MAFS.8.EE Expressions and Equations - math …dspmsmath.weebly.com/uploads/2/3/7/0/23700515/mafs_8_ee_all...MAFS.8.EE.1.2 Use square root and cube root symbols to represent solutions

Grade 8 Mathematics Item Specifications Florida Standards Assessments

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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.1 Work with radicals and integer exponents. MAFS.8.EE.1.1 Know and apply the properties of integer exponents to generate

equivalent numerical expressions. For example, 32 ∙ 3−5 = 3−3 =1

32 =1

27.

Assessment Limits Exponents must be integers. Bases must be whole numbers. Variables may not be used.

Calculator No

Item Types Equation Editor GRID Matching Item Multiple Choice Multiselect

Context No context

Sample Item Item Type

Which expression is equivalent to 1

27?

A. 31 ∙ 3−10 B. 3−1 ∙ 310 C. 3−4 ∙ 37 D. 34 ∙ 3−7

Multiple Choice

Which expression is equivalent to (43) 2 ∙ 42? A. 47 B. 48 C. 410 D. 412

Multiple Choice

Which expression is equivalent to 54 ∙ (5−3)2 ? A. 51

B. 52

C. ( 1

5 )

1

D. ( 1

5 )

2

Multiple Choice


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Equation Editor


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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.1 Work with radicals and integer exponents. MAFS.8.EE.1.2 Use square root and cube root symbols to represent solutions to equations of the form 𝑥2 = 𝑝 and 𝑥3 = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.

Know that √2 is irrational.

Assessment Limits Square roots and cube roots may be used to represent solutions to equations. Radicands may be rational or irrational. Radicands may not include variables.

Calculator Neutral

Item Types Equation Editor Matching Item Multiple Choice Multiselect

Context Allowable


𝑝3 = 0.064

What is the value of 𝑝 in the equation shown?

Equation Editor

A cube with an edge of length s has a volume of 64 units. What is the length of the edge?

Equation Editor

Equation Editor


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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.1 Work with radicals and integer exponents. MAFS.8.EE.1.3 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. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

Assessment Limits N/A

Calculator No

Item Types Equation Editor Multiple Choice Open Response

Context Allowable


The average mass of a giraffe is approximately 1 × 103 kilograms. The average mass of a blue whale is approximately 2 × 106 kilograms. About how many times more mass does a blue whale have than a giraffe?

Equation Editor

Equation Editor


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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.1 Work with radicals and integer exponents.

MAFS.8.EE.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Assessment Limits N/A

Calculator No

Item Types Equation Editor Matching Item Multiple Choice

Context Allowable


What is the sum of 4 × 10−5 and 3 × 10−5 written in standard form? Equation Editor

Multiple Choice


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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.2 Understand the connections between proportional relationships, lines, and linear equations. MAFS.8.EE.2.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Assessment Limit Numbers in items must be rational numbers.

Calculator Yes

Item Types Equation Editor GRID Matching Item Multiple Choice Multiselect Open Response

Context Allowable


The graph of a proportional relationship is shown.

What is the unit rate?

Equation Editor

The graph of a proportional relationship is shown.

What is the unit rate?

Equation Editor


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GRID


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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.2 Understand the connections between proportional relationships, lines, and linear equations. MAFS.8.EE.2.6 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.

Assessment Limits All triangles must be right triangles and on a coordinate grid. Numbers in items must be rational numbers. Functions must be linear.

Calculator Yes

Item Types Equation Editor GRID Matching Item Multiple Choice Multiselect Open Response Table Item

Context Allowable


Select all pairs of triangles that can be used to show the slope of a line is the same anywhere along the line.

□

□

□

□

□

Multiselect


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Table Item


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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.3 Analyze and solve linear equations and pairs of simultaneous linear equations.

MAFS.8.EE.3.7 Solve linear equations in one variable.

o MAFS.8.EE.3.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 𝑥 = 𝑎 , 𝑎 = 𝑎, or 𝑎 = 𝑏 results (where 𝑎 and 𝑏 are different numbers).

o MAFS.8.EE.3.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Assessment Limit Numbers in items must be rational numbers.

