options: 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.

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.

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

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.

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.

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.
problem_activity: Narrative
The purpose of this activity is for students to use what they’ve learned about multiplication to solve and represent situations that involve equal groups. Students now have experience with multiple representations and have the opportunity to choose which representation is most helpful to represent multiplication situations.
The launch of the activity is an opportunity for students to share their experiences and ask questions about the objects to ensure each student has access to the context. If it is helpful, display images of the items for students to reference.
MLR8 Discussion Supports.
Synthesis: As students describe their representations of the problems, use gestures to emphasize the number of groups and how many are in each group. For example, trace with your finger around each group, and point to each object in each group to show how many there are.
Advances: Listening, Representing
Representation: Access for Perception
. Provide access to connecting cubes. Ask students to identify correspondences between the concrete and visual representation used.
Supports accessibility for: Conceptual Processing
Launch
Groups of 2
Write the list of objects (“teams, earrings, pencils, pieces of glass, carrots”) on a display for all students to see.
“Take a minute to read this list. When you are done, discuss the objects you know or have questions about.”
3 minutes: partner discussion
Share a few responses.
“Now we’re going to represent and solve more problems with equal groups. Take a couple of minutes to begin working on the problems before you work in partners.”
2–3 minutes: independent work time
Activity
“Work with your partner to solve each problem.”
5–7 minutes: partner work
Identify students who use different representations like drawings of equal groups or tape diagrams as they solve the problems.
Student Facing
Solve each problem. Show your thinking using diagrams, symbols, or other representations.
There are 4 soccer fields. Two teams are on each field. How many teams are there altogether?
There are 7 windows. Each window has 2 pieces of glass. How many pieces of glass are there in the windows?
Jada has 5 bags. Each bag has 10 earrings. How many earrings does Jada have?
Kiran has 4 boxes. Each box has 5 pencils in it. How many pencils does Kiran have?
Andre has 3 bags of carrots. Each bag has 10 carrots. How many carrots does Andre have?
Student Response
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Advancing Student Thinking
If students add or subtract instead of multiply to solve the problems, consider asking:
“Tell me about how you solved this problem.”
“How does the problem involve equal groups?”
Activity Synthesis
For each problem, display different representations, one at a time.
“How does this representation help us see what’s happening in the problem?” (You can see there are 4 groups for the fields and 2 dots in each group for the teams. The diagram is split into 5 parts for the 5 bags, and each section has a 10 in it for the number of earrings.)
“How could each representation help us solve the problem?” (Counting the dots. Counting by 10.)
If needed, “What expression could we write to represent this situation?”


correct_option_index: 5