Home

Math

Grade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8Grade 9Grade 10Grade 11Grade 12Math Themes

Programs

Explorers (Grades 1-3)Explorers Elite (1-3)Navigators (Grades 4-6)Navigators Elite (4-6)Challengers (Grades 7-9)Challengers Elite (7-9)Scholars (Grades 10-12)Scholars Elite (10-12)Schedule an Evaluation

About

Mobius MethodFlexible ClassesCompanySupport
Pricing
Ctrl+k
​
Sign InJoin

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

  1. Math
  2. /
  3. Themes
  4. /
  5. Calculus

Calculus

Introduction to Calculus including derivatives and integrals

more
Our mission at Mobius is to inspire a love of math in every student by reinventing how it is taught.
Links
Terms of UsePrivacy PolicySupport
footer bg

info@mobius.academy

Unit Details

Select a unit to see its details

Pinch or scroll to zoom in and out

Drag to move the map around

Trigonometry Fundamentals - Intro

This math unit begins with foundational trigonometry, starting with identifying different sides of a right triangle—opposite, adjacent, and hypotenuse. It progresses to understanding and labeling the side ratios in right triangles, using the SOHCAHTOA acronym to deepen the comprehension of trigonometric relationships such as sine, cosine, and tangent. As students become more comfortable with these definitions, they move on to applying and manipulating these ratios to solve for unknowns in trigonometric expressions and focusing on approximating trigonometric values from diagrams. The unit further advances into calculating and approximating side length ratios and explicit side lengths using trigonometric principles, scaling up to more complex applications where geometric figures and ratios are used extensively. Towards the end, the unit incorporates fact families within trigonometry to link geometric and algebraic representations, fostering a comprehensive grasp of the relationships between angles, sides, and trigonometric identities.Skills you will learn include:

  • Ratios of line lengths
  • Opposite, adjacent, hypotenuse
  • Sin, cos, tan
  • Solving triangles with trignometry
more
PlayGameViewUnitTryUnit
Trigonometry Fundamentals - Practice

This math unit initially focuses on understanding and calculating ratios of line lengths in various geometric configurations, including parallel and right angle line displays. It introduces students to basic trigonometry through the practical application of calculating these ratios and progresses to more complex tasks. As the unit develops, students begin working with trigonometric identities and ratios such as sine, cosine, and tangent. They learn to solve for unknown angles based on given side lengths and to express relationships using trigonometric formulas. The later sections of the unit continue to emphasize interpreting and solving problems using trigonometric ratios and identities but introduce more complex applications, involving decimal representations and extracting trigonometric values from diagrams. The unit concludes with a comprehensive understanding of using trigonometric principles to solve geometric problems, setting a strong foundation in trigonometry by systematically building fluency from simple ratio calculations to complex trigonometric applications.Skills you will learn include:

  • Sin, cos, tan
  • Solving triangles with trignometry
more
PlayGameViewUnitTryUnit
Trigonometry and the Unit Circle - Intro

In this math unit, students begin by learning the fundamental skills of converting angles between degrees and radians using the unit circle. They start with basic conversions, practicing both from degrees to radians and vice versa. As they progress, students further explore these conversions with a wide range of specific angles, enhancing their fluency and comprehension of angular measurements in both units. Midway through the unit, the focus shifts towards applying this knowledge to calculate the trigonometric values sine and cosine for angles defined in both radians and degrees. Students practice identifying the coordinates of points on the unit circle based on these angles. This includes exercises that provide angles in radians and degrees, for which they have to determine the cosine and sine coordinates. Towards the unit's conclusion, learners refine their understanding of mapping these angles and trigonometric coordinates visually and numerically on the unit circle. This involves more complex problem sets where they are required to interpret trigonometric functions and their corresponding coordinates or visualize angles based on provided coordinates, solidifying their comprehension of trigonometry’s relationship with the unit circle.Skills you will learn include:

  • Unit circle
  • Radians and degrees
  • Cos and Sin values
more
PlayGameViewUnitTryUnit
+2
Functions - End Behaviour - Intro

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:

