Countdown to the April 2012 State Math 8 Tests
Hi Everyone!
With just a few instructional days left before the state tests for Math grades 3-8 and
thinking about what could be done as a last minute push to help our students, we’re
providing you with a “Countdown to the State Tests” agenda that covers the ten days
before the tests. This will start when you return from April Break.
FYI...8th graders will take their NYS Math 8 Wednesday- Friday, April 25th – 27th
The table below explains what area is addressed on each day for grade 8. The
accompanying pages give you mini lessons to use with your students. Appropriate
materials such as reference sheets, problems addressing specific standards, rubrics, and
state guidelines for testing and scoring are attached.
Please choose a constructive way to use this packet to help your students.
Good Luck to you and your students!
DATE
GRADE 8
Day 1
Dates, Times, Format
Day 2
Reference Sheet
Day 3
Directions on test
Day 4
Rubrics
Day 5
Tools (Ruler)
Day 6
Algebra
Day 7
Algebra
Day 8
Geometry
Day 9
Geometry
Day 10
Number Sense & Operations and
Measurement
Countdown-to-the-Tests
Mini Lesson Day 1
TOPIC: Dates, Times, Format
GRADE 8
Curriculum Planning: http://www.p12.nysed.gov/osa/mathei/2010/3-8math2010.pdf
1. Test is administered over three days, , Wed. April 25, Thurs. April 26, and Fri.
April 27
2. Rulers are provided for both days of the test
3. Day 1 & 2, Book 1 & 2: (Wednesday and Thursday)
o Book 1: 38 multiple-choice questions
o Book 2: 37 multiple choice questions
o State estimates 60 minutes + prep time
o Students are allowed 90 minutes
o NO calculator permitted
o Students will record their answers on a pre-headed answer sheet using a
#2 pencil
o NO reference sheet is allowed
4. Day 3,
o
o
o
o
o
o
o
Book 3: (Friday)
5 short-response questions
4 extended-response questions
60 minutes + prep time
Scientific calculator is required
All answers will be written in the test book
NO PENS are allowed; must use #2 pencils
Reference sheet may be used
Countdown-to-the-Tests
Mini Lesson for Day 2
TOPIC: Pi & Reference Sheet
GRADE 8
 The Reference Sheet may be used when doing the short-response and extended-response questions
only. If a formula or conversion is needed for a multiple-choice question, it will be written near the
question.
 The Reference Sheet for Grade 8 is attached
 Walk through the reference sheet with the students.
 Review the different formulas with them.
 Review the conversions on the sheet.
LESSON
Problem 1: What formula do you use if you are to find simple interest?
Answer: Simple Interest:
I = prt
Problem 2: Find the amount of simple interest earned if $7,300 is invested for 8 years at a rate of 4%.
I = prt
I = (7,300)(.04)(8)
I=$2,336
Problem 3: If the outdoor temperature is 77F , what is the temperature in Celsius?
Show your work.
5
( F  32)
9
5
C  (77  32)
9
C
C  25
Answer:
(write correct formula)
(substitute given values)
(use calculator to simplify)
C  25
IMPORTANT!!!!!
IMPORTANT!!!!!
IMPORTANT!!!!!
This is from the NYSED website article entitled Instructional Recommendations for
Elementary and Intermediate Mathematics Instruction Updated May 2006.
Pi
Students should learn that  is an irrational number and, unless otherwise specified, the  key and the full
22
display of the calculator should be used in computations.  is not equal to 3.1416, 3.14 nor
. When
7
working without a calculator, students should leave their answers in terms of  for greatest accuracy.
NAME ______________________________________
Day 2
GRADE 8
Problem 1: Find the amount of simple interest earned if $7,300 is invested for 8 years at a rate of 4%.
Answer _____________________________
Problem 2: If the outdoor temperature is 77F , what is the temperature in Celsius?
Show your work.
Answer: __________________
Mathematics Reference Sheet – Grade 8
FORMULAS
_____________________________________________________________________________________
Simple Interest
I = prt
_____________________________________________________________________________________
Distance Formula
d = rt
_____________________________________________________________________________________
CONVERSIONS
Temperature Conversions
F
9
C  32
5
C
5
( F  32)
9
Measurement Conversions
1 mile = 5,280 feet
1 yard = 3 feet
Countdown-to-the-Tests
Mini Lesson for Day 3
TOPIC: Directions on test
Each year when we score the NYS tests we find student errors based on not following or
not interpreting the directions correctly. This mini lesson is designed to highlight some
of those errors. The following information applies to both Grade 7 and 8.
GRADE 8
Multiple-choice questions
 Encourage students to answer ALL of the multiple-choice questions. Tell them to take an
“educated” guess and to not leave any blanks.
 Students may do their work in Book 1and 2 that contains the multiple-choice questions.
 Students may NOT use scrap paper for Book 1 and 2.
