Preparing Students for HSPA Mathematics

By: Diane Viehweg

March 5,6, 7 and 8, 2007
Regular Testing (Science, for first-time eleventh-grade students ONLY,  Mathematics and Language Arts Literacy Days 1 and 2)

NJ HSPA Mathematics Component

• The mathematics assessment includes both multiple choice and open-ended questions that engage students in mathematical processes within the four strands of the mathematics Core Curriculum Content Standards

NJ HSPA Mathematics Clusters

• Number and Numerical Operations

• Geometry and Measurement

• Patterns and Algebra

• Data Analysis, Probability, and Discrete Mathematics

Mathematics Cluster Distribution of Point Value:
Cluster I. Number Sense, Concepts & Applications - 25%
Cluster II. Spatial Sense & Geometry - 25%
Cluster III. Data Analysis, Probability, Statistics & Discrete Mathematics 25%
Cluster IV. Patterns, Functions & Algebra 25%

• Total Number of Points = 56

Open Ended Questions

• Students have a very difficult time explaining – "How they solved a problem"

• Students need practice answering questions that require thinking and explaining.

• Students like to explain things that they enjoy and find interesting.

Sample Open Ended Question and Rubric

• 3 points – The student finds area of 148 square yards. Diagram is clearly marked to show how floor was divided. For each section an appropriate formula is correctly used although actual work may not be shown. Diagram may be labeled with needed dimensions or their correctness may be determined from their use in the formulas. Any flaws are minor. (One mislabeled dimension or one computational error is considered a minor flaw.)

• 2 points – The student displays a reasonable method for finding the area but shows a pattern of errors in computation,  OR finds the area of one section inappropriately. (Includes both misapplication of a formula and failing to correctly determine a needed dimension.)

• 1 point –The response fails to meet the requirements of a "2" but shows some evidence of understanding or begins to answer the question; for example, correctly finds area of one subsection of floor.

• 0 points – The response is irrelevant, inappropriate, or otherwise without merit.

Where to find FREE resources!!!

General Information

• General Rubric for Open Ended Questions = http://njpep.org/assessment/TestSpecs/MathTestSpec/GEPAMath/HolisticScoringGuide.html

• Calculators = http://njpep.org/assessment/TestSpecs/MathTestSpec/GEPAMath/useofcal.html

• Cluster and Marcros http://njpep.org/assessment/TestSpecs/MathTestSpec/GEPAMath/MathIndex.html

Opened Ended Questions and Answers:

• Grade 5

• http://www.stfx.ca/special/mathproblems/grade5.html

• Grade 6

• http://www.stfx.ca/special/mathproblems/grade6.html

• Grade 7

• http://www.stfx.ca/special/mathproblems/grade7.html

• Grade 8

• http://www.stfx.ca/special/mathproblems/grade8.html

Opened Ended Questions and Answers:

• Open Response Question Strategy http://www.murraystate.edu/prism/kyprism/openrp1.htm

• HSPA Online 10 Question Quiz http://inet.paterson.k12.nj.us/~schools/school11/class%20stuff/v8mc_t1/index2.html

HSPA Like Test FREE

• Illinois http://tp1.clearlearning.com/ISBE/2003/grade8math/index.html?USER_ID=student

Internet Virtual Manipulatives

·         Algebra Balance Scales - Negatives

·         Bar Chart

·         Base ten blocks 

·         Chip Abacus

·         /Money

·         Fraction Bars

·         Fraction Pieces

·         Geoboard –

·         Geoboard - Circular –

·         Geoboard - Coordinate

·         Geoboard - Isometric

·         Pattern Blocks

·         Pentominoes

·         Polyominoes

·         Stick or Switch - Probability

·         Tangrams  

·         Tessellations

·         Whammy Awards

HSPA Internet Resource

• Bernard’s Bag – Open Ended Problems http://nrich.maths.org./prime/oct98/bbag.htm

HSPA Internet Resource

• Brain Teasers - http://www.eduplace.com/math/brain/

• Interactive Puzzles Can Be copied for Class use - http://www.sprucelog.com/lmp/interactive/

• Problem Of the Week Archive http://mathcounts.org/Queries/POW_Archive.taf?_function=CompleteArchive&_UserReference=9504F589BDBBB15A3F9B19EE

• Penta Problems http://nrich.maths.org/prime/oct03/penta.htm

HSPA Internet Resource

• Interactive Activities http://www.shodor.org/interactivate/activities/#num

HSPA Internet Resource

• Franklin Institute - http://k12science.ati.stevens-tech.edu/k12partner00/gepa.html

• PBS - http://www.pbs.org/teachersource/math.htm

• Math Forum Archives and Libraries

• http://mathforum.org/escotpow/solutions/toc.ehtml?start_date=20010101&stop_date=20010531

• http://mathforum.org/escotpow/solutions/toc.ehtml?start_date=20001001&stop_date=20001231

• http://mathforum.org/library/problems/

National Council of Teachers of Mathematics

• Interactive multimedia lessons http://illuminations.nctm.org/imath/index.html

• Lesson Plans http://illuminations.nctm.org/lessonplans/index.html

• By grade levels http://illuminations.nctm.org/pages/prek2.html

Track Star

• Data Base of Plans http://trackstar.hprtec.org/

A+Math.com

• Worksheets on & offline http://aplusmath.com/Worksheets/index.html

• Homework help http://aplusmath.com/

• Fun Games http://aplusmath.com/Games/index.html

Virtual Manipulatives

• NUMBER OPERATIONS http://matti.usu.edu/nlvm/nav/grade_g_2.html

• Algebra http://matti.usu.edu/nlvm/nav/category_g_2_t_2.html

• Geometry http://matti.usu.edu/nlvm/nav/category_g_2_t_3.html

• Measurement http://matti.usu.edu/nlvm/nav/category_g_2_t_4.html

• Data Analysis http://matti.usu.edu/nlvm/nav/category_g_2_t_5.html

Fun Activities

• Weekly Brain Teasers http://www.eduplace.com/math/brain/

• Great site for Tessellations http://mathforum.org/sum95/suzanne/tess.intro.html

• Problems and Puzzles http://mathforum.org/k12/mathtips/

• Fun Activities http://teams.lacoe.edu/documentation/support/carole/weblinks/4thstudentsmath.html

Ask ERIC

• Homepage http://ericir.syr.edu/cgi-bin/lessons.cgi/Mathematics

• Lessons – Arithmetic http://ericir.syr.edu/cgi-bin/lessons.cgi/Mathematics/Arithmetic

Fun Brain

• Educational Online games http://www.funbrain.com/kidscenter.html

New Jersey Department of Education

• Various downloads for teachers http://www.state.nj.us/njded/stass/index.html

Higher Level Thinking

• http://www.period.com/puzzles/

NJ Department of Education

• NJ PEP Resources

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Summary

• Make your life easier with high interest activities for your students.

• Make your classroom fun and interesting.

• Get your students thinking about thinking.

• Instill a love of learning in your students.