  • End behaviour of functions
  • Highest power and leading coefficient rules
  • Identify functions from end behavour
more
PlayGameViewUnitTryUnit
Trigonometry Fundamentals - Advanced

This math unit begins by introducing students to the foundational concepts of trigonometry, focusing initially on understanding and using the basic trigonometric ratios—sine, cosine, and tangent—associated with right triangles. Early topics cover identifying trigonometric relationships and learning how to formulate correct trigonometric expressions based on given side lengths or angles. Progressively, the unit moves into more practical applications, teaching students to approximate these trigonometric ratios from diagrams and visual representations, further ingraining the fundamentals. The problems evolve to include calculating unknown angles from given side ratios, both in fraction and decimal forms, utilizing trig identities to facilitate these computations. Towards the latter part of the unit, the complexity increases as students apply their acquired skills to solve for unknown side lengths, angles from diagrams, and exact trigonometric values. Each successive topic builds on prior knowledge, culminating in more advanced practice that combines theoretical trigonometric principles with practical problem-solving skills, reinforcing understanding and application of trigonometry in geometric contexts.Skills you will learn include:

  • Sin, cos, tan
  • Solving triangles with trignometry
more
PlayGameViewUnitTryUnit
Trigonometry and the Unit Circle - Practice

This math unit centers around advanced trigonometry skills, emphasizing the use of the unit circle to calculate and understand the trigonometric functions sine and cosine for angles measured both in degrees and radians. Initially, the unit introduces learners to identifying sine and cosine as coordinates corresponding to specified angles on the unit circle, advancing to recognize and calculate these values directly from visual unit circle representations. As the unit progresses, students delve deeper into solving for trigonometric coordinates using both specific degrees and radians, enhancing their ability to visualize and translate between angle measures and coordinate points on the circle. Further topics solidify understanding by connecting coordinates back to angle measurements in radians, transitioning into the application of Pythagorean identities within the unit circle context. The final sections focus on deepening learners’ grasp of trigonometric identities, particularly how to convert between the dimensions or coordinates of points on the unit circle and their corresponding sine or cosine values through the Pythagorean theorem, underlining fundamental relationships and properties within trigonometry. This progression from basic identification to complex applications underscores a comprehensive mastery of the trigonometric unit circle.Skills you will learn include:

  • Unit circle
  • Trig identities
  • Pythagorean identities
  • Negative angle identities
more
PlayGameViewUnitTryUnit
+2
Functions - Composition and Inversion - Intro

This math unit starts with understanding the basics of function composition, focusing on identifying the input, output, inner, outer, first, and second functions in various composite configurations. Skills progress to calculating the outputs of these compositions, reinforcing comprehension through practical application. The unit then advances to evaluating the domains of these compositions, particularly when involving root, linear, rational, or quadratic functions, underscoring the importance of determining the set of input values that make the function compositions well-defined and meaningful. The culmination of the unit involves mastering the concept of function inverses, both for straightforward functions and more complex exponential and logarithmic forms. Students learn to discern whether pairs of functions are inverses and calculate the inverse of given functions to deepen their understanding of functional relationships, preparing them for more advanced studies in function operations and algebra.Skills you will learn include:

  • Composition of Functions
  • Domain of Composed Functions
  • Inversion of Functions
more
PlayGameViewUnitTryUnit
Trigonometry - Solving Triangles - Intro

This math unit begins by establishing foundational skills in identifying trigonometric identities and calculating angles and ratios from descriptions and diagrams. Initially, students focus on understanding basic trig identities, such as sine, cosine, and tangent, progressing into the practical application of these ratios to calculate angles using inverse functions and descriptions in word and arc notation. The unit advances to converting given ratios and angles into trigonometric values, both in decimal and exact forms, emphasized through the use of diagrams which help in visual understanding and approximation. Later, the unit advances to solving for unknown side lengths and angles in various triangles, demonstrating applications in geometry through practical problems. This progression solidifies the student's ability to manipulate and apply trigonometric principles in diverse scenarios, reinforcing comprehensive understanding of trigonometry from theoretical identities to their practical applications in solving geometric problems.Skills you will learn include:

