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

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.

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

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.

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 & 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.

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

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.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Activity
In this activity, students practice mentally dissecting a prism with a non-rectangular base into simpler prisms. The dissection corresponds to a dissection of the base into simpler figures. This expands on students’ ability to calculate the area of a base of a figure that has a rectangular base because here the base is not a rectangle. This prepares students to calculate the volume of this figure and other figures in future lessons.
As students work in their groups, monitor for the different ways students are decomposing or constructing the base of the figure into more familiar shapes.
Launch
Arrange students in groups of 3. Display the image for all to see throughout the activity. Tell students this is what the heart-shaped box mentioned in the task statement looks like.
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Give students 2–3 minutes of quiet work time followed by a whole-class discussion.
Engagement: Internalize Self Regulation.
Check for understanding by inviting students to rephrase directions in their own words. Provide a project checklist that chunks the various steps of the activity into a set of manageable tasks.
Supports accessibility for: Organization; Attention
Conversing: MLR5 Co-Craft Questions.
Display the image of the heart-shaped box and initial task statement without revealing the questions that follow. Ask students to write mathematical questions about the situation. Invite students to share their questions with their group and choose 1 question from their group to share with the class. Listen for questions that connect to finding the area of the base of the heart-shaped prism (e.g., “What’s the most 1 inch by 1 inch by 1 inch chocolates that can fit along the bottom of the box?”). This helps students produce the language of mathematical questions and begin reasoning about different approaches for finding the area of a non-rectangular shape.
Design Principle(s): Cultivate conversation
Student Facing
A box of chocolates is a prism with a base in the shape of a heart and a height of 2 inches. Here are the measurements of the base.
[IMG]
To calculate the volume of the box, three different students have each drawn line segments showing how they plan on finding the area of the heart-shaped base.
[IMG]
For each student’s plan, describe the shapes the student must find the area of and the operations they must use to calculate the total area.
Although all three methods could work, one of them requires measurements that are not provided. Which one is it?
Between you and your partner, decide which of you will use which of the remaining two methods.
Using the quadrilaterals and triangles drawn in your selected plan, find the area of the base.
Trade with a partner and check each other’s work. If you disagree, work to reach an agreement.
Return their work. Calculate the volume of the box of chocolates.
Student Response
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Student Facing
Are you ready for more?
The box has 30 pieces of chocolate in it, each with a volume of 1 in
3
. If all the chocolates melt into a solid layer across the bottom of the box, what will be the height of the layer?
Student Response
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Activity Synthesis
Select students to share whose method they decided to use and why. Ask students:
“Whose method could not be used? Why not?” (Lin’s, because we don’t know the base and  height of the trapezoids.)
“How did you find the areas of the base?”
“What was different about the base of this figure in comparison to other bases we have worked with?” (This base needs to be decomposed to calculate its area.)
“What was the first thing you did to find the volume?” (Use the area of the base and multiply it by the height of the figure.)
“Why would a chocolatier want to know the volume of a heart shaped box like this?” (He may want to know how many candies can fit inside of a box.)
Explain to students that they might encounter figures that have non-rectangular bases in future activities or lessons. It will be important for them to think about different strategies to calculate the area of the base.


correct_option_index: 4