Grade 8

In this math unit, students progress through a series of topics focusing on geometric concepts, specifically angles and transformations. The unit begins with foundational skills such as identifying and naming angles in various configurations like simple angles, angles within triangles, and specific degree angles. It steadily advances towards practical applications, like calculating missing angles in geometric figures—triangles, kites, and general shapes—by utilizing properties like the sum of interior angles and complementary angles that add up to specific totals like 90 or 180 degrees. The latter part of the unit introduces students to the concept of geometric transformations, starting with identifying reflections. Students learn to discern the type of transformation that has occurred between two shapes, whether through rotation, translation, or reflection. This integration of transformation knowledge builds on the previously established understanding of angle properties, culminating in a comprehensive approach to handling basic to intermediate geometric challenges. These skills pave the way for more complex studies in geometry involving properties and relationships between different shapes and the transformations that link them.

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 guides students through a progressive understanding of metric units and scientific notation. It starts with foundational skills in metric units, beginning with recognizing and converting metric prefixes to powers of ten and understanding unit comparisons and relative sizes. Students learn to use mnemonic devices to remember unit sequences and identify missing exponents, which deepens their understanding of the scaling of units. As the unit progresses, the focus shifts to scientific notation. Initially, students practice multiplying decimals by powers of ten to prepare for working with scientific notation. They then learn to convert numbers between standard decimal notation and scientific notation, gradually increasing the precision and complexity by including different decimal placements. This section of the unit emphasizes the compact and precise expression of both large and small numbers, cultivating an ability to handle and convert numbers efficiently in scientific contexts. The sequence of topics ensures that students build on their metric system knowledge and apply it to scientific notation, enhancing their mathematical proficiency across diverse scenarios.

Skills you will learn include:

This math unit progresses through a variety of mathematical skills focusing primarily on the interrelationships between speed, distance, and time. Initially, students calculate distance using speed and time, and then advance to determining the time needed for certain distances at given speeds. As the unit progresses, exercises involve computing speed from distance and time, and subsequent worksheets introduce more complex scenarios including changes in units (distance and time), multiple variables, and the use of algebra in contexts involving movement. Problems range from straightforward multiplications to more advanced manipulations involving algebra and variable isolation. Learners also engage in unit conversions, honing their ability to handle various units of measurement like meters, kilometers, seconds, and hours, which are crucial for solving real-world problems. The unit culminates in the ability to handle complex conversions and calculations involving changes in both distance and time units, emphasizing a deep understanding of the fundamental principles of motion.

Skills you will learn include:

This math unit begins by introducing students to calculating the perimeter of trapezoids, setting a foundational understanding of simple geometric forms. As the unit progresses, it delves into more complex area calculations, starting with basic areas of trapezoids and right triangles, using both traditional and graphical methods on grids. Later, the focus shifts to calculating the area of triangles (right, acute, and obtuse) within other geometric shapes such as squares and rectangles. This involves working out areas from provided dimensions and the utilization of more advanced spatial reasoning. Throughout the unit, students are faced with increasingly complex scenarios that require them to apply their skills in different contexts, including determining areas using side lengths, dimensions, and perimeters provided in various configurations. This progression from simple perimeter problems to complex area calculations within embedded shapes helps solidify students' understanding of geometry, enhancing their ability to handle a range of geometric configurations.

Skills you will learn include:

This math unit progresses through a comprehensive study of calculating the areas of triangles, beginning with basic exercises and advancing to more complex scenarios. Initially, students learn to calculate the area of different types of triangles, including obtuse, acute, and right triangles, using specific dimensions and images. As the unit progresses, the complexity increases with triangles placed within other geometric shapes like squares and rectangles, and students learn to calculate areas based both on the dimensions and the perimeters of these enclosing shapes. Further enhancing their skills, students then apply their knowledge to calculate areas using Cartesian grids with both positive and negative coordinates, requiring a more robust understanding of geometry and spatial reasoning. This gradual progression solidifies foundational concepts while building towards mastery in handling various geometric configurations and complex problems involving area calculations in two-dimensional spaces.

