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 begins by introducing students to the fundamental concepts of factorial notation and its application in calculating permutations where order is important. Students first learn to compute different ways to order sets of items, including cards, using factorial equations that address scenarios with repeated items. The progression continues as students delve deeper into probability calculations, specifically mastering nPm notation to interpret permutation scenarios and translating these into correct mathematical notations. The unit advances into probability calculations involving combinations, where students engage with nCm notation to compute the number of ways to choose subsets without considering order. This is developed further with problems that require converting factorial expressions into binomial coefficient notation, solidifying understanding of how to express selective combinations and arrangements in different notational systems. Finally, the unit rounds off by applying learned skills to practical probability scenarios, such as calculating the likelihood of drawing specific cards from a hand, always expressing outcomes in suitable mathematical formats. These exercises collectively enhance the students' comprehension of key probability concepts, from specific ordering to general counting of outcomes, underpinning the probability and statistical calculations required in advanced mathematical contexts.Skills you will learn include:
This math unit delves into the concept of standard deviation and its application to z-scores, refining students' understanding and skills in statistical analysis progressively through various contexts. Initially, learners grasp the basic interpretations of z-scores in relation to the mean, discerning whether certain values represented by z-scores are above or below the average. They then advance into calculating z-scores from given data points using the mean and standard deviations, enhancing their capability to quantify how far each data point is from the mean in standard deviation terms. As the unit progresses, students shift from theoretical understanding to operational application, utilizing z-scores to determine various statistical outcomes. They engage with statistical tables (Z-tables) to link z-scores with percentages, which is essential in estimating probabilities and making inferences about distributions. The unit continues into more complex aspects where learners compare performance between different sets of values and conclude the unit with interpreting and determining percentages of data falling above or below certain values in a normal distribution using z-scores and Z-tables. This progression solidifies the learners' proficiency in handling practical statistical analysis tasks using standard deviation and z-scores.Skills you will learn include:
This math unit initiates with foundational concepts in permutations, focusing on calculating various arrangements of distinct and repeating elements, exemplified through problems involving cards and letters. Initially, students learn to calculate permutations of five items with one repeating, using factorial operations. Over time, complexity increases as they tackle permutations with two repeating items and apply similar principles to scenarios involving four items. Subsequently, the unit explores binomial notation and combinations in depth, advancing from simple calculations of permutations to understanding and interpreting the `nCm` (binomial coefficient) notation. This progression is evident as the unit starts from specific permutation calculations and factorial expressions towards broader combinatorial principles and calculations. Students learn to choose subsets of items and understand the distinctions between permutations and combinations, culminating in the ability to calculate, interpret, and apply these principles in various probabilistic contexts.Skills you will learn include:
This math unit delves into the principles of probability, starting with basic probability counting using coins and advancing through various settings including spinners, dice, cards, and shapes. The unit begins with simpler tasks such as calculating probabilities of homogeneous outcomes (all same or specific) and progresses towards more complex scenarios involving multiple independent events with spinners. Students learn to express probabilities in different mathematical forms: fractions, equations, decimals, and percentages. This progression enhances their ability to analyze and compute probabilities in multiple-choice formats and through direct calculation. Later in the unit, the focus shifts to combining probability theory with applications in real-world contexts like card games or hypothetical scenarios involving shapes of different colors. The unit culminates with sophisticated exercises in probability counting using dice, where students need to handle diverse outcomes and express their answers through fraction equations, embracing both simple and complex probabilistic calculations. This sequence builds comprehensive skills in understanding, computing, and applying probability across various contexts and representations.Skills you will learn include:
