PAIRS

Build Understanding

Turn and Talk How could you use a mirror, instead of folding the snowflake, to see if two parts match exactly?

Name

Recognize Lines of SymmetryI Can identify a line of symmetry on a two-dimensional figure.

Spark Your LearningMehta’s class is studying the climate and wildlife of Argentina. They are following the activities posted in an online journal by a team of scientists working in Patagonia. Mehta’s class views photographs of snowflakes shared by the scientists.

Analyze this snowflake. Can you find a way to fold the snowflake along a line so that it has two parts that match exactly? How many different ways can you find? Draw the possible fold lines on the snowflake.

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If students . . . correctly find one or more lines of symmetry but fail to identify all lines of symmetry, these students have some understanding of lines of symmetry but may not understand how to look for additional lines of symmetry.

Activate prior knowledge . . . by guiding students to turn the image and repeat folding it as they did for the first line of symmetry. Ask:

Q How can you turn the snowflake image and fold it again to see if two parts match exactly?

Q How can you fold the snowflake in more ways to show two parts that match exactly?

If students . . . accurately find all lines of symmetry, they are demonstrating a good conceptual understanding of symmetry and good spatial visualization skills.

Have these students . . . explain how they know the fold lines show two parts that match exactly. Ask:

Q How do you know that the fold line shows two parts that match exactly?

Q Once you found one fold line, how did you find the other fold lines?

Find All Lines of Symmetry

If students . . . incorrectly identify a line of symmetry that does not divide the image into two matching parts, they may have difficulty visualizing whether the two parts match.

Then intervene . . . by guiding students to see that the line does not divide the image into two matching parts. Remind students to make their folds through the center of the image. Ask:

Q How can you find the center of the snowflake?

Q How can you make a fold through the center of the snowflake?

Q How can you check to see if the two parts match?

COMMON ERROR: Identify an Incorrect Line of Symmetry

Find Some of the Lines of Symmetry

During the Spark Your Learning, listen and watch for strategies students use. See samples of student work on this page.

Spark Your Learning • Student Samples

Strategy 1

Strategy 2

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PAIRS

Name

Build Understanding

Turn and Talk How could you use a mirror, instead of folding the snowflake, to see if two parts match exactly?

Recognize Lines of SymmetryI Can identify a line of symmetry on a two-dimensional figure.

Spark Your LearningMehta’s class is studying the climate and wildlife of Argentina. They are following the activities posted in an online journal by a team of scientists working in Patagonia. Mehta’s class views photographs of snowflakes shared by the scientists.

Analyze this snowflake. Can you find a way to fold the snowflake along a line so that it has two parts that match exactly? How many different ways can you find? Draw the possible fold lines on the snowflake.

The snowflake can be folded in 6 ways.

See possible answer at the right.

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Build Understanding

1 Spark Your Learning

▼ MOTIVATEIntroduce the problem. Ask students: What do you know

about Argentina? Tell students to discuss in a small group.

Have them discuss the wildlife and climate of areas near the

South Pole and what scientists may research.

SUPPORT SENSE-MAKING Three Reads

Have students read the problem three times. Use the

questions in the Three Reads box below for a different focus

each time

▼ PERSEVEREIf students need support, guide them by asking:

Q Assessing What are you trying to find out about the

image of the snowflake? Possible answer: if I can fold it

so there are two parts that match exactly

Q Advancing • Use Tools Which tool could you

use to solve the problem? Why is this tool more

strategic? Students’ choices of strategies or tools

will vary.

Q Advancing If you can find one way to fold the

snowflake so the two parts match exactly, how does

that help you find other ways to fold it? Possible

answer: Once I see the way the design looks for two

parts that match exactly, I can look to see if there are

other ways to show the same design by folding it along

a different line.

Turn and Talk Encourage students to share

their thinking. For students who may be

struggling, guide them to think about how a mirror

shows a reflection, or a copy of what is in front of the

mirror. Encourage students to describe how folding an

image and using a mirror can both be used to show two

parts of an image that match exactly. Possible answer:

I can place one edge of the mirror across the middle of

the snowflake and see if the reflection in the mirror

exactly matches the part of the snowflake not being

reflected.

▼ BUILD SHARED UNDERSTANDING Select students who used various strategies and tools to

share with the class how they solved the problem. Have

students discuss why they chose a specific strategy or tool.

Tell students to read the problem three times and prompt them with a different

question each time.

1 What is the situation about? Possible answer: analyzing photographs of snowflakes from scientists working in Argentina

2 What is the mathematical situation? Possible answer: folding the snowflake image to have two parts that match exactly

3 What are possible mathematical questions that you could ask for the situation? Possible question: Can you fold the snowflake so it has two parts that match exactly?

SUPPORT SENSE-MAKING • Three Reads

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