options: 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.

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.

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

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.

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.

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.

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

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.
problem_activity: Narrative
The purpose of this activity is for students to estimate whole number products in the context of volume. In the next activity students will calculate the smallest and largest volumes within the range recommended for each type of bird. The estimates here may or may not fall within the range, depending on the numbers students pick. When making reasoned estimates, there is always some tension between accuracy and using the most friendly numbers. During the synthesis, students explain the different strategies they use to make reasonable estimates with calculations that they can perform as simply as possible, often mentally (MP3).
Students may need a quick reminder of how to find the volume of a rectangular prism. If needed, remind students that the volume of a rectangular prism is the product of the length, width, and height, or alternatively, the product of the area of a base and the height for that base.
Launch
Display table from task.
“What do you notice and wonder about the table?” (There are different kinds of birds listed. There are side lengths for the floor but the height is a range. What do the numbers mean? Do smaller birds have smaller houses?)
1 minute: quiet think time
Share and record student responses.
If needed, display images of different kinds of birds.
Activity
2 minutes: quiet think time
5 minutes: partner work time
Monitor for students who consider friendly numbers to use for the height and also for estimating the product of the area of the floor and the height.
Student Facing
Different types of birds use different types of houses. The table gives you the recommended side lengths for birdhouses of various species.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "type of bird"}, {"_attributes": {"scope": "col"}, "_value": "side lengths of floor"}, {"_attributes": {"scope": "col"}, "_value": "height"}, {"_attributes": {"scope": "col"}, "_value": "volume estimate"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "chickadee"}], "td": [{"_value": "4 in by 4 in"}, {"_value": "6 to 10 in"}, {}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "wood duck"}], "td": [{"_value": "10 in by 18 in"}, {"_value": "10 to 24 in"}, {}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "barn owl"}], "td": [{"_value": "10 in by 18 in"}, {"_value": "15 to 18 in"}, {}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "red-headed woodpecker"}], "td": [{"_value": "6 in by 6 in"}, {"_value": "12 to 15 in"}, {}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "bluebird"}], "td": [{"_value": "5 in by 5 in"}, {"_value": "6 to 12 in"}, {}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "swallow"}], "td": [{"_value": "6 in by 6 in"}, {"_value": "6 to 8 in"}, {}]}]}]}]}
Estimate a possible volume for each birdhouse. Be prepared to explain your reasoning.
Student Response
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Activity Synthesis
“How did you estimate the volume of a house for a wood duck?”
I know
\(10 \times 18\)
is 180 and I multiplied by 10 since that just adds a zero.
I also used
\(10 \times 18 = 180\)
but multiplied by 20 since that is between 10 and 24. I got
\(3,600\)
cubic inches.
“How did you estimate the volume of a house for a red-headed woodpecker?”
I found that the area of the floor is 36 square inches. I multiplied this by 10 to get 360 and by 20 to get 720 and then picked a number in between, 500 cubic inches.
I found the area of the floor was 36 square inches. I rounded that to 40 since it is a nicer number and then found
\(40 \times 12\)
which is 480.
“Which numbers are the friendliest for estimating products? Why?” (10 is the friendliest because I can use place value. Multiples of 10, like 20, are also friendly as I can multiply by 10 and then double.)


correct_option_index: 6

7