options: Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
problem_activity: Activity
In this activity, students work together to investigate lines of symmetry and communicate their thinking in a visual display. As you monitor, ask groups if they have found all possible lines of symmetry and to explain how they know all shapes of that type have that same symmetry.
Launch
Arrange students in groups of 2–4. Provide each group with tools for creating a visual display.
Assign a different shape from the blackline master to each group and provide enough copies of that shape for each student in each group. Note that the cool-down uses a rectangle, so you may choose to assign the rectangle to a group of students who need more processing time.
Give students 5 minutes of work time followed by 5 minutes to put together their visual display. Explain that they will not have enough time to make the visual display perfect, so the purpose is to get their ideas down in an organized way.
Student Facing
Determine all the
lines of symmetry
for the shape your teacher assigns you. Create a visual display about your shape. Include these parts in your display:
the name of your shape
the definition of your shape
drawings of each line of symmetry
a description in words of each line of symmetry
one non-example in a different color (a description and drawing of a reflection
not
over a line of symmetry)
Student Response
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Student Facing
Are you ready for more?
Look at all of the shapes the class explored and focus on those which had more than one line of symmetry.
What is true for all the lines of symmetry in these shapes?
Give an example of a shape that has two or more lines of symmetry that do not intersect at the same point.
What would happen if you did a sequence of two different reflections across lines of symmetry for the shapes you explored in class?
Student Response
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for free access to Extension Student Response.
Anticipated Misconceptions
Students might think that any line that divides the area of a figure in half, like a diagonal of a non-square rectangle, is a line of symmetry. Ask students to reflect across these lines to see that the shapes are not taken onto themselves.
Activity Synthesis
The purpose of this discussion is to identify what types of shapes have reflection symmetry.
Ask groups to display their visual displays in the classroom for all to see in order of the number of lines of symmetry their shape has. They will have to communicate with other groups to accomplish this.
Invite students to do a “gallery walk” in which they leave written feedback on sticky notes for the other groups. Here is guidance for the kind of feedback students should aim to give each other:
Was there anything about the organization of the visual display that made the ideas especially clear? Was there anything about the organization that could be improved?
Was there anything about the way the ideas are explained that made the ideas especially clear? Was there anything about the explanations that could be improved?
Are there any lines of symmetry that the group missed?
Are there any lines of symmetry that don’t work for all shapes of the given type?
After the gallery walk, ask students to share their observations about reflection symmetries for the different shapes. Consider asking:
“Which shapes had the fewest lines of symmetry? Which had the most?” (The parallelogram that is not a rhombus didn’t have any lines of symmetry. The circle has the most since it has infinite.)
“Were there any lines that you thought would be lines of symmetry, but when you tried to reflect, they turned out not to be?” (The diagonal of a parallelogram that is not a rhombus seemed like it would be a line of symmetry, but it’s not.)
“Describe a shape that would have no lines of symmetry.” (A scalene triangle has no lines of symmetry.)
Save the visual displays if possible for comparison with displays of angles of rotation that create symmetry in a subsequent lesson.
Engagement: Develop Effort and Persistence.
Break the class into small group discussion groups and then invite a representative from each group to report back to the whole class.
Supports accessibility for: Language; Social-emotional skills; Attention


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