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Grade 10 Math Performance Task: The Park Design Challenge

This worksheet assesses Grade 10 students' ability to apply mathematical concepts to solve real-world problems in a multi-step performance task.

Grade 10 Math Math Word ProblemsPerformance Tasks
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Includes

Text3 Short AnswerFill in the BlanksMultiple ChoiceLong Answer

Standards

CCSS.MATH.CONTENT.HSA.CED.A.1CCSS.MATH.CONTENT.HSG.GPE.B.7CCSS.MATH.CONTENT.HSA.REI.C.6

Topics

performance taskgeometryalgebraproblem solving
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Grade 10 Math Performance Task: The Park Design Challenge

Name:

Date:

Score:

Read the scenario carefully and answer all questions, showing your work and reasoning for each step. You may use a calculator.

Scenario: Designing a Community Park

The local community council has tasked you with designing a new park. The park will be built on a rectangular plot of land measuring 200 meters by 150 meters. Your design must include a rectangular playground, a circular flower garden, and a triangular picnic area. You also need to plan for pathways and fencing.

1. What is the total area of the park plot in square meters? If the cost of the land is $50 per square meter, what is the total cost of the land?

2. You decide to place the rectangular playground with dimensions 40 meters by 25 meters. What is the area of the playground? How much area is left for other features?

3. The circular flower garden has a diameter of 30 meters. The radius of the garden is   meters. The area of the flower garden (rounded to two decimal places, using π ≈ 3.14) is   square meters.

4. The triangular picnic area has a base of 30 meters and a height of 20 meters. Calculate the area of the picnic area.

Height = 20mBase = 30m

5. You need to fence the entire perimeter of the park. What is the total length of fencing required?

a

300 meters

b

350 meters

c

700 meters

d

1400 meters

6. Imagine the park is placed on a coordinate plane with one corner at the origin (0,0). If the park extends in the positive x and y directions, what are the coordinates of the other three corners of the park? Plot these points on the graph below.

051015202530354045505560657075808590951001051101151201251301351401451501551601651701751801851901952002052102152205101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200205210215220

7. You have some remaining area after designing the playground, garden, and picnic area. Describe what other features you would add to the park and why. Justify your choices with mathematical reasoning, considering factors like space, cost, and community needs.