?”
“Many of you placed the angle next to the angle. Some of you placed it inside the angle. Similarly, many of you placed the angle next to the angle or the angle. Some of you placed it with the angle and the angle inside. How did the different choices affect the size of the angle in the last question?” (Putting the angle inside the angle made the last, unlabeled angle larger. Putting the angle and the angle inside the angle made the last, unlabeled angle larger.)
Activity 2
Standards Alignment
Building On
Addressing
4.G.A.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
In the first activity, students drew angles with some scaffolding in place: a line and a point were given, each step was described, and the vertex and the measurements of each angle were specified.
In this activity, students continue to draw angles but with less guidance. For each drawing, students are given only a range of angle measurements and no other criteria, prompting them to make additional decisions about how to draw the angles (for instance, where to position the vertex of an angle, how to orient the first ray or line, and so on). After drawing, students trade their cards and use a protractor to measure and check one another’s angles.
The drawings created here will be used in the next lesson. Consider collecting the cards from each group or otherwise supporting students in keeping the cards until then.
Launch
Groups of 2
Give each student one protractor and 4 blank (unlined) index cards.
Give students access to rulers or straightedges.
Activity
7–8 minutes: independent work time on the first question, and then switch cards to complete the second set of questions
Your teacher will give you 4 blank cards. Label each card with a letter A–D.
On each labeled card, draw an angle that meets the requirement with the same letter. Use a ruler and a protractor.
an angle that is less than
an angle that is between and
an angle that is greater than but less than
an angle that is greater than but less than
Trade cards with your partner.
Record the angle measurement for each angle. Check to make sure each angle meets the requirement.
Have your partner correct the angle if it does not meet the requirement. Save the cards for the next lesson.
If you have time:
Create a drawing that shows several angles. Then write some descriptions about your drawing. Be as specific as possible.
Ask a partner to recreate the drawing, based on your descriptions. Does their drawing look like your drawing? If not, adjust your descriptions and ask them to try again.
Activity Synthesis
Invite students to share 1–2 examples of an angle that meets each requirement.
Consider asking:
“Can you tell just by looking that this angle is _____?”
“If you say yes, explain.”
“If you say no, what would you need to make sure it is _____?”
Lesson Synthesis
“Today we used protractors to draw angles of different sizes, and to check one another’s drawings.”
“What were some challenges in drawing angles precisely?” (The distance between the closest tick marks, showing a angle, is very small. It’s easy to misread the marks. If the first ray is not lined up correctly at or , or if the vertex is not lined up exactly at the center point of the protractor, then the created angle would be off.)
“In the last activity, you drew a bunch of angles, some smaller, some larger. Did you find some sizes of angles easier to draw than others? Why or why not?”
“If we were explaining to a partner how to use a protractor to measure angles, what should we say?”
Student Section Summary
We learned ways to describe and measure the size of an angle.
We described angles as a turn of one ray away from the other. We learned that a degree is a measure of the turn around a circle and that 1 degree is of a full turn of a ray through a circle.
Finally, we learned that a protractor is a tool used to measure angles that also can be used to create angles of a certain measure.
A protractor has two sets of numbers that can be used to measure an angle. We learned to use a protractor to measure and draw different angles.
Standards Alignment
Building On
Addressing
4.MD.C.5
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