Calculator Yes

Item Types Equation Editor Matching Item Multiple Choice Multiselect Open Response

Context Allowable


How many solutions does the equation shown have? 1

4(𝑥 − 3) = 3𝑥 −

11

4𝑥 − 3

Open Response

What values of 𝑎 and 𝑏 would make the equation shown have infinitely many solutions?

3𝑥 = 𝑎𝑥 + 𝑏

Equation Editor

What values of 𝑎 and 𝑏, in the equation shown, will result in an equation whose only solution is 𝑥 = 3? – 3

5(𝑥 − 5) + 4𝑥 = 𝑎𝑥 + 𝑏

Equation Editor

Solve the equation shown for 𝑥. 2(𝑥 − 4) = 4𝑥 + 3𝑥 + 6

Equation Editor


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Explain why 3(𝑥 + 4) = 3(𝑥 − 5) has no solution. Choose the best response below. A. The 𝑥-terms are the same, but the constant terms are different. B. The 𝑥-terms are different, but the constant terms are the same. C. The 𝑥-terms are the same, and the constant terms are same. D. The 𝑥-terms are different, and the constant terms are different.

Multiple Choice

Enter values of 𝑎 and 𝑏 for which 𝑥 = 4 is a solution of the equation shown. 𝑎𝑥 + 4 = 5𝑥 + 𝑏 𝑎 = 𝑏 =

Equation Editor

Matching Item


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Content Standard MAFS.8.EE Expressions and Equations MAFS.8.EE.3 Analyze and solve linear equations and pairs of simultaneous linear equations.

A. MAFS.8.EE.3.8 Analyze and solve pairs of simultaneous linear equations.

o MAFS.8.EE.3.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

o MAFS.8.EE.3.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

o MAFS.8.EE.3.8c 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.

Assessment Limits Numbers in items must be rational numbers. Coefficients of equations in standard form must be integers. Items written for MAFS.8.EE.3.8a will include the graph. Equations used in items must be provided.

Calculator Yes

Item Types Equation Editor GRID Matching Item Multiple Choice Open Response

Context Allowable


A graph of a system of two equations is shown.

Use the Add Point tool to plot the solution of the system.

GRID


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How many solutions does the system of two equations shown have?

𝑦 = 3(𝑥 + 4) 𝑦 = 3(𝑥 − 4)

Open Response


What is the solution of the system? 𝑥 = 𝑦 =

Equation Editor


What is the approximate solution of the system? ( , )

Equation Editor

What is the solution to the system of two equations shown? 5𝑥 + 4𝑦 = 12 3𝑥 + 6𝑦 = 8 ( , )

Equation Editor


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A system of two equations is shown. 𝑦 = 5𝑥 + 3 𝑦 = 4𝑥 − 5 A. Use the Add Arrow tool to graph the two lines. B. Drag the palette image to show the solution of the system.

GRID

Radha is trying to choose between two bike rental companies, Company A and Company B. Company A charges a $25 initial fee and an additional $5 for each hour rented. Company B charges an initial $18 fee and an additional $6 for each hour rented. The total cost to rent a bike from Company A can be represented by the equation 𝑦 = 5𝑥 + 25. The total cost to rent a bike from Company B can be represented by the equation 𝑦 = 6𝑥 + 18. For how many hours of rental is the amount charged by the two companies the same? What is the cost, in dollars, of renting the bike for this many hours? Hours = Cost =

Equation Editor

Enter values for 𝑎 and 𝑏, so that the system of equations shown has one solution. 𝑦 = 3𝑥 + 4 𝑦 = 𝑎𝑥 + 𝑏 𝑎 = 𝑏 =

Equation Editor

X


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Matching Item

Documents

MAFS.8.EE Expressions and Equations - math …dspmsmath.weebly.com/uploads/2/3/7/0/23700515/mafs_8_ee_all...MAFS.8.EE.1.2 Use square root and cube root symbols to represent solutions