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

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.

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

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

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

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

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.

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.

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

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.
problem_activity: Narrative
In this activity, students identify right triangles. They also explain why certain given shapes are not right triangles. As they determine whether a triangle is a right triangle, students may use the corner of an index card or a piece of paper, use a protractor, or trace an angle in a triangle to compare with an angle elsewhere that they know to be a right angle. In doing so, students practice choosing tools strategically (MP5).
Required Materials
Materials to Gather
Index cards
Patty paper
Protractors
Launch
Groups of 2
Provide access to index cards, patty paper, and protractors.
Activity
5 minutes: independent work time
2 minutes: partner discussion
Monitor for students who use tools to check angles and those who estimate them visually. Ask the latter: “How might we check that the angles that look like right angles are
\(90^\circ\)
?”
Student Facing
Identify all shapes that are right triangles. For each right triangle, mark the right angle with a small square.
[IMG]
Explain why the other shapes are not right triangles.
Student Response
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Advancing Student Thinking
Students may not identify triangles C or D because of the orientation.
Consider asking:
“How can we show that a triangle has a right angle?”
“Where else do you see triangles that may have perpendicular sides?”
“What tools could you use to see if each triangle has any right angles?”
Activity Synthesis
Invite students to share their responses and how they found the right triangles in the set.
“Were there any triangles that appeared to be right triangles but are not, or don’t appear to be right triangles but are?” (Triangle H looks like one but isn’t.)


correct_option_index: 6