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* *Reflection: Intrinsic Motivation
Little Bears Vest - A lesson on Symmetry - Section 1: Warm Up

This warm up proved to be so fun and led to GREAT class discussion. I had intended to really review fractional parts of shapes in order for students to find the fractional monetary amount of each shape, but the discussion ended up being way more than that!

Immediatly after the video, a student said something like "yeah, like a circle has 360 lines of symmetry because it has 360 degrees." Another student then responded and said, "acutally it would be more like 180 lines of symmetry because of the half circle." Several more students added to the conversation, either agreeing with the intial statement or the 180 degree statement. At this point, I put a part of a protractor under the document camera and zoomed in very large. Then I simply asked, "do you think it's possible there are lines of symmetry between the one degree marks?"

Then, what happened was amazing. My students became a buzz of talking and thinking. It was so exciting to see them. They did not come to the conclusion that there are in fact infinite lines of symmetry, but they were very close. I was SO proud of them and thought about how far they've come in their mathematical thinking and communication since the beginning of their fourth grade year.

The conversation gave students a chance to reason about lines of symmetry and begin to discover that a circle has an an infinite number of lines of symmetry. Even though the concept of an infinite number of lines is fairly abstract, fourth graders can understand infinity in an informal way. Just as there is always a fraction between any two fractions on the number line, there is always another line through the center of the circle "between" any two lines through the center of the circle. So if you identify a certain number of lines, you can argue that there is always at least one more.

You hear more thoughts in my reflection video.

*How many lines of symmetry in a circle?*

*Intrinsic Motivation: How many lines of symmetry in a circle?*

# Little Bears Vest - A lesson on Symmetry

Lesson 11 of 11

## Objective: SWBAT identify lines of symmetry and solve problems involving money and fractional parts of shapes.

#### Warm Up

*7 min*

I begin this warm up by showing the video below. I fast forward past the clip that says "symmetry in nature" and instruct my students to watch the video and think about what is the SAME about each image. (Students have all had prior experience with symmetry through a daily computer math skills program as well as through art lessons in third and fourth grade). Most of my students right away identified that the objects had lines of symmetry.

After this video, I lead a discussion about what students noticed that was the same about all photos. (symmetrical, circular components are two of the things my students said.) I then lead students to a definition of symmetry and a line of symmetry.

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#### Application

*50 min*

For this lesson, I wanted to design an authentic and rich task that students could work on that involves symmetry. Most of my students have had prior experiences this year as well as years before with symmetry, especially in the area of art. I wanted to give them a real purpose for understanding and using symmetry. I happened upon this resource (I have used the NYC DOE resources in the past). This lesson is adapted and created from a task located on page 47 of the resource. -NYCDOE_G4_Math_

Before I show students the problem, I give them about 2 minutes and 12 seconds to "play" with the blocks and build something they like. (Note: the odd time is a strategy I use to get students attention. They are used to hearing things like, "just a second, I'll be there in one minute, so I find that using odd time limits help keep them focused and remembering they have just short amount of time)

I pass blocks out to each table. Students have more blocks than the problem requires. After the two minute time frame, I then display the Little Bear problem under the document camera and read through the problem with students. (the little bear problem is located on page 47 of the resource) In summary, the problem states that students must create a symmetrical design that has a value of $4.00. They are given the information that the small green triangle is 10 cents. Students must then find the value of the other pattern blocks because they are proportional to the green block.

Before students begin, I ask students to tell me what is important about this problem to ensure that students fully understand the task. Students then have about a half an hour to solve the problem and show ALL their mathematical thinking. I do clarify that in order to show ALL their thinking, students need to use WORDS, PICTURES, and NUMBERS.

Listen in as this student works to find what each block is worth.

In this video you can hear a student's misconception and my strategy for redirection.

This is an excellent example of student's symmetrical design for Little Bear. You can see the student kept track of his/her total to the left as well as kept track of how many of each kind of block used. The students work is organized and somewhat linear in thought. I can tell from previous experience with this student that she/he first identified the value of each block. You can see this on the paper in the upper left corner. The student has also identified that his/her design has two lines of symmetry.

In this photo, you can see another approach. This student found out what two of everything would cost and then continued to add on from there. You can also tell that this student is doing either addition or multiplication in his/her head when keeping a running total. Note on the left side the running total. The student does not need to add 30 cents twice, he is able to see he's added 2 of the trapezoids and adds 60 cents to his total.

You can see this students strategy (below) is similar to the above example. He/she first found what two of everything would cost and then built of from there.

#### Resources

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#### Wrap Up

*10 min*

An important part of this lesson is this wrap up. Students participate in a gallery walk for the conclusion of this lesson. As students move around table, I ask them to look for lines of symmetry and strategies. Students are directed to look for similarities between their work and classmates work as well as looking at the various designs. I also participate in the gallery walk and serve as a model about what students should be doing. (If I had more time, I would have like to have students be able to ask questions or comment on student work via sticky notes)

For students, Gallery Walks are a chance to read and look at different solutions and provide oral and written feedback to improve the clarity and precision of students' solutions. For me, it is a chance to determine the range of mathematics evident in the different solutions and to hear students’ responses to their classmate’s mathematical thinking. This assessment for learning (formative assessment) data helps me determine points of emphasis, elaboration and clarification for the benefit of the whole class discussion

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- UNIT 1: Getting to Know You- First Days of School
- UNIT 2: Multiplication with Whole Numbers
- UNIT 3: Place Value
- UNIT 4: Understanding Division and Remainders
- UNIT 5: Operations with Fractions
- UNIT 6: Fraction Equivalents and Ordering Fractions
- UNIT 7: Division with Whole Numbers
- UNIT 8: Place value
- UNIT 9: Geometry
- UNIT 10: Measurment
- UNIT 11: Fractions and Decimals

- LESSON 1: Angle and line art
- LESSON 2: Rainbow of Angles!
- LESSON 3: Angles and Pattern Blocks
- LESSON 4: Practice with Protractors
- LESSON 5: Mini Golf Mystery - Using a Protractor
- LESSON 6: Math and Art Collide - Using Protractors
- LESSON 7: Drawing Angles
- LESSON 8: Clay Creations - Modeling Angles
- LESSON 9: Adding up Angles
- LESSON 10: Angle Assessment
- LESSON 11: Little Bears Vest - A lesson on Symmetry