This math unit begins by teaching students how to apply standard deviation and Z-scores to interpret the distribution of data on a normal curve, relating to various real-world scenarios like test scores and heights. Initially, the unit focuses on determining what percentage of data falls within specified standard deviations from the mean. Progressively, it delves into more complex applications involving calculations of data points lying within or beyond certain standard deviation thresholds and translating these into interpretive graphical representations. As the unit progresses, students learn to utilize Z-scores to determine values' positions relative to the mean on unlabelled and labelled curves, enhancing their ability to analyze and estimate percentages of data in given sections. Towards the end, the focus shifts to applying these statistical concepts to calculate specific values within a dataset using information about means, standard deviations, and Z-scores, preparing students for in-depth analysis in probability and statistics. This progression effectively builds a comprehensive skill set for interpreting statistical data accurately in varying contexts.Skills you will learn include:
This math unit begins by introducing students to the concept of quartiles within data sets, particularly exploring how to identify and calculate the lower quartiles, median, upper quartiles, and considering outliers. Students learn to calculate the interquartile range to measure spread, and identify outlier boundaries, enhancing their understanding of data variability. As the unit progresses, students apply their understanding of quartiles to box plots, learning to determine whether specific data points are outliers based on their positions relative to the quartile ranges. The unit then shifts focus to standard deviation and normal distribution, starting with basic exercises in identifying the mean from bell curve graphs. The complexity increases as students match given means with their corresponding bell curves, discern which curves reflect higher or lower means, and then interpret which datasets demonstrate higher variability. Towards the end of the unit, students delve deeper into standard deviation calculations from provided variances and datasets. They compare these across different datasets to analyze variability and performance. They also learn to interpret and calculate percentages within standard deviation ranges on normal distribution curves, preparing them for more advanced statistical analysis and real-world applications. The culmination of this series reinforces proficiency in handling probabilities, variance calculations, and understanding the impact of standard deviation in various data-driven scenarios.Skills you will learn include:
This math unit advances students' understanding of probability, permutations, and combinations through a series of incremental and integrated topics, focusing heavily on factorial notation and applications in real-world contexts. It starts with an exploration of factorial multiplication, moves on to describing the transformation of factorial expressions into binomial coefficients (nCm notation), and then applies these principles to practical situations. The unit progresses from calculating factorial expressions for ordering a small number of items with no repetitions to more complex scenarios involving ordering larger sets and considering repetitions. As it progresses, students tackle increasing complexities in arranging items and translating these arrangements into factorial equations and multiplicative expressions. Later in the unit, there is an introduction to calculating probabilities of drawing cards, emphasizing combinatorial calculations and the formulation of probabilities as equations and fractions. Overall, this unit builds a robust understanding of probability, factorial calculations, and their applications in different statistical scenarios.Skills you will learn include:
This math unit initiates with lessons on basic set operations in probability, using practical contexts such as spinners to help students grasp the concepts of union, intersection, and complement. It progresses to visually interpret these operations through Venn diagrams, enhancing understanding and calculation skills. As the lessons evolve, other familiar items like coins, dice, and cards are incorporated, each bringing new levels of complexity to the probability scenarios being studied. Students transition from basic computation and identification of appropriate set operations to applying formulas to determine specific probabilities in more complex scenarios involving consecutive outcomes and conditional probabilities. The unit further develops skills in representing statistical data using Venn diagrams and set notation in word problems. Towards the end, it emphasizes translating real-world data into probabilities and percentages, making connections between theoretical probability concepts and practical applications in varying contexts, thereby rounding off with a comprehensive understanding of probability in diverse scenarios.Skills you will learn include:
This math unit begins by introducing students to the foundational concepts of probability, focusing on the union, intersection, and complement of events. Initially, learners recognize and apply probabilistic formulas based on these operations, translating different representations such as names, descriptions, and Venn diagrams into correct mathematical expressions. Progressively, students solve problems by identifying the appropriate formulas for given set operations and translating these back into different forms—ranging from naming and describing operations to graphically representing them through Venn diagrams. The unit emphasizes critical thinking as students learn to navigate between various forms of expressing probability operations, including visual, verbal, and symbolic. By the end, they are adept at handling basic probability scenarios, applying their knowledge to specific examples, enhancing their understanding and manipulation of probability concepts in multiple contexts.Skills you will learn include:
