options: 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.

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

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

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.

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.

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.

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.

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.

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.
problem_activity: Warm-up
The purpose of this warm-up is for students to notice and describe the features of graphs using their own language. Students will encounter a variety of graphs over the next several lessons and throughout these lessons they will gradually develop more precise language around graphs as the needs of activities dictate.
Launch
Arrange students in groups of 2–4. Display the image of the four graphs for all to see. Ask students to indicate when they have noticed one figure that does not belong and can explain why. Give students 1 minute of quiet think time and then time to share their thinking with their group. Follow with a whole-class discussion.
Student Facing
Which graph doesn’t belong?
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
After students have conferred in groups, invite each group to share one reason why a particular graph might not belong. Record and display the responses for all to see. After each response, ask the rest of the class if they agree or disagree. Since there is no single correct answer to the question of which graph does not belong, attend to students’ explanations and ensure the reasons given are correct.
Try to highlight the two facts that there are points with the same first coordinate and different second coordinates in graph B (which means it is not a function), the straight segments of C vs. curves of the others, and the discrete nature of D during this discussion, using whatever language students bring to it. Avoid introducing the traditional
\(x\)
and
\(y\)
names for the axes into the discussion unless students use them first. More formal vocabulary will be developed in later activities, lessons, and grades, and much of the motivation of this added vocabulary is to improve upon the somewhat clunky language we are led to use without it.


correct_option_index: 4