 Students will record answers on a separate scanning sheet, so make sure students understand that
accuracy in recording answers is very important.
 Only answers on the scanning sheet will be corrected. Students must transfer their answers to this
sheet.
Short-response and extended-response questions
 If “Answer __________” is provided…
o If the student shows appropriate work, arrives at a correct answer BUT writes an
incorrect answer on the answer blank, the student may NOT receive full credit.
o If a student fails to write the answer in the answer blank when the question requires that
work must be shown, but shows appropriate work and clearly identifies a correct answer,
the student should still receive full credit.
o If there is one numerical answer space provided and work is required, a correct
numerical answer with no work shown receives a score of 1.
o If there are two numerical answer spaces provided and work is required for both parts,
then one correct numerical answer with no work shown receives a score of 0. If no work
is shown the student must have BOTH numerical answers correct to receive a score of 1.
o In a 3-point question that has two numerical answer spaces but work is required for only
one of them, then the student can receive a score of 2 if both numerical answers are
correct but no work is shown.
 Encourage your students to always write their answers in the answer spaces
provided.
 If “On the lines below, explain…” is provided…
o If ruled lines are provided, the student must write his/her explanation ON THOSE
LINES. Mathematical work shown elsewhere on the page may NOT be considered
unless the student explicitly points to the work as part of the answer.
 So train your students on the use of the ruled lines when lines are provided.
 If “Show your work” is required…
o If a student does the work in other than the “show your work” area, that work may still
be scored.
o If the question indicates “show your work”, a student will NOT receive full credit for a
correct numerical answer unless appropriate work is shown.
o If the student shows appropriate work, arrives at a correct answer BUT writes an
incorrect answer on the answer blank, the student may NOT receive full credit.
o If the question does not indicate for the students to show their work, then teachers may
NOT score any work that the student shows.
 If “Trial-and-error” OR “Guess-and-check” method is used….
o Student must show evidence of three rounds of trial-and-error to receive credit for the
process. One of the trials must result in the correct answer.
o If the student uses this method, he/she may cross out some trials and still receive full
credit if three trials are shown.
 “Run-on math sentence”
o You may see this error when students simplify an expression.
o An example is: Simplify this expression (4+7)  5
 And the student writes this, 4+7 = 11  5 = 55
 The student will NOT receive full credit because this math sentence says that
4+11 is 55 which is an incorrect statement.
 “Expressions vs. equations”…
o If a student is asked to provide an expression but instead provides an equation, then the
student will NOT receive full credit.
 Graphs… (Graphs are part of the Grade 7 Statistics & Probability Strand)
o If a student is asked to provide a bar graph, the bars MAY NOT TOUCH.
 “Rounding vs. estimating”…
o If a question requires an estimated answer but the student calculates an answer using
the given values and then rounds the answer, the student will NOT receive full credit.
 Show your students the difference between rounding and estimating.
 “Crossed-out work”…
o If the student provides one legible response (and one response only), teachers should
score the response, even if it has been crossed out. If the student has written more than
one response but has crossed some out, teachers should score only the response that
has not been crossed out.
NAME _____________________________________
Day 3 GRADE 8
Problem 1:
Rowan raised $640 in a charity walk last year. This year he raised 15% more than he raised last year. How
much money did Rowan raise this year?
Show your work.
Answer $______________________
Problem 2:
Countdown-to-the-Tests
Mini Lesson for Day 4
TOPIC: Rubrics
We score the short-response and extended-response questions on the NYS tests using
the 2-Point and 3-Point Holistic Rubrics provided by NYSED.
The following information applies to both Grade 7 and 8.
GRADE 7 AND GRADE 8
 Using the rubrics and the other information learned earlier of requirements that must be done when
completing short-response and extended-response questions, have the students use their skills to
score questions.
 Have the students work independently to complete the problems for day 4.
 Once the papers are completed, have two or three students volunteer to put their answers on
transparencies or on newsprint. FYI…this would be a perfect time to use an ELMO if one is available
in your school!
 Have the class discuss what score the paper should receive based on the rubrics and other
knowledge they have of scoring papers.
 Now have students score their own papers. Have them write their answer as Score A. Have
students write a justification for the score.
 Once this is completed, have the students exchange papers and re-grade them to see if they score
the papers the same. This score is recorded as Score B. Have students justify the score.
NAME _____________________________________
Day 4
GRADE 8
Problem 1:
Tyrone travels internationally on business. On a trip to Japan, Tyrone uses the exchange rates in
the tables shown below.
U.S. Dollar Japanese Yen
$1.00
115.19¥
Japanese Yen U.S. Dollar
1¥
$0.008681
What is the value of 75 U.S. dollars in Japanese yen? Round your answer to the nearest yen.
Show your work.
Answer ________ ¥
Score Problem 1 using the 2-Point Holistic Rubric.
