options: 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 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.

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

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

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.

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

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.

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
The purpose of this warm-up is to review factors and multiples while eliciting ideas on common factors and common multiples that will be useful in the activities of this lesson. While students may notice and wonder many things about the numbers they have circled, it is important for students to notice the multiples 4 and 6 have in common and wonder what other multiples they would have in common if the counting sequence continued.
Launch
Arrange students in groups of 2. Tell students 10 is a multiple of 5 because
\(10 = 5 \boldcdot 2\)
. One way you can find multiples of a number is by skip counting. For example, the multiples of 5 are 5, 10, 15, 20. . . and so on. Give students 1 minute of quiet work time to circle the multiples of 4 and 6. Give students 1 minute to discuss the things they notice and wonder with a partner, followed by a whole-class discussion.
Student Facing
Circle all the multiples of 4 in this list.
1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26
Circle all the multiples of 6 in this list.
1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26
What do you notice? What do you wonder?
Student Response
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Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After each response, ask the class if they agree or disagree and to explain alternative ways of thinking, referring back to the images each time. If there is time, ask students what other multiples 4 and 6 would have in common if the counting sequence continued. Ask them to explain their reasoning. Record and display their responses for all to see.


correct_option_index: 1