  • Working with ratios
  • Sin, cos, tan
  • Solving triangles with trignometry
more
PlayGameViewUnitTryUnit
Trigonometry - Solving Triangles - Practice

In this math unit on trigonometry fundamentals, students begin with basic skills such as solving trigonometric ratios (sine, cosine, tangent) using given side values of right triangles, and then advance to calculating unknown angles from side measurements. As they progress, they apply these ratios to solve for missing side lengths in right triangles using angles and side measurements provided, enhancing their problem-solving skills in practical scenarios. Further into the unit, students tackle more complex tasks such as solving for angles and sides from detailed diagrams, as well as computing and approximating trigonometric ratios and angles from visual information and decimal representations. This steadily builds their ability to interpret and analyze geometric data and apply trigonometric identities in more advanced problems. Towards the end of the unit, the focus shifts to refining the understanding of trigonometric relationships and identities through problems involving ratios described in both fraction and decimal forms, extracted or approximated from diagrams. This comprehensive approach ensures a deep and practical mastery of trigonometry principles, equipping students for further mathematical challenges.Skills you will learn include:

  • Sin, cos, tan
  • Solving triangles with trignometry
  • Solving angles
  • Solving side lengths
more
PlayGameViewUnitTryUnit
Trigonometry - Law of Sines, Cosines - Intro

This math unit begins with foundational trigonometry skills, focusing on calculating trigonometric ratios given triangle side lengths and progressing to determine angles using these ratios. Students practice solving for unknown side lengths and angles from basic numerical data and then advance to solving from diagrams. As the unit progresses, the complexity increases as students engage with specific trigonometric rules—the Rule of Sines and Rule of Cosines—starting with setups and moving into full calculations. These principles are applied to solve for side lengths and angles in various triangles, including non-right triangles. Towards the end of the unit, students use trigonometric functions to solve for practical aspects like the areas of triangles, utilizing these more advanced concepts to setup and compute areas using given sides and angles. This progression builds a comprehensive skill set in solving common and complex trigonometric problems in geometry.Skills you will learn include:

  • Law of Sines
  • Law of Cosines
  • Solving triangles and triangle area with trignometry
more
PlayGameViewUnitTryUnit
Trigonometry - Heron's Formula - Intro

This math unit begins with students learning to apply Heron's Formula in the context of solving triangles. Initially, the focus is on selecting the correct formula for computing the area of triangles based on given side lengths and preparing them for application by understanding different scenarios and their requirements. As the unit progresses, learners move towards performing full calculations using Heron's Formula. They solve problems to determine the area of various triangles using precise triangulation specifics and rigorous application of the trigonometric relationships and geometry principles. This sequence from setup to full application hones the students' ability to manipulate and use trigonometric formulas effectively, improving their problem-solving skills within the realm of trigonometry.Skills you will learn include:

  • Heron's formula
  • Sin, cos, tan
  • Solving triangles with trignometry
more
PlayGameViewUnitTryUnit
+2
Functions - Domain and Range Solving - Advanced

This math unit ushers students through a progressive exploration of the domain of functions represented by various types of fractional expressions. It begins with simpler concepts like determining the domain of functions formed by fractions where the denominator is a linear or quadratic expression, emphasizing understanding whether denominators could hit zero or if roots are complex. The unit then escalates to handle square roots in the denominator, moving from linear roots to more complex quadratic roots, immediately instructing students to address non-negative conditions that ensure valid domains. Equipped with these foundational skills, students advance to scenarios where both numerators and denominators incorporate linear functions, quadratic functions, or square roots. Each type of fractional function challenges students to consider multiple domain constraints such as avoiding undefined expressions and non-negative square roots. By the culmination of the unit, students are proficient in graphically representing these domains on number lines. The skill set includes algebraic manipulation to identify domain boundaries and use of number lines to clearly illustrate valid ranges of inputs for diverse and increasingly complex rational functions.Skills you will learn include:

  • Domain and range of functions
  • Unions in domain and range
  • Domain of Linear Functions
  • Domain of Fractions
  • Domain of Radicals
more
PlayGameViewUnitTryUnit