The Angle Tangle

Summary

By the end of this activity students should be able to identify three types of angles, know that angles are measured in degrees, and be able to measure angles using protractors or angle rulers.

Materials

• 2 balls of yarn
• A-Z cards
• 12 angle cards
• Rulers
• Overhead projector
• Angle rulers
• Protractors
• Pattern blocks
• 360-degree Circle
• Whiteboards
• Dry erase markers
• 4" Angle manipulative
• Large angle manipulative
• Angle Assessment
• Crayons
• White art paper

Additional Resources

Media

• Find-the-Angle Pro Ruler: Item #FA-779 Lakeshore Elementary 2007-08 1-800-778-4456 http://www.lakeshorelearning.com
• AngLegs Item #DG205057TS Summit Learning 1-800-777-8817 summitlearning.com
• Basic Geometry Blackboard Topper. This is a chart to display in your room for a quick review of line concepts. (It includes lines, angles, polygons, and solid shapes) Summit Learning 1-800-777-8817 or online at www.summitlearning.com. Item Number DG20368ITS

Background for Teachers

Prior knowledge needed to complete this activity: Be able to identify parallel, intersecting, and perpendicular lines. By the end of this activity students should be able to identify:

Right angle: A 90-degree angle
Acute angle: An angle that is less than 90 degrees
Obtuse angle: An angle that is greater than 90 degrees
Know that angles are measured in degrees and develop benchmark angles (e.g. 45 degrees, 60 degrees, 120 degrees) and be able to measure angles using protractors or angle rulers.

Intended Learning Outcomes

5. Connect mathematical ideas within mathematics, to other disciplines, and to everyday experiences.
6. Represent mathematical ideas in a variety of ways.

Instructional Procedures

Invitation to Learn

Divide class into two groups. Have them stand arm length apart in a circle. Give each group a ball of yarn. Instruct them to pass the yarn to make a web. They may not pass the yarn to the person next to them; encourage them to pass across the circle as much as possible. Each child needs to hold onto the yarn and not let go. When they are all holding onto the yarn have them carefully lay their web down on the ground, stretching it slightly so the yarn is in straight lines.

Review parallel, intersecting, and perpendicular lines by finding them within the web. Have students identify the places where the lines intersect and mark them with points. Explain that when two lines meet together at one point we call that the VERTEX and that the lines, which are called rays, extending from the vertex form an ANGLE. Now look at the web to see if you can identify angles. Review how lines are named by points. Explain that angles are named using three points, with the vertex point always in the middle (ABC) and that we use this symbol < for angle. (Instructional Procedure

1. Classifying Angles (Right, acute, obtuse)

   Before the lesson prepare 12 angle cards. Use cardstock and draw one angle on each card--make 4 right angles, 4 acute angles, and 4 obtuse angles. Label the points and write the angle name (example: Place the angle cards on the board. Ask the class to carefully examine them and see if they can classify them into three groups. Have students come to board and move the angle cards into three groups. Continue working until students have correctly grouped them into right, acute, and obtuse angles. Write the name of each type of angle above the cards. Have class practice reading the names and identify the characteristics of each.

2. Identifying Angles

   Put students into small groups or partners. Give each group a set of pattern blocks.

   Tell them they need to look at each type of pattern block and identify the types of angles on each. Give each student a piece of art paper. Have them divide it into three sections labeled: Right Angle, Obtuse Angle, and Acute Angle. Have them trace the angles of the pattern blocks into the correct section.

3. Identifying Benchmark Angles using fraction circles

   Give each student a copy of the 360-degree Circle worksheet, which has been copied on cardstock.

   Discuss how a circle has 360 degrees. Link it to skateboard and snowboard tricks like the 180 and the 360. As you discuss each one have the students find it on their 360-degree Circle worksheet.

   If you divide a circle in half how many degrees to you have? 180. Have them jump and spin and try to land at 180 degrees. Now start at 0 degrees on your circle and trace your finger around to 180 degrees. What about a half of the half? That would be 90 degrees. Jump 90 degrees at a time and see if they can figure out the degrees--link it to the 9 times tables. So if you could jump all the way around you would be doing a 360!

   Have students put away their 360 degrees Circle paper so they cannot see it during the following activity. Give each student a piece of 9 x 12 art paper. Put students into partners and give each group a set of fraction circles cut out of foam board. You need to have a whole, halves, fourths, eighths, sixths, and thirds.

   Have students fold their art paper to make four boxes. Have them trace their whole circle in each of the boxes on the front and in two boxes on the back. (Total of 6 boxes)

   Work with students to identify the benchmark angles.

