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* *Reflection: Connection to Prior Knowledge
Measurement and Symmetry - Section 1: Warm Up

We are not teaching in a vacuum. Our students come to us with an array of prior knowledge. Some of that knowledge students are very aware of and use regularly. Other knowledge is there but may need to be retrieved or called upon.

The term symmetry is one that was presented in first grade but has probably not been used since then. Students need to be reminded of this prior learning. I could just say, "you learned about symmetry last year and we are going to work more with it today," but instead I give examples and see if students can make the connections themselves. My job is to build the bridge and see if students can cross that bridge on their own. If they make the connection, it will be more lasting for them than if I just tell them of the connection and they hear it and forget it.

I realize that the term symmetry is not in the second grade Common Core standards, but it is a term that is often used in math curriculums and standardized tests and so I have introduced it here. The lesson could just stress the measurement aspect and still have the students design something that is the same on 2 sides of a center line using the idea of a mirror image, but because the term does come in standardized tests, I believe that introducing it here is appropriate.

*Drawing on Past Knowledge*

*Connection to Prior Knowledge: Drawing on Past Knowledge*

# Measurement and Symmetry

Lesson 2 of 9

## Objective: SWBAT use measurement and symmetry to create a design.

#### Warm Up

*10 min*

Today I start by discussing how we measure an object and why we measure. We review why we would measure with a ruler, yard stick and a tape measure. Students recently used the tape measure so they should be familiar with the fact that it measures larger objects, or curvy objects. They should be aware that rulers are good for measuring smaller objects, but the purpose of the yardstick may be harder for students to understand.

Next I hand each student a square piece of paper (about 6 inches square). I ask them to fold it in half. It does not matter if they fold into 2 rectangles or 2 triangles because my purpose is for them to notice that the two sides of the fold are the same size and shape. I even mention to students to look around and see if everyone folded the paper the same way? Are both corner to corner and side to side ways to fold the paper in half?

Next I ask them to open it up. What do they notice about the paper on the 2 sides of the fold? They are the same. I ask students to refold the paper in half and then fold it in half again. We open the paper up and I repeat my question about what they notice about the paper on each side of the original fold? (Both are the same). I repeat this one more time.

I ask students if anyone knows what it is called when the two sides of something are exactly alike. I take suggestions and if no one remembers the word symmetry from first grade, I may give a hint such as the beginning sound. I also show that if I drew a line down the center of me the 2 halves would be exactly alike.

We discuss that symmetry means that 2 things are the same on either side of a line down the middle. I talk about how some things only have 1 line that will make them have 2 equal sides, but some shapes can have more than one line, and I ask for examples of things that are in the classroom that have symmetry.

I tell students that today we will be working with both symmetry and measurement to create a piece of wrapping paper (you could create any large drawing using these 2 ideas.)

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#### Teaching the Lesson

*10 min*

I show students a large blank white paper. I tell them that they will begin by folding the paper in half to create 2 sides that are 2 feet by 1 1/2 feet, and tracing the fold line. The paper I have chosen is rectangular and approximately 2 feet by 3 feet in size. The fold line will be their line of symmetry. They will use pre cut out leaves that are symmetrical, and their own drawings to create a symmetrical design on their paper. This means that if they want to put a picture on one side of the line, they would have to copy the picture on the other side. The resulting picture will be a reflective symmetrical design where there is a mirror image of the design on the left of the line with the design on the right side of the line.

I ask how they would know where to put the second picture? Hopefully one child will suggest using a ruler to measure the distance from the center line. If not, I will demonstrate how to measure from the line to my first drawing, and then how to measure from the line to the place for my second drawing.

We discuss how we might add additional drawings or cut outs using measurement to keep our design symmetrical.

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#### Independent Work

*30 min*

Students spread out around the room with their large paper, a ruler, and crayons, markers, cut outs, etc. I walked around to encourage students to use their rulers to maintain symmetry in their designs.

I remind students to measure carefully when they place something on one side of the line and then want the same thing on the other side of the line. This is a lesson where attending to precision is very important if the students want to create true symmetry (MP6).

In this case the students knew that the finished paper would be used to wrap a gift they had created in writing for a parent.

#### Resources

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Math Treasure Hunt
- LESSON 2: Measurement and Symmetry
- LESSON 3: Adding and Subtracting with Lengths
- LESSON 4: Working with Larger Numbers
- LESSON 5: Larger Distances
- LESSON 6: How Big Is A Foot?
- LESSON 7: Bigger Than A Foot
- LESSON 8: Centimeters and Inches
- LESSON 9: Measuring in Centimeters