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

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

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.

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.

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

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.

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

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

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

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.

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.
problem_activity: Warm-up
In this activity, students practice determining the measurement of unknown angles using their relationship to angles with known angle measure and what students already know about the measurement of right angles and straight angles. After they have worked on the activity and shared their solutions, they are introduced to the vocabulary terms complementary and supplementary. Complementary describes angles whose measures sum to 90 degrees and supplementary describes angles whose measures sum to 180 degrees.
Some students may wish to use protractors, either to double check work or to investigate the different angle measures. This is an appropriate use of technology (MP5), but ask these students what other methods they could use instead.
Launch
Provide access to geometry toolkits.
Student Facing
Find the measure of angle
\(JGH\)
. Explain or show your reasoning.
[IMG]
Find and label a second
\(30^\circ\)
angle in the diagram. Find and label an angle congruent to angle
\(JGH\)
.
Angle
\(BAC\)
is a right angle. Find the measure of angle
\(CAD\)
.
[IMG]
​​​​​
Student Response
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Anticipated Misconceptions
If needed, remind students that right angles have a measure of
\(90^\circ\)
and straight angles have a measure of
\(180^\circ\)
.
Activity Synthesis
The goal of this discussion is to introduce students to the terms complementary and supplementary for describing relationships between pairs of angles. Display the images for all to see and select students to briefly share their response to each question, recording any calculations used.
Explain to students that the term
complementary
describes a pair of angles whose measures sum to 90 degrees, and the term
supplementary
describes a pair of angles whose measures sum to 180 degrees. This is true even for pairs of angles that are not adjacent. Conclude the discussion by inviting students to identify pairs of angles that are complementary (
\(CAD\)
and
\(DAB\)
), supplementary (
\(FGJ\)
and
\(JGH\)
,
\(JGH\)
and
\(HGI\)
,
\(HGI\)
and
\(IGF\)
, or
\(IGF\)
and
\(FGJ\)
), or vertical (
\(FGJ\)
and
\(HGI\)
or
\(JGH\)
and
\(IGF\)
) from the activity.


correct_option_index: 2