Score _______
______________________________________________________________________
Problem 2: (8.G.4) AND (8.G.5) Lines SR and NU are parallel.
PART A
M
Find the value of x.
Show your work.
(4x-29)
S
R
P
N
Answer _____________
T
U
(3x+12)
Q
PART B
What is the measure in degrees of MPR ?
Show your work.
Answer _____________ degrees
Score Problem 2 using the 3-Point Holistic Rubric.
Problem 3. Solve the following system of equations graphically:
Score _______
y = 2x – 5
y = -x + 1
Answer __________
Score Problem 2 using the 3-Point Holistic Rubric.
Score _______
2-Point Holistic Rubric
Countdown-to-the-Tests
Mini Lesson for Day 5
TOPIC: Tools (Protractor & Ruler)
Each student must have a ruler and each Grade 7 student must also have a protractor
for his or her exclusive use during the test. In the past NYSED provided new plastic
rulers and protractors. Your building’s math specialist or test liaison received these
tools. Use these tools PRIOR to the state exam on May 5 and 6 so that your students
are familiar and comfortable using these tools before they need them on the state exam.
Rulers and protractors will NOT be replaced by NYSED if they are lost or broken. This
will be the responsibility of the school. This is the web address to find the SED guidelines
for rulers and protractors. http://www.p12.nysed.gov/apda/sam/math/mathei-sam-11.pdf
Grades 5-8 Mathematics Tests – Specifications for Rulers
� Rulers may be constructed of plastic, wood, metal, cardboard, or other suitable material.
� Rulers must be between 6" and 12" long.
� Rulers must include inch to
1
" subdivisions.
16
� Rulers must include centimeters with millimeter subdivisions.
� Rulers must be calibrated accurately with the Ruler/Protractor Calibration Sheet.
Grades 5 and 7 Mathematics Tests – Specifications for Protractors
� Protractors must be of clear plastic and measure no shorter than 3
15
3
" in diameter and no longer than 4 "
16
4
in diameter.
� Protractors must be calibrated accurately with the Ruler/Protractor Calibration Sheet.
If the ruler or protractor icon is shown on a particular question it means that the student
MUST use this tool to complete the question.
If the ruler or protractor icon is NOT shown on a particular question it means that the
student should not use the math tools to solve the problem. When this occurs the
question will show [NOT DRAWN TO SCALE].
GRADE 8
 Measurement Strand:
 Performance Indicator 7.M.1 is “calculate
distance using a map scale”
(FYI…this is a May-June PI for Grade 7 so it is
tested on the Grade 8 exam.)
NAME ______________________________________
MEASUREMENT STRAND
Day 5
GRADE 8
Problem 1: (7.M.1) What is the actual distance between City A and City B on a map with
a scale of
1
inch = 40 miles?
2
Use your ruler to help you solve this problem.
City A
Show your work.
City B
Answer: _______________ miles
-------------------------------------------------------------------------------------------------Problem 2:
Directions: Use your ruler to help you solve this problem.
Maria is planning a car trip from Niagara Falls to East Aurora.
What is the approximate driving distance from Niagara Falls to East Aurora?
ANSWER_____________
NAME _____________________________________
ALGEBRA STRAND
Day 6
GRADE 8
Problem 1: (7.A.10)
PART A
Write the equation for the rule of the pattern in the table.
x
1
2
3
4
y
8
13
18
23
Answer ________________________
PART B
Using the equation you wrote for the rule of the pattern in the table; find the value of y when
x is 12.
Show your work.
Answer ________________________
-------------------------------------------------------------------------------------------------Problem 2:
(8.A.1)
Rashid wrote the sentence below.
Forty-eight is greater than or equal to four plus the product of a certain number, x , and eleven.
Write Rashid’s sentence as an algebraic inequality.
Answer _____________________________________________________________
------------------------------------------------------------------------------------------------Problem 3: (8.A.11)
a.
Write these expressions in factored form.
x 2  6x  8
b. n  7 n  10
2
c.
y2  y  6
Answer a. ___________________
b. ____________________ c.____________________
Problem 4: (8.A.3)
NAME ______________________________________
ALGEBRA STRAND
Day 7
GRADE 8
Problem 1: (8.A.2) Write an algebraic expression that represents this phrase:
six years younger than twice Denita’s age
Use the variable, d, to represent Denita’s age.
Answer _________________________
-------------------------------------------------------------------------------------------------Problem 2: (8.A.1) The 8th grade class wants to rent a tent for its Pi Day celebration. There is a flat fee
of $50 plus $20 per hour to rent the tent. The class has a budget of $180 to use for the
tent rental.
PART A
Write an inequality to find h, the number of hours the class can rent the tent and still stay
within its budget.
Answer _________________________________
PART B
The Company will only rent the tent for WHOLE number of hours. How many hours will the
class be able to rent the tent and still stay within its budget?