This math unit delves into the fundamentals and complexities of statistics, particularly focusing on the concepts of mean and quartiles. Initially, students practice calculating the mean in advanced scenarios, both by adding and removing values from a data set to achieve a target mean. This improves their understanding of how individual data points affect the overall average. The unit progresses into quartiles, starting with simpler data sets without outliers. Students explore calculating median, upper and lower halves, quartiles, interquartile range, and constructing box plots. As they advance, the complexity increases with the introduction of outliers in the data sets. They continue practicing calculating the median, quartiles, and interquartile range and move to constructing box plots with these more complex data sets, ultimately learning how to identify outliers. Through this progression, students enhance their abilities in data manipulation and statistical analysis, adaptively applying theoretical concepts to varying contexts, thereby gaining a profound mastery of handling statistical data comprehensively.Skills you will learn include:
This math unit begins by enhancing students' understanding of how specific values affect the mean of a dataset, both through addition and removal of a value, and progresses to more complex statistical analysis involving histograms and box plots. Initially, students focus on adjusting sets of numbers to reach a specific target mean by adding or subtracting a value, thereby deepening their grasp of the mean calculation and its sensitivity to changes in data. As the unit advances, students transition into constructing and analyzing histograms, identifying distribution types, and discussing data characteristics like skewness and modal class. They also learn to interchange between graphical representations such as histograms and box plots, increasing their skill in interpreting data visually and numerically. This progression from basic mean adjustments to comprehensive data representation and analysis allows students to acquire a holistic understanding of statistical concepts and data manipulation.Skills you will learn include:
This math unit progresses from fundamental to more intricate probability calculations. Initially, students practice calculating probabilities of specific outcomes using dice and coins, expressing results in fractions and decimals. The unit advances into scenarios involving multiple probabilities and dependent events, with problems framed around spinners, cards, and shapes to enhance real-world applicability. As students progress, they calculate probabilities for sequences of events, such as drawing cards or shapes in specific orders and conditions, represented through equations and percentages. This gradual increase in complexity helps students build a robust understanding of basic probability concepts, practice essential counting principles, and apply these skills to complex, multi-event scenarios using different representations like fractions, decimals, and percentages.Skills you will learn include:
This math unit begins by introducing students to basic combinatorial concepts, starting with calculating the number of ways to order sets of cards and letters without repetition, expressed through factorial multiplication. As the unit progresses, it delves deeper into probability and statistics, shifting focus to scenarios involving permutations with repetitions. Students learn to determine the number of possible arrangements for various card sets with one repeated card, incrementally increasing from three to five cards. Each worksheet elevates the complexity of problems and understanding, from simple factorial calculations to application in different ordering scenarios. Towards the end of the unit, the focus transitions to more theoretical applications, introducing the binomial coefficient notation (`nCm`) and calculating values for combinations in given scenarios. This progression builds a comprehensive understanding of factorials, permutations, and combinations, ultimately equipping students with the skills to tackle more complex probability scenarios.Skills you will learn include:
This math unit begins with foundational probability concepts using simple scenarios like dice rolling, coin flipping, and card drawing, first focusing on specific outcomes and fraction notation. It progresses to calculating and expressing probabilities in decimal form, enhancing students' ability to transition between different numerical representations. As the unit continues, the complexity increases, introducing scenarios that require calculating probabilities for group selections and multiple events. Students encounter more advanced topics that involve multiple spins on a spinner and multiple shapes picked from sets, where they learn to compute probabilities of intertwined events and express these probabilities in fraction equations, decimals, and percentages. The unit emphasizes a thorough understanding of probability principles and their application in varied and increasingly complex real-world-like scenarios, culminating in multi-event probability calculations.Skills you will learn include:
