HSPA Mathematics

•The HSPA is an exam administered statewide in Marchto high school juniors. •It is designed to test our students’ proficiencies in Mathematics and Language Arts.

•A passing score of 200 in each section is necessary for graduation.

Successful Strategies for the HSPA

Answering Math Multiple Choice Questions

1. Each question is worth one point.

2. You are not penalized for guessing. Do not leave an answer blank.

3. Try to eliminate incorrect choices to help select the best answer.

4. Use the math reference sheet for formulas and added information.

Answering Math Open-ended Questions

1. Read the questions carefully.

2. Make sure to show all your work.

3. Try to give a written explanation. Labeled diagrams can be included.

4. As with the reading open-ended, if you can’t answer completely, make an attempt.

5. These questions are worth 0-3 points. Therefore a partial answer can earn you some points.

•The Mathematic Test of the HSPA assessment is divided into three 40 minute sections.

•Each of these segments reflects knowledge and skills specified in the Core Curriculum Content Standards.

•All three parts consist of 10 multiple-choice and 2 open ended questions.

•Four different mathematics clusters are addressed in each section.

HSPA Clusters

Number and Numerical Applications Geometry and Measurement Data Analysis, Probability, and Discrete

Mathematics Patterns and Algebra

Number and Numerical Applications

Number Sense Numerical Operations Estimation

The following sample questions are from http/www.njpep.org

(The answer key is at the end of this presentation.)

1. Alan bought a dozen donuts. He gave half to his mother, kept a third of the remaining donuts for himself, and gave the rest to his friends. How many donuts did Alan keep?

a. 2

b. 4

c. 3

d. 6

Geometry and Measurement

Geometric Properties Transforming Shapes Coordinate Geometry Units of Measurement Measuring Geometric Objects

The following sample open-ended question is from the HSPA website.

2. In triangle XYZ, angles x and y are congruent. What is the length of YZ. Explain and show all your work.

3x-20

Z

X+40

X Y

Data Analysis, Probability, and Discrete Mathematics

Data Analysis (Statistics) Probability Discrete Mathematics- Systematic

Listing and Counting Discrete Mathematics- Vertex- Edge

Graphs and Algorithms

The following sample question is from the HSPA website.

3. A drawer contains 4 red pens, 5 blue pens, and 2 black pens. If you reach into the drawer without looking and pull out a pen for you and a pen for your work partner, what is the probability that the first pen will be blue and the second pen will be black?

21

2

40

11

3

1

11

1

a.

b.

c.

d.

Patterns and Algebra

Patterns and Relationships Functions Modeling Procedures

The following sample open-ended question is from the HSPA website.

4. Belinda wants to determine the number of dots in the 30th step of the following pattern, but she does not want to actually draw all 30 steps.

Step 1:

**

**

Step 2:

***

***

***

Step 3:

****

****

****

****

Explain how Belinda could find the number of dots in Step 30 without actually drawing them.What would be the number of dots in the 30th step?Write an algebraic expression for the number of dots in the nth step.

The answer key to questions 1-4 is on the following four slides.

1. a 1/2 of a dozen =6 1/3 of 6 = 2 He kept 2 for himself It does not ask what he gave to his

friends.

2. This picture in the response helps to clarify the answer.

The length of line yz is 70

3x-203(30)-2090-20=70

x+4030+40=70

Both sides havethe same lengthbecause theirangles are equal.

Z

X Y

3x-20=x+402x=60x=30

(3x-20) is equal to (x+40)because its opposite sides are congruent

This responses scored a “3” because it shows a knowledge of congruent angles and basic geometry.

3. d•There are a total of eleven pens.•Since five of the eleven are blue, we use the ratio 5/11.•By taking out one of the blue pens, we are left with 10 pens in the drawer.•Since two of the remaining ten pens are black, we use the

ratio 2/10.•We now have two independent events, therefore we multiply the two ratios to get our answer.

5/11 x 2/10 = 1/11

4.This response received a “3” because it is answered correctly, although the seventh part of the answer is not asked for in the question.

• The number of dots in step 1, 2 ,and 3 are perfect Squares. • In step 1, 22 = 4 dots. • In step 2, 32 = 9 dots. • Step 30 would be 312 .• The number of dots in step 30 is 31 x 31= 961• N= (x+1)2 (x = step #)• The 9th step would be 102, which gives you 100.