Show your work.
Answer ________________ hours
--------------------------------------------------------------------------------------------------2
Problem 3: (8.A.7) The area of Rectangle A is x  5 x  6 square units. The area of Rectangle B is
6 x 2  7 x  2 square units.
How much larger is Rectangle B than Rectangle A?
Show your work.
Answer ________________ square units
Problem 4: (8.A.6)
Problem 5: (8.A.7)
NAME ______________________________________
GEOMETRY STRAND
Day 8
GRADE 8
Problem 1: (8.G.4) AND (8.G.5) Lines m and n are parallel and cut by transversal t.
Find the value of x.
m
2(x+7)
Show your work.
4(23-x)
n
t
[not drawn to scale]
Answer ___________
--------------------------------------------------------------------------------------------------Problem 2: (8.G.4) AND 8.G.5) Lines m and n are parallel and cut by transversal t .
PART A
Find the value of x.
Show your work.
m
4(x + 50)
(5x + 151)
n
t
[not drawn to scale]
Answer ___________
PART B
Find the measure of the angle represented by the expression (5x +151).
Show your work.
Answer ___________ degrees
Problem 3: (8.G.2)
Problem 4: (8.G.1)
NAME ______________________________________
GEOMETRY STRAND
Day 9
GRADE 8
Problem 1: (8.G.11)
The table below shows the coordinates of triangle RST and the coordinates of R' in triangle R'S'T'. Triangle
R'S'T' is a dilation of triangle RST.
Triangle
RST
R (-2, -3)
S
(0,2)
T
(2, -3)
Triangle
R'S'T'
R' (-6, 9)
S'
T'
Part A
What are the coordinates of point S' and point T'?
Answer S' = (____, ____)
T' = (____, ____)
Part B
On the grid below, draw triangle RST and triangle R'S'T'
--------------------------------------------------------------------------------------------------
Problem 2: (8.G.10) Draw the translation of the figure ABCD 4 units down and 3 units left.
y-axis
A
B
x-axis
D
C
Be sure to
 draw the translated shape
 label the translated shape
ABC D
What are the coordinates for point A ?
Answer ( _____ , ______)
Day 9 continued GRADE 8
GEOMETRY STRAND
Problem 3: (8.G.9) Draw the reflection of the figure ABCD in the x-axis.
y-axis
A
B
x-axis
D
C
Be sure to
 draw the reflected shape
 label the reflected shape
ABC D
What are the coordinates for point B  ?
Answer ( _____ , ______)
-------------------------------------------------------------------------------------------------------------Problem 4: (8.G.8) Rotate figure ABCD 180 counterclockwise.
y-axis
A
B
x-axis
D
C
Be sure to
 draw the rotated shape
 label the rotated shape
ABC D
What are the coordinates for point
C ?
Answer ( _____ , ______)
NAME ______________________________________
Day 10
NUMBER SENSE & OPERATIONS AND MEASUREMENT STRANDS
GRADE 8
Problem 1: (8.N.4) The number of students at Kennedy High School last year was 1045. This year the
high school has 1390 students.
Find the percent of increase in the student population. Round your answer to the nearest
whole percent.
Show your work.
Answer ___________
-------------------------------------------------------------------------------------------------Problem 2: (8.N.4) The Williams family borrowed money to expand their restaurant. They borrowed
$100,000 From the bank at 7.5% simple interest for 8 years.
How much total interest will they pay? Use the formula I = prt .
Show your work.
Answer $___________
--------------------------------------------------------------------------------------------------3
Problem 3: (8.N.3) Write % as a decimal value.
8
Show your work.
Answer ___________
--------------------------------------------------------------------------------------------------------------------Problem 4: (7.M.1) The scale on the map is 1 cm = 50 miles. If the distance on the map from New
York City to Yonkers is 0.3 cm, then what is the actual distance?
Show your work.
Answer ___________ miles
Day 10 continued GRADE 8
NUMBER SENSE & OPERATIONS AND MEASUREMENT STRANDS
Problem 5: (7.M.5) A 17-ounce package of pasta costs $4.12. What is the unit price of the pasta?
Show your work.
Answer ___________
------------------------------------------------------------------------------------------------Problem 6: (8.N.2) What is the value of x
5
when x = 2 ?
Show your work.
Answer ___________
------------------------------------------------------------------------------------------------Problem 7: (8.N.5) In a survey of 505 people, about 57% said they have traveled to Niagara Falls.
Which is the best estimate of the number of people in the survey who said they traveled to
Niagara Falls?
Choose from:
250, 300, 350, or 400
Show your work.
Answer ___________
--------------------------------------------------------------------------------------------------2
Problem 8: (8.N.2) Evaluate x  10 x  25 when x  15 .
Show your work.
Answer ___________