This math unit begins by introducing foundational concepts of probability involving union, intersection, and complement set operations, using various problem-solving approaches. Initially, learners associate names and descriptions with these operations through theoretical examples. Progression occurs through the use of Venn diagrams to visualize and identify relationships among sets, moving from basic representations to more analytical tasks involving set operations and their graphical and formulaic expressions. As students advance, they learn to translate complex probability formulas into corresponding set operations and verbal descriptions, enhancing their understanding of how probabilities are computed in diverse scenarios. The unit culminates in applying these concepts to real-world-like situations, where learners practice deriving appropriate formulas for calculating probabilities of specific events. This structured approach solidifies their ability to interpret and apply probability laws to theoretical and practical problems.Skills you will learn include:
This math unit focuses on developing student proficiency with factorials, starting from the basics and progressing to more advanced applications within probability and combinatorial contexts. Initially, the unit introduces students to converting factorials into multiplication strings and calculating factorial values. Students are then guided through recognizing and converting multiplication strings back into factorials, an essential skill for understanding permutations and combinations. Further into the unit, more complex operations involving factorials are taught, such as simplifying factorial expressions through division and understanding the equivalent values of factorial divisions. By converting factorial multiplication strings to divisions, students enhance their ability to manipulate and rationalize factorial expressions crucial for accurate probability computations. Towards the later part of the unit, students engage with a variety of factorial calculations, including those with simpler forms, and gradually move to manipulating expressions involving brackets and mixed operations. This progression sharpens their skills in handling complex factorial-based calculations, underpinning higher-level studies in statistics and probability.Skills you will learn include:
This math unit begins by introducing students to the concept of the arithmetic mean with exercises that involve finding a missing value needed to achieve a specified mean. It progressively covers more complex scenarios, such as removing or adding values to alter the mean, and calculating the impact of changing a specific value in a data set. Students practice these concepts with multiple-choice problems and scenarios that require both basic and advanced analytical skills. As the unit advances, it emphasizes a deeper understanding of how individual data changes affect the overall average, reinforcing the students' ability to manipulate and interpret sets of numbers within different statistical contexts. This progression builds from fundamental calculations to more sophisticated statistical manipulations, showcasing applications of the mean in various contexts to enhance problem-solving and analytical thinking in statistics.Skills you will learn include:
This math unit starts with basic permutation concepts, teaching students to calculate the number of ways to order cards and letters without repetition, gradually advancing from three to five items. As the unit progresses, it introduces problems involving spinning a labeled spinner, first teaching students to calculate specific outcomes in multiple formats (equations, fractions, percentages), and then broadening to include calculations for any occurrence within two spins, expressed in various numerical forms. The unit deepens understanding by exploring factorial notation in probability scenarios, leading to advanced applications in combinatorics. The skills progress from foundational permutations to complex factorial operations and probability calculations involving multiple scenarios and various forms of numerical expression, reinforcing the understanding and application of probability through diverse practical examples and increasingly complex mathematical operations. Toward the end, the unit integrates the concepts of factorials more directly, culminating in practical applications related to card-drawing probabilities.Skills you will learn include:
This math unit begins by introducing basic probability concepts through the use of spinners, progressing students from calculating probabilities in decimal format to percentage representation. It further explores these concepts using card scenarios, starting with the probability of drawing single cards in decimal and percentage formats, then advancing to more complex scenarios involving groups of cards or specific outcomes. As the unit advances, it engages students with multiple event probabilities that include ordered and unordered card drawing, using fractions and equations to express probabilities. The unit also delves into permutations by calculating the number of ways cards and letters can be arranged, enhancing students' understanding of probabilistic outcomes and counting principles. Overall, the unit scaffolds learning from foundational individual outcomes to complex multiple event calculations, emphasizing diverse methods of expressing probability (decimals, percentages, fractions, and equations) while tackling practical and increasingly challenging scenarios.Skills you will learn include:
