options: 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.

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

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.

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

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.

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

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
problem_activity: Activity
Students begin to think about common multiples and the least common multiple when finding ways to place two types of flowers into groups that contain the same number of each flower. Students find all multiples up to 100 for two different numbers. They compare these multiples to determine which ones are the same, and then they determine the least common multiple.
Look for different strategies and representations students use to describe the situation. Some students may draw pictures of groups of flowers, other students may use tables or lists, and other students may do a combination of these.
Launch
Arrange students into groups of 2. Give students 5–7 minutes of quiet work time, then 2 minutes of partner discussion. Follow with whole-class discussion.
Student Facing
A florist can order roses in bunches of 12 and lilies in bunches of 8. Last month she ordered the same number of roses and lilies.
If she ordered no more than 100 of each kind of flower, how many bunches of each could she have ordered? Find all the possible combinations.
What is the smallest number of bunches of roses that she could have ordered? What about the smallest number of bunches of lilies? Explain your reasoning.
Student Response
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Activity Synthesis
Invite students to share how they organized the different combinations of flowers, and highlight the different strategies they used. Strategies to highlight include tables, lists, snap cubes, and other pictorial representations. Confirm that there are 4 different order combinations, and each time there are 24 more of each flower added. Discuss why the smallest number of flowers of each type is 24, and that it takes 2 bunches of roses to equal 24, and 3 bunches of lilies to equal 24. If there was a group that used snap cubes, ask them to share what this arrangement looks like when represented with two different colors. If possible, use student responses to create a visual display of the concept of least common multiple and display it for all to see throughout the unit.
Speaking: MLR8 Discussion Supports.
Use this routine to amplify mathematical uses of language to communicate the multiple strategies used by different students. Provide sentence frames for students to use when they are comparing and contrasting different representations such as: “All ____ have ____ except ____.”, “What makes ____ different from the others is ____.”
Design Principle(s): Support sense-making; Cultivate conversation


correct_option_index: 9