In an earlier lesson, students had folded paper and used supplemental tools to form and draw some benchmark angles (, , , and so on). In this activity, they apply their ability to measure and draw angles, with a protractor, to create a reasonably accurate clock face. The measuring and drawing here prepare students to reason about the angles formed by the hands of a clock in the next activity.

Students may notice that lines that give the positions of 1 and 2 on the clock can be extended through the center of the clock to give the positions of 7 and 8, respectively. Students, who use these observations to create the drawing, practice making use of structure (MP7).

The clock that students draw in this activity can be a helpful reference in the next activity.

• Display the incomplete clock face. Select students to share their completed drawing and their drawing process. Sequence the presentation in the order shown in the monitoring notes.
• “How did you find the size of the angle formed between the numbers 1 and 2?” (Divide 90 by 3, or divide 180 by 6, or divide 360 by 12.)
• “Is the angle formed by rays that point at any two consecutive numbers always ? How do you know?” (Yes, because the angle is always of 360.)

In grade 3, students learned to tell and write time to the nearest minute and to measure time intervals in minutes. They understand that moving from one number on the clock to the next means 5 minutes have elapsed. In this activity, students build on those understandings to solve problems about angles formed by the hands of a clock.

Many students would benefit from having a visual reference of a clock as they are solving these problems. Encourage them to use their clock drawing from the previous activity for support.

Some students may try to answer the questions by drawing each indicated time and then measuring the angles formed by the hands. Ask them to consider finding the size of the angles by reasoning, without measuring. For example, ask: “What do you know about the angle that is formed when a hand goes from 12 to 3? From 12 to 1?” This encourages students to use the structure of the clock and the equal parts into which the numbers divide the clock face (MP7).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

• Display a clock face. Invite students to share their responses to the first question and the last two.
• When discussing the first set of questions, highlight that the positions of the hour and minute hands produce two angles—a larger angle and a smaller angle. Once each hour, the hands form a straight angle, dividing the clock into two equal semicircles. Once each hour, the hands overlap each other, producing one angle.
• Likewise, when discussing the third question, if no students mentioned that there are two possible times that meet the described constraint, bring it up.
• “How did you find out the number of degrees the minute hand turns in 10 minutes and 1 minute?” (Ten minutes is twice 5 minutes, so it is twice , or . One minute is 10 minutes divided by 10, so it is divided by 10, which is .)