Instructional Week 7: February 16-19
Grade 8 ISTEP+
Focus Topic: Spiral Review
Assessed Standards:
8.C.1: Solve real-world problems with rational numbers by using multiple operations.+
8.AF.1: Solve linear equations with rational number coefficients fluently, including equations whose
solutions require expanding expressions using the distributive property and collecting like terms.
Represent real-world problems using linear equations and inequalities in one variable and solve such
problems.+
8.AF.6: Construct a function to model a linear relationship between two quantities given a verbal
description, table of values, or graph. Recognize in y = mx + b that m is the slope (rate of change) and b is
the y-intercept of the graph, and describe the meaning of each in the context of a problem.+
8.GM.8: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and other mathematical problems in two dimensions.+
PS: 1, 2, 3, 4, 5, 6, 7, and 8 +
Process Standards to Emphasize with Instruction
PS.1: Make sense of problems and persevere in solving them.
PS.2: Reason abstractly and quantitatively.
PS.3: Construct a viable argument and critique the reasoning of others.
PS.4: Model with mathematics.
PS.5: Use appropriate tools strategically.
PS.6: Attend to precision.
PS.7: Look for and make use of structure.
PS.8: Look for and express regularity in repeated reasoning.
Data
Analyze your classroom data from the weekly assessments and Acuity tests to determine where students are
struggling and why. Use the resources in the ISTEP+ plan, the resource documents, and online resources to
implement a new teaching plan.
Assessment
This week’s assessment is longer and is intended to take 45-50 minutes. The assessment is written in the
format of Applied Skills Part 1. Students should use a calculator and the ISTEP+ Mathematics Reference
Sheet Grade 8, which is attached on the last page of this plan. It is important to simulate the testing
environment in class to help prepare the students for ISTEP Applied Skills Part 1. The four standards
chosen for the assessment this week are all check plus standards, critical standards.
Instructional Week 7 Assessment
ISTEP+ Grade 8
Name______________________________
(8.AF.1) 1. Anthony’s cell phone company charges $35 a month for unlimited calls, and $0.25 for each text message.
In January his cell phone bill was $55.75.
Part A: Write an equation that can be used to determine the number of text messages Anthony made in
January. Be sure and define the variable in your equation.
Define your variable________
Equation_________________
Part B:
How many total text message did Anthony make in January?
Show all work.
Answer_____________________text messages
Part C: In February, Anthony’s cell phone bill was $54.25. He claims he made 72 text messages in February.
Explain why Anthony’s claim is incorrect.
_______________________________________________________________________________________________
_______________________________________________________________________________________________
_______________________________________________________________________________________________
Part D: How many text messages did Anthony make in February?
Show all work.
Answer:________________text messages
(8.AF.6) 2. A car is traveling down a long, steep hill. The elevation, E, above sea level (in feet) of the car when it is d
miles from the top of the hill. The table represents the distance from the top of the hill and the elevation
above sea level.
d miles
0
1
2
3
4
5
6
E feet
7500
7250
7000
6750
6500
6250
6000
Part A: Write an equation for the elevation of the car in terms of the distance the car is from the top of
the hill.
Equation:______________________________
Part B: Find the slope and y-intercepts of the graph of this function and explain what they mean in the
context of the moving car.
Slope is ________________________________
intercept is ___________________________
Explain_____________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
Part C: If the elevation is 6,400 feet above sea level, how far is the car from the top of the hill?
Show all work.
Answer:__________________miles
Part D: Does your answer in Part C make sense? Explain.
Explain_____________________________________________________________________________
___________________________________________________________________________________
(8.GM.8) 3. A cruise ships’ captain knows that a lighthouse on the coast is 150 m tall. The distance from the front of the
cruise ship to the top of the lighthouse is 230 m.
Part A: Write an equation to determine how far away is the cruise ship from the center of the base of the
lighthouse?
Equation:________________________
Part B: Solve the equation from Part A. Round up to the nearest meter.
Show your work.
Answer:________________________meters
Part C: Is your answer to Part B reasonable? Explain.
Explain_____________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
(8.C.1) 4. When working on a report for class, Catrina read that a woman over the age of 40 can lose approximately
0.0762 centimeters of height per year.
Part A: Catrina's aunt Nancy is 40 years old and is 5 feet 7 inches tall. Assuming her height decreases at this rate
after the age of 40, about how tall will she be at age 65? (Remember that 1 inch = 2.54 centimeters).
Show your work.
Nancy’s height_________________
Part B: Catrina's 90-year-old grandmother is 5 feet 1 inch tall. Assuming her grandmother's height has also
decreased at this rate, about how tall was she at age 40? Explain your reasoning.
Catrina’s grandmother height____________________
Explain______________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Instructional Week 7 Assessment Key
ISTEP+ Grade 8
(8.AF.1) 1. 2 points per part.
Part A: Define your variable t = number of text messages per month.
Equation: 55.75 = 35 + 0.25 t
Part B: 83 text messages
Part C: Anthony’s bill would be $53, if he made 72 text messages.
Part D:77 text messages
(8.AF.6) 2. 2 points per part.
Part A: E= 7500-250d
Part B: Slope is -250
intercept is 7,500
The slope is −250, which can be interpreted as a rate of change:
The elevation will decrease by 250 feet for every mile it travels.
The E intercept is 7500, which means the elevation of the car is 7500feet above sea level at mile 0.
The d intercept is 30, which means that if the car traveled in this same manner for 30 miles, it would
be at an elevation of 0.
Part C: 6,400 = 7,500 -250d Answers may vary in method of solving equation
4.4 miles
Part D: My answer of 4.4 miles makes sense. On the table given in the problem when the distance is 4 miles
from the top the elevation is 6,500 feet and when the distance is 5 miles the distance is 6,250 feet, so
it makes sense that when the elevation is 6,400 feet the distance from the top is between 4 and 5
miles from the top of the hill. Answers will vary
(8.GM.8) 3. 2 points per part.
Part A: 1502 + x2= 2302
Part B: 175 meters
Part C: The answer of 175 meters makes sense. The leg of the triangle cannot be longer than the
hypotenuse which is 230 meter. 175 is less than 230 so therefore it is a reasonable answer.
Explanations may vary..
(8.C.1) 4. 2 points per part.
Part A: In the 25 years from age 40 to age 65, Nancy could be expected to lose
25(.0762/2.54)=0.75 inches. Subtracting this from Nancy's current height, Nancy's height at
age 65 could be expected to be approximately 5 feet, 6 1/4 inches.
Part B: In the 50 years from age 40 to age 90, Catrina's grandmother could be expected to lose approximately
twice Nancy's loss in height, or 1.5 inches. Adding this to Catrina's grandmother's current height,
Catrina's grandmother could be expected to have been 5 feet, 2 ½ inches tall at age 40.
All constructed response problems will be graded using the ISTEP+ Content Rubric.