This math unit begins with a focus on understanding permutations involving the arrangement of letters and cards, systematically increasing in complexity from arranging sets of 3 to sets of 5 items without repetition. Initially, students express solutions through straightforward multiplication equations, transitioning into factorial notation as their understanding deepens. Throughout these initial topics, students enhance their capacity to manipulate and calculate factorials and permutations, foundational elements of probability and statistics. Midway through the unit, the focus shifts to probability and statistics principles involving shapes and colors. These lessons build on single-event probabilities, starting from calculating percentages, transitioning into decimal representations, and later reintroducing percentages. Students practice scenarios where they calculate the likelihood of picking certain shapes or colors from sets containing varying shapes in multiple colors. Each step gradually introduces more complex scenarios, requiring students to strengthen their skills in basic probability and fractional, decimal conversions. Finally, the unit ends with factorials revisited, translating factorial problems back into multiplication strings, ensuring a firm grasp of the connections between factorial operations and their expression in sequential multiplications. This progression not only deepens understanding of permutations and probability but also integrates these concepts practically into real-world scenarios, enhancing overall mathematical literacy.Skills you will learn include:
This math unit progresses through a comprehensive introduction and practice of probability concepts, beginning with simple probability based on spinner scenarios and transitioning to probability involving playing cards and ordering scenarios. Initially, students practice calculating probabilities with spinners and cards, expressing these probabilities first as decimals and then moving to percentage form. This progression ensures understanding of both the calculation and representation of probabilities in different forms. As the unit develops, students engage in more complex problems involving combinations and permutations, where they calculate the probability of various ordered events without repetitions using cards or letters. These are expressed through equations or answering queries directly, enhancing their grasp of factorial calculations and permutation formulas. Towards the end, the unit shifts focus to include probability with shapes in different colors, calculated from simple selection scenarios. Students continue to express probabilities in various forms - fractions, decimals, and percentages - adapting their skills to more everyday contexts, such as drawing specific colored shapes from a set. The unit culminates with the integration of multiple variables in probability scenarios, reinforcing the foundational understanding and practical application of probability in varied situations.Skills you will learn include:
This math unit focuses on developing skills in basic statistics, particularly emphasizing the understanding and application of mean, median, mode, and range. Initially, students learn to calculate the mean from given sums and counts, setting a foundational knowledge of averages. Progressing further, learners engage in exercises to calculate sums based on known means and counts, and then sharpen their ability to find the mean of smaller sets of numbers directly. The unit builds on these concepts by teaching how to determine the median and range, enhancing students' ability to analyze data sets fully. As students gain proficiency in these areas, the unit introduces more complex scenarios, such as finding a missing number to achieve a specified mean, and understanding the impact of adding a number to a set on the mean. These advanced topics not only reinforce earlier skills but also prepare students for deeper statistical analysis by understanding how individual data points affect overall data characteristics. Through a mixture of calculation and problem-solving, learners are trained to manipulate and interpret statistical data effectively within the framework of probability and statistics.Skills you will learn include:
This math unit focuses on building foundational skills in probability and statistics, starting with simple events and evolving into more complex probability calculations expressed in different formats. Initially, students learn to compute probabilities in fraction form by selecting specific outcomes from defined sets involving coins, dice, and shapes of different colors. As they progress, they transition to expressing these probabilities as percentages, enhancing their understanding of numerical conversion and representation. Later in the unit, the problems become more elaborate, involving cards and spinners where they calculate probabilities for specific draws or outcomes, transitioning from computing probabilities in fractions to decimals and then to percentages. This progression not only deepens their understanding of basic probability concepts but also introduces them to a variety of practical scenarios, enabling them to visualize and manipulate statistical data effectively.Skills you will learn include:
This math unit introduces students to the core concepts of statistics including mean, median, mode, and range using a progression of skills that starts with visual and conceptual understanding and advances to computation and application. Initially, students learn to calculate the mean, median, and range by analyzing visual representations—shapes in images—to grasp these statistical concepts fundamentally. As the unit progresses, the focus shifts from understanding statistics through pictures to solving problems that involve direct computation using formulas and equations. Students practice determining statistical measures from given numerical data sets, emphasizing the distinction between different measures like mode (most frequent), median (middle value), median (average), and range (difference between largest and smallest numbers). This progression from visual interpretation to calculation enhances students’ abilities to analyze and interpret data, providing a thorough introductory understanding of basic statistics.Skills you will learn include: