School Improvement in Maryland

Public Release Item: Public Release items have appeared on HSA forms and then are released for public viewing and use. Releasing items is one step to ensuring that schools, districts, and other stakeholders understand how the core learning goals are assessed on the HSA.

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

Indicator 2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.

Assessment Limits:

  • “Validate properties” in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.
  • Students may use a compass, straightedge, patty paper, a MiraTM, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.
  • Students may use a compass, ruler, patty paper, a MiraTM, a mirror and/or a protractor as drawing tools.
  • It is acceptable to do a construction when the item asks for a drawing.
  • Paper folding and the use of MirasTM and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.
  • Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.

Extended Constructed Response (ECR) Item - Released in 2000

Use the segment below to complete each of the following constructions.

Complete the following in the answer box below:

  • Using segment AB, construct equilateral triangle ABC. Use mathematics to explain the process you used to construct the triangle. Use words, symbols, or both in your explanation.
     
  • Construct circle O so that ΔABC is inscribed in circle O. Use mathematics to explain your process. Use words, symbols, or both in your explanation.
     

/share/clg/xml/public_release/mathematics/2000_214_geo31.xml

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Brief Constructed Response (BCR) Item - Released in 2000

Elizabeth draws a right triangle with angles of 52° and 38°.

Complete the following in the answer box below:
  • Draw a right triangle using these angle measurements. Label the measure of each angle.
     
  • Will any right triangle with angles of 52° and 38° be congruent to Elizabeth's triangle? Use mathematics to justify your answer.
     

/share/clg/xml/public_release/mathematics/2000_214_geo38.xml

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Extended Constructed Response (ECR) Item - Released in 2003

A community pool is equidistant from the three schools shown below.

Complete the following in the answer box below, and/or on a piece of paper:
  • Use geometric construction to determine the location of the pool.
     
  • Explain the steps you used in your construction. Use words, symbols, or both in your explanation.
     
  • Justify that the location you found is equidistant from all three schools.
     

/share/clg/xml/public_release/mathematics/2003_214_geo31.xml

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Brief Constructed Response (BCR) Item - Released in 2001

Two factories are located near a railroad. There is a loading platform on line l equidistant from the two factories.

Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

  • Use geometric constructions to determine the location of the loading platform. Label the loading platform with an X.
     
  • Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2001_214_geo30.xml

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Extended Constructed Response (ECR) Item - Released in 2001

The Department of Public Works wants to put a water treatment plant at a point that is an equal distance from each of the three towns it will service. The location of each of the towns is shown below.

Use the answer box to complete the following. (You will also need to use additional paper to complete the answer satisfactorily.)

  • Locate the point that is an equal distance from each of the towns.
     
  • Explain how you determined this location. Use words, symbols, or both in your explanation.
     
  • Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2001_214_geo43.xml

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Extended Constructed Response (ECR) Item - Released in 2004

Kerry plans to build a picnic table. She needs to create a drawing of the picnic table surface.

Complete the following on a piece of paper and/or in the answer box below:

  • Draw a regular hexagon with side lengths of 4 centimeters each. Label the vertices of your hexagon A, B, C, D, E, and F. Label the center of your hexagon O. Explain the steps you used in your drawing.
     
  • Classify ΔAOF according to its sides and/or angles. Use mathematics to justify your answers.
     
  • Classify ΔABD according to its sides and/or angles. Use mathematics to justify your answer.
     
  • Classify ΔABC according to its sides and/or angles. Use mathematics to justify your answer.
     

/share/clg/xml/public_release/mathematics/2004_214_geo31.xml

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Extended Constructed Response (ECR) Item - Released in 2002

The floor plan for an office in a new building is shown below. The interior designer wishes to place a desk so that it is equidistant from all the walls in the office.

Complete the following in the answer box below:
  • Use construction techniques to locate the point where the desk should be.
  • Explain the steps you used in your construction. Use words, symbols, or both in your explanation.
  • Use mathematics to justify that the location of the desk is equidistant from the walls of the office.

/share/clg/xml/public_release/mathematics/2002_214_geo31.xml

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Resources for 2.1.4:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |