Addition and Subtraction
Grades 0-4
Algebra
Grades 6-12
Calculus
Grades 10-12
Circles
Grades 6-12
Complex Numbers
Grades 10-12
Data/Graphing
Grades 1-9
Exponents
Grades 5-12
Factors/Primes
Grades 4-10
Fractions/Decimals
Grades 1-11
Functions
Grades 10-12
Geometry 2D
Grades 2-12
Geometry 3D
Grades 6-11
Matrices
Grades 9-12
Metric Units
Grades 6-12
Multiply/Divide
Grades 1-9
Numbers, Divisibility, Negatives
Grades 5-9
Numeracy
Grades 0-4
Patterning
Grades 5-12
Percentages
Grades 6-10
Place Value
Grades 0-6
Probability
Grades 5-12
Pythagoras
Grades 7-11
Radicals
Grades 8-12
Rates/Ratios
Grades 5-10
Scientific Notation
Grades 6-12
Shapes and Angles
Grades 0-6
Slope/Linear Equations
Grades 9-12
Speed/Distance/Time
Grades 6-12
Statistics
Grades 5-12
Time
Grades 2-8
Trigonometry
Grades 10-12
Visual Patterning
Grades 1-4
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This math unit covers essential aspects of function transformations, starting from understanding how simple transformations affect the vertex of a function, to more complex manipulations that alter the domain and range. It begins by teaching students how to identify and apply transformations like shifts and reflections that lead to changes in the vertex of functions. The unit progresses to more intricate transformations affecting the domain and range, requiring students to reverse-engineer transformations from changes in these properties. The unit further expands into function composition, focusing on determining and representing the domain of composite functions, which is complemented by ensuring understanding of conditions around real roots in quadratic functions nested within other functions. Additionally, the course transitions into determining inverses specifically between exponential and logarithmic functions, and thoroughly explores sinusoidal functions where students progressively learn to identify and relate parameters like amplitude, phase shifts, and vertical shifts from both algebraic forms and their corresponding graphs. This comprehensive approach not only strengthens algebraic manipulation skills but also enhances visual and theoretical understanding of various function transformations and their applications in greater math contexts.Skills you will learn include:
This math unit progresses through a focused exploration of sinusoidal functions, starting by understanding how individual parameters like amplitude, period, and phase shift influence the function's graph. It begins with basic exercises that require students to match sinusoidal functions and their parameters to corresponding graphs. As the unit progresses, the complexity increases as students deal with multiple parameters simultaneously, analyzing how these combine to transform functions graphically and algebraically. Students then move to reverse tasks, where they identify sinusoidal functions from graphs and deduce parameters from functions. Ultimately, the unit covers up to four parameters, enhancing the learners' ability to handle more complex transformations and deepening their understanding of how variations in amplitude, period, phase shift, and vertical shift affect the mathematical expressions and visual representations of sinusoidal functions. The unit is grounded in developing analytical skills necessary for function transformations, composition, and inversion, which is crucial for higher mathematics and applied sciences.Skills you will learn include:
This math unit focuses extensively on analyzing and determining the domain of various functions involving fractions with numerators and denominators that include quadratic expressions and their roots. Initially, students engage in identifying the domains of functions with quadratic denominators, both with real and complex roots, utilizing number lines and set notation to express these domains. As the unit progresses, complexities increase with the introduction of radical expressions in the denominators and numerators, challenging students to consider additional constraints like the non-negativity of radicands (expressions under square roots) and ensuring denominators are non-zero. The skills evolve from simple domain identification on number lines to more nuanced definitions involving complex roots and square roots, requiring a deeper understanding of function behavior and restrictions, particularly in the context of real and complex numbers. Students learn to map accurate domain representations and handle functions with various root conditions, enhancing their problem-solving abilities in algebraic contexts.Skills you will learn include:
This math unit focuses on developing a comprehensive understanding of function transformations. Initially, students learn to identify and describe single transformations from graphs or algebraic expressions, including shifts, reflections, and stretches or compressions. They progress to recognizing how specific transformations affect functions, both graphically and in terms of function notation. The unit also introduces complex scenarios involving double transformations, requiring identification of the effects from a combination of transformations on functions. As the unit advances, the focus shifts to specific attributes of functions such as the vertex, and domain and range. Students learn how transformations affect the vertex of a function, with exercises that include calculating new vertex positions and reverse-engineering transformations from a given vertex position. Similarly, they explore how transformations influence the domain and range of functions, identifying transformed domain or range values from given transformations and vice versa. This comprehensive approach solidifies their understanding of how algebraic manipulations impact function properties.Skills you will learn include:
This math unit starts with the basics of function composition by identifying roles within composite functions, such as input, output, inner, outer, first, and second functions. It progresses to practical applications, requiring students to substitute functions into each other to evaluate composite function outputs. The unit then advances to a more complex skill set involving the determination of domains for composite functions, combining different types of functions such as linear, root, integer, and quadratic operations. This part teaches students how different functions influence the constraints on domain values, often visualized on number lines to help with conceptual understanding. Towards the end, the unit explores function inversion, challenging students to recognize and verify the inverses of given functions, including more complex scenarios involving exponential and logarithmic functions, fostering a deep understanding of functions and their interrelationships in algebra.Skills you will learn include:
This math unit focuses on progressively developing students' understanding and skills in identifying the domain of various functions, beginning with simpler quadratic functions and moving toward more complex rational functions involving polynomials, square roots, and complex roots. Initially, students learn to determine and visually represent the domain of quadratic functions on a number line. They then explore polynomial functions of higher powers, followed by functions involving square roots of linear and quadratic expressions, requiring careful analysis of conditions that ensure real number outputs. The unit advances into exploring the domain of functions where integers and linear expressions are in the numerator, and quadratic expressions, including those with complex roots, are in the denominator. Further complexities involve understanding and representing domains of functions combining square roots and quadratic components in both the numerator and the denominator, culminating in an analysis of conditions that maintain function validity, particularly focusing on real numbers and avoiding undefined behaviors like division by zero.Skills you will learn include:
This math unit focuses on the end behavior of polynomial functions, progressing from basic understanding to more complex application and analysis. Initially, students learn to interpret the end behavior of polynomials through graphical analysis, identifying trends as \(x\) approaches positive or negative infinity. They then progress to matching these behaviors with appropriate graphical representations and deducing rules based on graph trends. As the unit advances, students deal with the correlation between the highest power and the leading coefficient of polynomials and how these influence the end behavior. They learn to determine these elements from graphs, rules, and directly from polynomial functions. Finally, the unit covers predicting polynomial graphs based on a given set of highest power and leading coefficient values, wrapping up with an ability to match polynomial functions to their respective end behaviors and rules, essentially preparing them for practical applications and deeper studies in polynomial functions.Skills you will learn include:
This math unit progresses through a series of skills, focusing on understanding and defining the domain and range of functions through various representations and conditions. Initially, the unit addresses basic visual and symbolic representations involving the translation of inequalities and verbal descriptions into number lines and set builder notation, utilizing unions to depict composite intervals. As students progress, they learn to convert these representations into interval notation, further solidifying their understanding of function behavior over specified domains and ranges. The unit advances into more complex scenarios where students must determine function domains involving higher polynomials, linear and quadratic expressions under square roots, and functions defined by fractional expressions over linear, quadratic, and radical denominators. The tasks require careful analysis to avoid undefined expressions and adhere to the conditions provided by each mathematical model, enhancing proficiency in translating between different mathematical representations of domains, such as number lines and algebraic conditions. The increasing complexity aids in mastering the algebraic and graphical understanding necessary to analyze functions critically within defined parameters.Skills you will learn include:
This math unit begins by teaching students how to visually interpret and define functions through relation maps and progresses to detailed explanations of domain and range using various mathematical notations and representations. Starting with basic function definitions, students learn how to find domain and range using number lines and inequalities, gradually moving to translating these into set builder and interval notations without unions. The complexity increases as students learn to navigate between different representations, including verbal descriptions and symbolic expressions. Towards the end of the unit, the scope expands to include unions in domains and ranges, enhancing their ability to handle more complex scenarios by interpreting inequalities, set builder notations, and intervals that involve combining separate mathematical intervals. This progression builds a foundational understanding of functions, crucial for further study in calculus and algebra.Skills you will learn include:
This math unit delves into the fundamentals of graphing circles on a coordinate plane, beginning with basic identification and placement of circle centers. Students first learn to graph circles given the center coordinates and then advance to calculating circle graphs based on specified radii. Progressing further, the unit teaches conversion of a circle's equation into its graphical representation by interpreting the meaning of value coefficients in the standard circle equation \( (x-h)^2 + (y-k)^2 = r^2 \). Students continue to refine their skills by extracting center coordinates and radii directly from the circle equations, enhancing their ability to visualize and plot these geometric forms accurately. The subsequent lessons expand these concepts by guiding students to derive a circle's standard equation using both center coordinates and radius. Towards the end of the unit, learners are equipped to transform a complete circle graph back into its algebraic equation, solidifying their understanding of the relationship between a circle’s graphical and algebraic representations. This step-by-step progression effectively builds foundational knowledge crucial for solving geometry and coordinate graphing problems involving circles.Skills you will learn include:
This math unit begins by developing students' ability to identify and verify the midpoint of a line segment using graphical representations. As the unit progresses, it adds complexity by introducing the concept of perpendicular slopes and the calculation of slopes that are perpendicular to a given line segment. Students start with true/false questions to confirm their understanding of midpoints and perpendicular slopes and then move on to using formulas. The unit evolves to focus on finding the equation of the perpendicular bisector of line segments, both from graphical representations and by analyzing points directly. Towards the end, the unit consolidates these skills by requiring students to verify if equations presented to them correctly represent the perpendicular bisector of specified line segments, using both graphical and point-based information. Overall, this unit builds from basic midpoint validation to advanced application of formulas for constructing perpendicular bisectors, enhancing students' analytical geometry skills.Skills you will learn include:
This math unit begins with the foundational concept of identifying y-intercepts from linear equations in slope-intercept and standard forms using integer coefficients. As the unit progresses, it introduces the concept of x-intercepts, requiring students to manipulate equations set to zero in either variable while still using integer values. The complexity increases as the unit shifts to equations involving decimal coefficients. This additional challenge tests the students' ability to work with more precise values and enhances their algebraic manipulation skills. Towards the end of the unit, the focus shifts to finding intersection points between different types of lines including horizontal, vertical, and other linear equations demonstrating both integer and decimal solutions. This progression from basic intercept identification to solving for intersections between various lines helps students understand the graphical behavior of linear equations and their points of intersection.Skills you will learn include:
This math unit begins by building foundational skills in understanding slopes of line segments, both graphically and through coordinates, initially focusing on finding and verifying the slope values of line segments. Students practice calculating the slope using the formula and assess given slopes for accuracy in true/false formats. The unit progresses to finding the midpoints of segments, utilizing both graphical presentations and coordinate data, again using true/false questions to confirm understanding. Later, the unit introduces more complex concepts like perpendicular slopes and bisectors. Students learn to determine perpendicular slopes by applying the negative reciprocal rule and verify their correctness in true or false questions. The unit advances to constructing equations for perpendicular bisectors using both graphical and coordinate data, enriching students' skills in applying geometric concepts to solve problems involving midpoints, slopes, and perpendicular relations in line segments. The sequence moves from basic slope and midpoint identification to more intricate applications, such as creating and verifying perpendicular bisectors.Skills you will learn include:
This math unit focuses on understanding and applying the concept of perpendicular slopes within different contexts of linear equations. It begins with basic calculations to find the negative reciprocal of given integer slopes and progresses to handling fractional and decimal slopes to identify perpendicular lines. The unit further develops by having learners convert and determine perpendicular slopes between different forms of linear equations, such as slope-intercept form, zero-intercept form, and standard form. Additionally, learners practice converting these equations for graphical representation, aiding in visual understanding and verification of perpendicular relationships. The depth of the unit increases as students move from initially identifying perpendicular slopes in simpler formats to manipulating complex algebraic forms and graphing them, thus building a comprehensive skill set in analyzing and constructing perpendicular lines within coordinate geometry. Throughout the unit, the primary emphasis remains on mastering the concept that the product of the slopes of perpendicular lines is -1, and applying this understanding in various mathematical scenarios.Skills you will learn include:
This math unit begins by developing students' abilities to interpret and identify different types of function graphs based on their corresponding algebraic equations. Initially, students match specific graphs to their equations and recognize the type of function each equation represents. The unit progresses to enhance understanding of function domains and ranges through visual representations, starting from identifying domains and ranges, to determining whether given relations qualify as functions based on their visual mappings. Further along, the unit delves deeper into defining and describing domains and ranges more formally. Students learn to translate number line visuals into verbal descriptions and vice versa, convert verbal descriptions into mathematical inequalities without unions, and then express these inequalities using set builder notation. Finally, the unit teaches students to transform set builder notations into interval notations and accurately represent these intervals on a number line, further solidifying their comprehension of domain and range concepts in the context of functions.Skills you will learn include:
This math unit develops the understanding and skills related to slopes and equations of lines, with a specific focus on parallelism. Initially, students learn to recognize and convert line equations between different forms, starting from understanding simple forms such as slope-zero intercept and slope-intercept forms, to more complex transformations involving standard forms and decimal representations of slope. As the unit progresses, the emphasis shifts to applying these foundational skills to understand parallel lines. Students practice identifying parallel slopes by converting equations between various formats including zero-intercept, slope-y-intercept, fraction form, and graph representation to standard forms. Through these exercises, students enhance their ability to interpret and manipulate different algebraic expressions of linear equations, deepening their grasp of how slopes indicate parallelism and how lines can be graphically and algebraically analyzed and compared for this property.Skills you will learn include: