standard_description: Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
problem_activity: Narrative
The purpose of this warm-up is to elicit observations about differences in costs of living in different parts of the United States. It prepares students to look for and make sense of multiplicative comparisons later in the lesson. It also helps elicit what students know about how the different costs may be different depending on where you live.
Students may notice and wonder many things about the data in the table and both additive and multiplicative comparisons are likely to come up. Some students may note that an item costs “some dollars more” in San Francisco than in Fort Wayne, while others may say it costs “some number of times as much” based on the quantities or their estimation of the quantities. In the synthesis, focus student discussion on additive and multiplicative comparison.
Launch
Groups of 2
Display the table.
Activity
“What do you notice? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice? What do you wonder?
{"table": [{"_attributes": {"border": "1", "style": "width:95%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}}, {"_attributes": {"scope": "col", "style": "text-align:center; width:25%"}, "_value": "San Francisco, CA"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:25%"}, "_value": "Fort Wayne, IN"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "population"}, {"_value": "805,235"}, {"_value": "253,691"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "milk (1 gallon)"}, {"_value": "\\$4.45"}, {"_value": "\\$2.14"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "bread (1 loaf)"}, {"_value": "\\$3.54"}, {"_value": "\\$1.82"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "gasoline (1 gallon)"}, {"_value": "\\$3.70"}, {"_value": "\\$2.42"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "movie ticket"}, {"_value": "\\$15"}, {"_value": "\\$12"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "internet connection (1 month)"}, {"_value": "\\$70"}, {"_value": "\\$50"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "rent for a 3 bedroom apartment in the city center (1 month)"}, {"_value": "\\$6,000"}, {"_value": "\\$1,500"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "cost of a house"}, {"_value": "\\$1,400,000"}, {"_value": "\\$160,000"}]}]}]}]}
Student Response
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Activity Synthesis
“How could you compare the cost for renting an apartment in San Francisco to the cost in Fort Wayne? How could you use multiplication to compare the costs?”
As needed, “About how many more times as much is the cost of a house in San Francisco compare to the cost of a house in Fort Wayne?”
“The prices of the things you need to live, like food, clothing, and shelter, are called the cost of living. The cost of living can be very different depending on where in the world you live. Today we are going to compare the cost of living in different places around the world.”


aligns: no