Mathematics Vision Project Year 3: Achievement Levels by Module

Created Feb. 7, 2024 by David Parascand

Integrated 3
Achievement Levels by Module

Functions and their inverses: Year 3 Module 1-skip	Level 1	Level 2	level 3	level 4
Equivalence Determine the equation for the inverse of a function. (Linear, quadratic, exponential, square root) Convert between exponential and logarithmic form.		Can write the equation for the inverse of a simple function	Can write the equation for the inverse of any function	Can identify if equations are inverses using multiple methods
Analyze / Interpret Identify the domain and range of a function. (Linear, quadratic, exponential, square root) Restrict the domain to make a function invertible.		Can identify the domain and range of basic functions	Can identify the domain and range of functions and restrict the domain to make a function invertible	Satisfies all requirements for a level 3 and can explain their reasoning
Solving Evaluate a function for a specific value. (numerical and variable) Describe process of “solving by undoing”. (Linear, quadratic, exponential, square root)		Can evaluate a function for a specific value/variable Can solve basic equations by “undoing”	Can compose functions Can solve multi-step equations by “undoing	Satisfies all requirements for a level 3 and can explain their reasoning

Logarithmic functions: Year 3 Module 2	Level 1	Level 2	level 3	level 4
Equivalence Evaluate logarithmic expressions and place in order Apply properties of logarithms to write expressions in equivalent forms.		Can evaluate logarithms with integral values Can apply a single property to re-write an expression	Can evaluate / estimate logarithms without technology Can apply all properties to re-write expressions	Satisfies all requirements for a level 3 and can explain their reasoning
Analyze / Interpret Graph logarithmic functions and describe transformations Identify the domain and range of a function. (Linear, quadratic, exponential, Logarithmic, square root)		Can describe transformations given graphical or algebraic representation Can describe domain/range from a graph or algebraic representation	Can describe transformations given graphical and algebraic representation Can describe domain/range from a graph and algebraic representation	Can describe transformations and explain connections to algebraic representation Can describe domain/range from a graph and explain connections to algebraic representation
Solving Solve exponential and logarithmic equations. Describe process of “solving by undoing”. (Linear, quadratic, exponential, square root)		Can solve basic equations	Can solve multi-step equations	Satisfies all requirements for a level 3 and can explain their reasoning

Polynomial functions: Year 3 Module 3	Level 1	Level 2	level 3	level 4
Equivalence Add, subtract, and multiply polynomials algebraically, graphically and numerically (Table). Write a polynomial in factored form.		Can perform operations with a single representation	Can perform operations using multiple representations	Can perform operations using multiple representations and explain connections
Analyze / Interpret Identify key features of a polynomial function: Domain & Range Relative maximum & minimum values Increasing / decreasing intervals End behavior Graph a polynomial function given features		Can identify most key features of a polynomial functions given graph and/or equation	Can identify all key features of a polynomial functions given graph and/or equation Can sketch the graph given key features	Satisfies all requirements for a level 3 and can explain connections between representations
Solving Determine the zeros of a polynomial function Evaluate a polynomial function		Can apply the fundamental theorem of algebra to determine the roots of a polynomial function given some representations	Can apply the fundamental theorem of algebra to determine all of the roots of a polynomial function given in any representation	Satisfies all requirements for a level 3 and can explain their reasoning

Rational functions Year 3 Module 4	Level 1	Level 2	level 3	level 4
Equivalence Perform arithmetic operations on rational expressions Rewrite a rational expression in quotient and remainder form		Can perform arithmetic operations on simple forms of rational expressions	Can perform arithmetic operations on all types of rational expressions	Can perform arithmetic operations on all types of rational expressions and explain connections to rational number operations
Analyze / Interpret Identify the vertical intercept, x-intercepts, domain, range, asymptotes, and end behaviors of a rational function. Graph rational functions without technology. Identify the parent function and transformations applied to the parent function.		Can identify most key features of a polynomial functions given graph and/or equation	Can identify all key features of a rational functions given graph and/or equation Can sketch the graph given key features	Satisfies all requirements for a level 3 and can explain connections between representations
Solving Determine the roots of rational functions Solve rational equations		Can determine all the roots of a rational function given a specific representation	Can determine all the roots of a rational function given any representation, identifying any extraneous solutions	Satisfies all requirements for a level 3 and can explain their reasoning

Trigonometric functions Year 3 Module 6	Level 1	Level 2	level 3	level 4
Equivalence Convert between radians and degrees Identify angles with equivalent Sine or Cosine values I can fluently identify trigonometric values of common angles on the unit circle.		Can convert between radians and degrees	Can explain relationship between radians and degrees Can determine angles with equivalent values	Can determine angles with equivalent values and explain connections between trigonometric properties and unit circle representations
Analyze / Interpret Sketch a trigonometric function. Identify key features of a trigonometric function (amplitude, period, phase shift, and midline) given an equation, graph or verbal description. Identify the effect of transformations on the graph of a trigonometric function in and out of context.		Can identify most key features of a trigonometric functions given graph and/or equation	Can identify all key features of a trigonometric functions given graph and/or equation Can sketch the graph given key features	Satisfies all requirements for a level 3 and can explain connections between representations
Solving Evaluate trigonometric functions at specific values Determine the roots of trigonometric functions Solve trigonometric equations		Can evaluate and determine solutions to trigonometric equations using graphical representations / technology	Can evaluate and determine solutions to trigonometric equations algebraically	Satisfies all requirements for a level 3 and can explain connections to graphical representation

Statistics Year 3 Module 8	Level 1	Level 2	level 3	level 4
Equivalence
Analyze / Interpret Identify key features of a normal distribution Identify sampling methods Identify methods to investigate a parameter		Can identify if data is normally distributed Can identify if sample is random or non-random Identify most methods to investigate a parameter	Understand how changes in mean & standard deviation affect normal distribution Utilize z-scores to analyze distribution Can identify all six sampling methods Identify all methods to investigate a parameter	Satisfies all requirements for a level 3 and can explain strengths and weaknesses of each method
Solving