Skills you will learn include:

This math unit progresses through various skills associated with multiplying fractions, starting with fundamental concepts and gradually introducing more complex scenarios. Initially, the unit focuses on multiplying simple fractions by whole numbers without simplifying the results, establishing a basic understanding of the operation. It then moves to include simplification of these products, reinforcing the methods needed to reduce fractions to their simplest form. The complexity increases as students practice multiplying improper fractions by whole numbers, both with and without simplification. This helps solidify their grasp on handling numerically larger fractions and develops their skills in managing the results of these multiplications. Towards the end of the unit, the focus shifts to multiplying mixed numbers by whole numbers. Students are challenged to compute these products without simplification, before eventually incorporating this final step. Each stage involves multiple-choice questions to aid in learning and assessment, ensuring students are comfortable with each concept before moving to more challenging material. The unit aims to enhance students' abilities in handling different types of fractions in multiplication, culminating in a comprehensive understanding of the topic.

Skills you will learn include:

This math unit starts by developing students' proficiency with positive exponent division, initially emphasizing simplifying expressions by canceling out similar terms and understanding quotient rules through varied problem structures like expanded forms and direct simplification. Gradually, the unit introduces the complexities of dealing with negative exponents, guiding students from basic division that results in negative outcomes to more intricate divisions where both numerator and denominator have negative exponents. By the end, learners are adept at simplifying divisions involving negative exponents and grasping how these can result in either negative or positive exponents depending on the rules of exponent division. The unit is structured to progressively deepen understanding and application of exponent rules in diverse algebraic contexts.

Skills you will learn include:

This math unit begins by establishing foundational knowledge in understanding and converting common metric prefixes into numerical factors and their corresponding powers of ten, focusing on scales ranging from milli to kilo. Progressively, learners then apply these concepts practically by performing conversions within specific metric measurement units such as volume, mass, and length, making comparisons and calculations that incorporate decimal precision. The unit further evolves by incorporating scientific notation, where students practice converting small and large numbers to and from scientific notation, refining their ability to manipulate powers of ten for precision in representation. Initially, conversions maintain zero decimal places, gradually advancing to maintaining up to two decimal places to enhance exactitude in scientific calculations. Towards the end, the unit integrates scientific notation with metric units, extending the learners’ capacity to handle very large and small numbers by converting them into appropriate metric unit abbreviations. This encompasses handling units from terabytes and terajoules to nanometers, reinforcing a comprehensive understanding of the metric system and scientific notation in various contexts.

Skills you will learn include:

This math unit progresses from foundational concepts of exponents toward more complex applications and variations. Students begin by learning to calculate perfect squares and identify whether a number is a perfect square. Skills further develop into solving equations involving squares and square roots, enhancing their mastery of these operations as they apply them to find unknown variables. The unit then delves deeper into general exponent calculations and explores the impact and rules of exponents involving negative bases and negative exponents, including their application in fractional forms. Advanced topics also include calculating powers when the base is a negative number or a fraction, requiring a comprehensive understanding of how exponents influence the magnitude and sign of results. This progression solidifies students' skills and understanding of exponents, preparing them to handle complex algebraic operations involving varying powers and bases with confidence.

Skills you will learn include:

This math unit guides students through a structured exploration of the relationships between fractions, decimals, and percents. Initially, the unit focuses on converting fractions to decimals, helping students understand how these representations are related by providing practice with straightforward conversions. The unit then progresses to converting decimals into fractions, reinforcing inverse operations and deepening comprehension of these concepts. The exercises evolve to include operations involving powers of ten, which scaffold students' ability to manipulate and simplify fractions and decimals in more complex scenarios. This skill is crucial as it leads into converting these simplified forms into percents, a vital aspect of understanding proportional reasoning and the interconnectedness of these mathematical concepts. Toward the end of the unit, students transition from converting fractions and decimals into percents to converting percents back into decimals, mastering the bidirectional flow between these numerical forms. This full-circle understanding equips students with the necessary skills to handle a variety of problems involving fractions, decimals, and percents, emphasizing the application of powers of ten to achieve precision in conversions.

