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Difficult Readiness Standards

Standard	# of items	% mastery	Standard	# of items	% mastery
A.11B	2	30.5	A.2I	1	39
A.7C	1	48	A.5A	2	42.5
A.8A	1	30	A.9C	2	43.5
A.2A	2	39	A.6A	2	45.5
A.9D	2	49.5	A.5C	2	49.5

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A.11B (Reporting Category 1) - 30.5% overall mastery

simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents

#10 - 38% correct #35 - 4% full credit, 38% partial credit, 58% no credit

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A.11B (Reporting Category 1) - 30.5% overall mastery

simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents

Fractions add a layer of complexity to dividing exponents or finding the power of a power
The drag and drop response required you to use the same number twice (not all drag and drops allow using a response more than once)
Utilize fractions when asking students to multiply or divide by exponents
Bundle multiple laws of exponents into a single problem (e.g., radicals and division)
Have students practice rewriting dividing exponents as multiplying by negative exponents (e.g., x = x x )

4 4 -2

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A.7C (Reporting Category 4) - 48% overall mastery

determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d

#38 - 30% full credit, 35% partial credit, 35% no credit

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A.7C (Reporting Category 4) - 48% overall mastery

determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d

Drag and drop removed certainty for partial guesses
Students had to analyze both a vertical and horizontal transformation simultaneously
The horizontal transformation (- 3) actually moves the vertex to the right
Bundle problems so that students multiple transformations together
Have students practice graphing the child function (correctly with exponent) to analyze the vertex

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A.8A (Reporting Category 4) - 30% overall mastery

solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

#41 - 30% correct

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A.8A (Reporting Category 4) - 30% overall mastery

solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

Distribution of answer selections (30%, 28%, 27%, 14%) indicative of guessing
Answer choices required simplifying a radical
Multiple strategies could have been used to solve the problem
Focus on correctly applying quadratic formula
Emphasize problems that require simplifying a radical
Have students solve the same problem using at least two different strategies

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A.2A (Reporting Category 3) - 39% overall mastery

determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities

#7 - 33% full credit, 22% partial credit, 44% no credit

#46 - 34% correct

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A.2A (Reporting Category 3) - 39% overall mastery

Responses were required in verbal form (rather than as inequalities)
Students had to differentiate between open and closed circles
Problems required analysis of both domain and range simultaneously
Bundle problems so that students assess both domain and range together
Have students draw rays that satisfy requirements of both domain and range
Provide error analysis opportunities for students to disprove why graphs do NOT represent a given domain and range

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A.9D (Reporting Category 5) - 49.5% overall mastery

graph exponential functions that model growth and decay and identify key features, including y- intercept and asymptote, in mathematical and real-world problems

#42 - 55% correct

#9 - 14% full credit, 59% partial credit,

27% no credit

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A.9D (Reporting Category 5) - 49.5% overall mastery

graph exponential functions that model growth and decay and identify key features, including y- intercept and asymptote, in mathematical and real-world problems

Both problems asked students to identify features of exponential graphs (i.e., asymptote, y-intercept)
Common error for asymptote was most likely labeling x-axis as x = 0
When working with standard form (y = ab ), also have students identify a as the y-intercept and explain why
When given an exponential function in equation or graph form, have students create a real-world situation to describe it, including naming the y-intercept

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A.2I (Reporting Category 3) - 39% overall mastery

write systems of two linear equations given a table of values, a graph, and a verbal description

#37 - 39% correct

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A.2I (Reporting Category 3) - 39% overall mastery

write systems of two linear equations given a table of values, a graph, and a verbal description

Distribution of answer selections (16%, 21%, 24%, 39%) indicative of guessing
Solving the problem required

Finding slope of each line
Substituting an ordered pair and solving for b for each line
Transforming each resulting slope-intercept form equation into standard form

Focus on applying correct sequence of formulas
Practice building stamina and how to check their answers with substitution or by graphing discrete points along with the systems of equations

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A.5A (Reporting Category 3) - 42.5% overall mastery

solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

#4 - 22% correct

#29 - 63% correct

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A.5A (Reporting Category 3) - 42.5% overall mastery

solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

Distribution of answer selections (27%, 21%, 30%, 22%) indicative of guessing
This type of problem (linear equations and distributive property) has never been asked without explicitly providing the equation
Find and utilize verbal descriptions of linear equations (using the distributive property) that do not explicitly provide the equation
Have students work in pairs to create their own problems (w/o explicit equations) and exchange with peers to solve

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A.9C (Reporting Category 5) - 43.5% overall mastery

write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

#14 - 37% correct #36 - 50% correct

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A.9C (Reporting Category 5) - 43.5% overall mastery

write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

Students were not provided a growth factor for one problem
Growth factor of 4% had to be translated to 1.04
Have students practice finding growth/decay factor when given initial and first-year amount
Provide rationale for translating a growth factor to 1 + decimal and a decay factor to 1 - decimal
Give students percentage (e.g., decay rate of 22%) and practice converting to decay factor (e.g., 0.78)

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A.6A (Reporting Category 4) - 45.5% overall mastery

determine the domain and range of quadratic functions and represent the domain and range using inequalities

#11 - 47% correct #32 - 44% correct

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A.6A (Reporting Category 4) - 45.5% overall mastery

determine the domain and range of quadratic functions and represent the domain and range using inequalities

Students needed to graph at least one problem to correctly identify range
Improper fractions in the table made visual sequencing challenging
Reinforce difference between domain and range and that domain is rarely limited in quadratic equations
Practice identifying range from a table by sketching a rough parabola with given points
Practice plotting discrete points in a graphing calculator to visually determine range

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A.5C (Reporting Category 4) - 49.5% overall mastery

solve systems of two linear equations with two variables for mathematical and real-world problems

#23 - 68% correct #40 - 31% correct

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A.5C (Reporting Category 4) - 49.5% overall mastery

solve systems of two linear equations with two variables for mathematical and real-world problems

Distribution of answer selections for #40 (16%, 26%, 27%, 31%) indicative of guessing
A system of equations question has never been asked using a table
Have students practice taking systems of equations questions (verbal descriptions and equations) and translating them to tables
Reinforce the qualities that define a system of equations (two or more equations that share variables) to better identify them in real-world situations