Geometry in Basketball G.MG.A

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Problem: The dimensions of the area known as the “key” in high school basketball are above.  The rectangular area is 12 feet by 19 feet.  The area connected to the top of this rectangle is a half circle and has a radius of 6 feet.  Find the combined area of the two shaded regions.

The CCSS aligned with this problem is:

CCSS.MATH.CONTENT.HSG.MG.A.1
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

I selected this problem because basketball season is beginning and many students connect with the sport.  However, many students who do follow basketball aren’t aware of the dimensions of the court, so I felt that it would be an interesting topic.  This task requires students to use their knowledge of areas of rectangles and circles, as well as their mathematical reasoning abilities to solve for the overall area.  If I was teaching this lesson I might leave the dimensions off of the picture and have the students measure the dimensions in the school gym as partners, then solve for the area using their own measurements.  This makes the activity more involved and engaging.

Hot Water vs. Boiling Water: Modeling with Linear Equations A.CED.A

A commonly asked question among students in math classes is “how will I ever use this in real life?” Math is extremely applicable to real world problems, but students do not always realize just how useful it can be.  For this reason, modeling real world, hands on problems is an extremely effective strategy to engage students in learning concepts, and it shows them the relevance of math concepts in the real world.  For this assignment, students will use Vernier temperature probes and a LabQuest2 to model and compare the temperature change of hot water and boiling water.

In this activity, students will use two temperature probes simultaneously to record the temperatures of boiling and hot water.  They will record the temperatures over the span of two minutes and use the LabQuest2 to generate linear equations for each cup of water (boiling and hot).  They will record the equation for each cup and graph the two lines on the same graph.  After recording their data, they will discuss and answer questions about the equations they found.  First, they will work with their partner to decide which cup of water is cooling faster.  Then they will compare the two lines and equations to determine whether the lines are parallel or intersecting and find where the two equations intersect.  Lastly, they will show their ability to create their own linear equation using two given points.  The students will display their understanding of the following CCSS by analyzing the real world data from the activity.

CCSS.MATH.CONTENT.HSA.CED.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Vernier Probe Worksheet-2dfsi46

Evaluating Functions in a Context: CCSS.Math.Content.HSF.IF.A.2

Assessment Task:

Basketball Jerseys

The basketball coach at Cashmere High School is planning on buying new jerseys for his team.  There is an initial design fee of 500 dollars plus a fee of 110 dollars per jersey.  The total cost of n jerseys can be written as the function

C(n)=500+110n

  • Find C(16). Explain in words what this solution means.

 

 

  • Find C(20). Explain in words what this solution means.

 

 

  • If the coach has a budget of $2,000, how many jerseys can he afford?

 

 

  • The coach then went to a different brand to check their jersey prices. They told him there is a design fee of $200 and each jersey is an additional $150.  Write a new function, F(n), that represents the total price of these jerseys.

 

An assessment commentary and the solutions for this task can be found in the attached document.

Assessment Item (IM Format)-2jyo2l6