Grade 8 - Instructional Information Services â€“ … · Web viewA cone has a radius of 1.2 inches and a height of 2.9 inches. What is the volume, to the nearest tenth of a cubic

Grade 8 AIR POD Day #1 Name: ______________________________________________




Common Core State Standard: 8.G.7Apply the Pythagorean Theorem to determine the unknown side lengths in right triangles with real-world and mathematical problems in two and three dimensions.


Common Core State Standard: 8.G.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

A cone has a height of 6.4 inches and a diameter of 6 inches.

What is the volume, in cubic inches, of the cone? Use 3.14 for π.

Answer: __________


Common Core State Standard: 8.NS.1Understand informally that every number has a decimal expansion; the rational number are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.


Answer: m = __________ and n = __________



Common Core State Standard: 8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.


Common Core State Standard: 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

A cone has a radius of 1.2 inches and a height of 2.9 inches. What is the volume, to the nearest tenth of a cubic inch, of the cone?

Answer: __________


Common Core State Standard: 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.


Common Core State Standard: 8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Jenny wants to rent a truck for one day. She contacted two companies. Laguna’s Truck Rentals charges $20 plus $2 per mile. Salvatori’s Truck Rental charges $3 per mile. After how many miles will the total cost for both companies be the same?

Answer: __________


Common Core State Standard: 8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.


Common Core State Standard: 8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

A line has a slope of 2 and includes the points (4, 9) and (2, q). What is the value of q?

Answer: _________


Common Core State Standard: 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

You are given the graph of a rectangle. Draw the rectangle that would result from a reflection over the x-axis.


Common Core State Standard: 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Answer: __________


Common Core State Standard: 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Answer: __________


Common Core State Standard: 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

You are given a graph. Find the slope (m).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer: __________


Common Core State Standard: 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Solve the proportion.

4540

= h32

Answer: __________


Common Core State Standard: 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Shade the circle next to each of the expressions below that are equivalent to 2−3

23.

26

126

12−1

2−6


Common Core State Standard: 8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Read the following description of a relationship:

In every Olympic event, 3 medals are awarded.

Let v represent the number of events and m represent the number of medals.

Below are numbers representing possible values for m. Drag the correct values into the m column in the table at right that complete the function m = 3v.


Common Core State Standard: 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Use the equation editor to write the linear equation that gives the rule for the table below:


Common Core State Standard: 8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Tanner baked 10 cookies with 2 scoops of flour. Another day, he baked 15 more cookies with 3 scoops of flour. How many cookies can be made with one scoop of flour?

Answer: __________


Common Core State Standard: 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.


Common Core State Standard: 8.EE.8 Analyze and solve pairs of simultaneous linear equations.

Answer: __________


Common Core State Standard: 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Answer: __________


Common Core State Standard: 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.


Common Core State Standard: 8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Answer: __________

Grade 8 AIR POD Day #1 ANSWER KEY ANSWER KEY

The point value of this type of question is not known at this time. A question like this could be worth three points: one for each row of the table. Students likely would have to mark all correct choices for each row in order to be awarded the point for that row.



Be careful: that’s a “plus” sign in between the ( ).


Students should understand that they need to find all three sides of the triangle and mark all three answer choices.


A cone has a height of 6.4 inches and a diameter of 6 inches.

What is the volume, in cubic inches, of the cone? Use 3.14 for π.Answer: 60.288

This question specifically tells students to use 3.14 for π. If a student uses the π button on the calculator instead, the answer will have more decimal places than expected and may be scored as incorrect.


It’s not known at this time whether a question like this is worth 1, 2, or even 4 points.


Answer: m = 1 and n = -3


Note that credit for this problem is likely all-or-nothing. Make sure no answers are left out.


Common Core State Standard: 8.EE.6

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.


Common Core State Standard: 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

A cone has a radius of 1.2 inches and a height of 2.9 inches. What is the volume, to the nearest tenth of a cubic inch, of the cone?

Answer: 4.4

Be careful when rounding. Answers must be answered as decimals rounded to the correct number of places.


Common Core State Standard: 8.G.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.


Common Core State Standard: 8.EE.8c

Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Jenny wants to rent a truck for one day. She contacted two companies. Laguna’s Truck Rentals charges $20 plus $2 per mile. Salvatori’s Truck Rental charges $3 per mile. After how many miles will the total cost for both companies be the same?

Answer: 20


Common Core State Standard: 8.F.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.


A line has a slope of 2 and includes the points (4, 9) and (2, q). What is the value of q?

Answer: 5


You are given the graph of a rectangle. Draw the rectangle that would result from a reflection over the x-axis.

This question can be asked in a variety of ways. Students could be given a list of new ordered pairs and have to select the correct set of pairs that would represent a reflection. When testing on a computer, students could be required to use the graphing tools to plots points and create the line segments. Make sure students practice the sample tests, available on the CCS website (Math page), in order to become familiar with using the graphing tools.


Answer: 86


Answer: 4


You are given a graph. Find the slope (m).

Simplify your answer (in lowest terms) and write it as a proper fraction, improper fraction, or integer.

Answer: 13

Make sure students follow directions when told to write an answer as a fraction or decimal. If the test is expecting a fraction, and a decimal is entered (or vice versa), the problem may be marked incorrect. Also, make sure fractions are reduced.


Solve the proportion.

4540

= h32

Answer: 36


Shade the circle next to each of the expressions below that are equivalent to 2−3

23.

Remind students that some problems can have more than one answer. They should look for keywords such as “each” or “all” when referring to choices below.


Read the following description of a relationship:

In every Olympic event, 3 medals are awarded.

Let v represent the number of events and m represent the number of medals.

Below are numbers representing possible values for m. Drag the correct values into the m column in the table at right that complete the function m = 3v.


Use the equation editor to write the linear equation that gives the rule for the table below:


Tanner baked 10 cookies with 2 scoops of flour. Another day, he baked 15 more cookies with 3 scoops of flour. How many cookies can be made with one scoop of flour?

Answer: 5



Answer: -2


Answer: 300



Answer: -1

This type of question could appear on the calculator or non-calculator section.

SOURCES

The following sources were referenced in creating these problems:

Problems 1-13:http://www.fsassessments.org

Problems 14-28:http://www.ixlmath.com

http://www.ixlmath.com/

http://www.fsassessments.org/

Documents

Grade 8 - Instructional Information Services â€“ … · Web viewA cone has a radius of 1.2 inches and a height of 2.9 inches. What is the volume, to the nearest tenth of a cubic