   Begin with the whole circle. Review how many degrees are in a complete circle. Write: "A whole circle has 360 degrees". Ask how much of the circle 180 degrees would be. Have them find the fraction pieces that would cover half the circle. In the second box have the students trace the halves onto the circle, write 180 degrees on the circle in the correct place, trace the 180-degree angle in crayon and shade it in. Above the circle write "180 degrees is half the circle." (You can also teach your students that this is called a straight angle)

   Note: As you do these fraction pieces make sure they lay the first fraction piece so its baseline is on the 0 degree line of the circle, this will form the angle correctly.

   Continue with 90 degrees. Remind them how far they had to jump. How could you relate 90 degrees to a fraction of your circle? Lay your fraction pieces on your circle and see which ones correspond to 90 degrees on the circle. Find the fractions that would make 90-degree angles. Trace the fourths, highlight the first one-fourth, and label 90 degrees on the circle and then above the circle write "90 degrees is 1/4 of the circle". As you work through the rest of these angles have the students compare them to the 90-degree angle to give them a reference point.

   Repeat for 45 degrees, 60 degrees, and 120 degrees.

4. Make an angle manipulative. Give each student two 1" x 6" strips of oaktag and a fastener.

   Draw a ray on each strip. Mark an endpoint on each ray, then put the strips together to form a vertex and put the fastener through them. Make a larger version for you to use to demonstrate on the board. Have them look at their fraction circle papers and try to reproduce the angles using their angle manipulatives.

5. Formative Assessment: Have students use whiteboards or white art paper and crayons. Example: Draw two angles, one 90 degrees and one 45 degrees, on the board or overhead. Instruct students to copy the 90-degree angle. Have them hold up their white boards or papers to check. Continue with other angle comparisons; include right, acute, and obtuse angles also.
6. Measuring Angles using an angle ruler or protractor

   Show students an angle ruler and a protractor; explain that these are the tools we use for measuring angles. Demonstrate how they work. Put students into partners and let them experiment with the tools. Draw different angles on the overhead and measure them. Have students draw and measure them with you. Have students use their angle manipulative. Have them work in partners. One student will make an angle using their manipulative; the other student will use the angle ruler or the protractor to measure the angle.

7. Play "What's Your Angle?"

   Draw angles on the board or overhead. Have students estimate and write down the angle's degrees. Then have students come up and measure. If their estimate is exactly correct they get 10 points. Deduct one point for every degree they are off--if they are one degree off they will get 9 points, continuing down to 9 degrees off they will get 1 point, 10 or more degrees off they will get 0 points. Variation: Play STOP! Use a large angle manipulative on the board. Tape the bottom ray so that it stays at 0 degrees. Identify the degree of angle you want to make. Choose a student to come to the front. Their job is to yell, "STOP" when they think you have made that degree of angle. They can solicit help from the other students. Move the other ray slowly (remember that angles are measured going counterclockwise) The student yells stop when they think you have reached the correct degree. Tape the ray down and measure the angle. Choose your "winner" criteria before starting. Example: They have to be within 5 degrees to win. If they win give them a small treat.

Extensions

• Struggling learners can be paired with more advanced learners
• Angle Tangle: Assign students to draw 5-7 straight lines with several intersections. Then connect the endpoints of the lines. Mark the angles created within in the design and color code them by right, acute, and obtuse angles. Color the rest of the design.
• String Art: Do a line design but give students string, oaktag, and safe plastic needles. Have them make the design using the string.
• Use AngLegs sets which include connecting pieces to form angles and a protractor that attaches to the pieces for independent practice in measuring angles.
• Integrating Technology: Take a digital camera and take your class on an "Angle Hunt". Have them identify angles in architecture, machines, nature, etc. Take photographs of the students and the angles. Use them to make a Power Point presentation.

Family Connections

• Have students enlist the help of their families to go on an "Angle Hunt" at their homes. Have them find and describe at least one example of each type of angle.

Assessment Plan

Use the Angle Assessment blackline as a final assessment.

Bibliography

John Sutton, J., Krueger, A., (2002). EdThoughts: What We Know About Mathematics Teaching and Learning, (92).

Brain research demonstrates that: the more senses used in instruction, the better learners will be able to remember, retrieve, and connect the information in their memories. Physical experiences or meaningful contexts can provide learners with strong blocks for building knowledge. Providing our students with many different types of activities will help them learn the concepts or skills we are presenting.

Marzano, R.J., Pickering, D., & Pollack, J.S. (2001). Classroom Instruction that Works: research based strategies for increasing student achievement. ASCD, Alexandria, VA.

This text identifies instructional strategies most likely to lead to improved student learning. It looks at the research and theories behinds these strategies and gives suggestions for implementing in the classroom. One of the strategies discussed is kinesthetic activity that uses physical movement to generate an image of the knowledge in the learner's mind. Physically making things such as geometric shapes helps students connect terms and definitions to the actual things. Drawing pictures or symbols is also a powerful way to generate nonlinguistic representations in the mind.