Exploring Parks and Playgrounds:
The focus of this unit is the development of students' understanding of mulitplication and division with rational numbers. The context of parks and playgrounds is used to introduce the double number line and the array models as helpful tools.
Big Ideas:
The focus of this unit is the development of students' understanding of mulitplication and division with rational numbers. The context of parks and playgrounds is used to introduce the double number line and the array models as helpful tools.
Big Ideas:
- Fractions represent a relation
- The whole matters
- To maintain equivalence the ratio of the related numbers must be kept constant
- The properties (distributive, associative, and commutative) that hold for whole numbers, also hold for rational numbers
- The relationship between multiplication and division of fractions
The Marathon InvestigationThe marathon is a 26-mile-long race that winds through the park. Rachel knows that she ran 7/12 of the route because she counted the markers as she ran and she stopped when she got to the seventh marker. Mark really wanted to do better than he did last year. He used water stations to keep track of how he was doing. They stand at every eighth of the course. He knew when he got to the fourth water station that he had run halfway. He ran to the next one- the fifth- and then he stopped.
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The Training Investigation |
Focus Questions:
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Exploring Playgrounds and Blacktop Area
BROOKLYN- Today we're going to work on a problem that affects a neighborhood in Brooklyn, a real-life problem. Brooklyn is a really large borough (village/area) that is part of New York City, and the problem is that it has very few small parks; there are not many places where people can play basketball or kickball, or sit on a bench.
The good news is that in two neighborhoods in Brooklyn, people are thinking about developing two parks.
The good news is that in two neighborhoods in Brooklyn, people are thinking about developing two parks.
Carroll GardensOne of the neighborhoods is called Carroll Gardens. There's an empty lot in Carroll Gardens that measures 50 yards by 100 yards.
Here's what was decided in Carroll Gardens. The residents agreed that 3/4 of the lot will be devoted to a playground for children. Then 2/5 of that playground will be covered in blacktop, so that the children can play games like kickball and basketball. |
FlatbushThere is another neighborhood in Broolyn called Flatbush, and there is also an empty lot there. This lot also measures 50 yards by 100 yards.
The discussion in Flatbush was a little different when the residents thought about their playground. This is what they decided in Flatbush. They decided that 2/5 of the lot would be used for children. 3/4 of that space would be used for blacktop. |
Questions
- Is there more blacktop space in one lot than in the other lot?
- How would you convince the people in the two neighborhoods that your conclusion is correct?
Comparing the Cost of Blacktopping
Now the community planning committees are considering the cost of creating the playgrounds, specifically the cost of the blacktopping. The price of the blacktopping in Carroll Gardens is $9 per square yard, but because it is a community project, the contractor says he won't charge his full price. He will do the job for 80% of what he normally charges. In Flatbush, however, the contractor normally charges only $8 per square yard and offers to do it at 90% of the normal price. Now there is a question about the cost. Will the blacktopping cost more in one of the parks than the other?