Skills you will learn include:

This math unit advances students from basic to advanced understanding of the order of operations, also known as BEDMAS. Initially, the unit emphasizes memorizing the BEDMAS acronym and understanding what each letter represents for operations in mathematics. As the unit progresses, students practice applying these rules through increasingly complex scenarios. Beginning exercises focus on identifying the sequence of operations for basic arithmetic functions. Later, the worksheets introduce more challenging components such as parentheses and exponents. Advanced topics challenge students to practice order of operations in expressions that combine multiple operations, including long expressions without parentheses, and ones containing both parentheses and multiple arithmetic operations, often involving up to five numbers. This unit thoroughly prepares students to systematically break down and solve complex mathematical expressions by adhering to the hierarchy of operations.

Skills you will learn include:

This math unit progresses students through a comprehensive understanding of prime factorization, beginning with basic prime factorization tasks and extending into more complex exercises that require a deeper understanding. Initially, students learn to decompose numbers into sets of three prime factors, using tools like factor trees and multiple-choice questions to guide their understanding. As the unit progresses, the complexity increases as students work with four and eventually five prime factors. They practice expressing these factors in exponential form, which is particularly useful for succinctly representing repeated prime factors. Towards the middle and end of the unit, the focus shifts to applying prime factorization in various contexts, such as completing and explaining parts of factor trees, and identifying missing factors. The unit culminates in ensuring students can differentiate between prime and composite numbers, enhancing their foundational understanding of number properties and ultimately strengthening their skills in recognition and categorization of numbers based on their factorization. This progression not only solidifies their comprehension of prime factorization but also enhances their analytical and problem-solving skills in mathematics.

Skills you will learn include:

This math unit initiates students into the concept of scientific notation by teaching them to convert large and decimal numbers between standard and scientific notation formats. Initially, students learn to express large numbers without decimal places in scientific notation and then shift towards handling numbers in standard form with one or two decimal places for precision. As the unit progresses, attention turns to converting various units and decimal values to scientific notation with exact digits and maintaining precision up to two decimal places. Further, the unit advances into more complex numerical operations within the realm of scientific notation, such as multiplication and division of numbers (involving both positive and negative exponents) without decimal places in the factors or products. These exercises help students master the efficient representation and manipulation of numbers, crucial for applications in science and mathematics.

Skills you will learn include:

This math unit progresses learners through a thorough exploration of exponent operations, beginning with basic multiplication and division of positive exponents. As the unit advances, students practice more complex scenarios involving negative and fractional exponents. Initially, the focus is on multiplying and dividing terms where both the bases and their exponents are positive, honing skills in simplifying expressions by adding or subtracting exponents. The complexity increases as learners encounter division problems yielding negative or fractional results, requiring a deeper understanding of how exponent signs affect outcomes. Further sophistication in handling exponents emerges with multiplication and division operations involving negative exponents, challenging students to manipulate powers with opposite signs and simplify to both negative and positive outcomes. The unit leads to proficiency in manipulating and simplifying expressions across a variety of exponent-related scenarios, reinforcing a robust understanding of exponent rules and their practical applications in algebra.

Skills you will learn include:

This math unit starts with foundational algebra concepts, encouraging students to develop algebraic thinking through balance problems and simple substitutions without explicitly introducing variables and equations. As the unit progresses, students move on to solving linear equations by isolating one variable and manipulating three-term equations using basic arithmetic operations including addition and subtraction. The unit further deepens comprehension of algebra by introducing variable substitution in simple algebraic expressions and balancing equations from visual cues. Later, students engage with the manipulation and evaluation of algebraic functions involving negative integers, fractions, and bracketed squared terms. The curriculum culminates in calculating exponents, solidifying an understanding of advanced algebraic operations. Throughout this progression, the focus shifts from intuitive problem-solving and basic operations to complex algebraic manipulations and computational skills in various algebraic contexts.

Skills you will learn include:

This math unit begins with students identifying and describing nets of 3D shapes to understand how these shapes unfold, establishing foundational geometry concepts. Progressively, the unit transitions into calculating areas, starting with relatively simpler forms like right triangles, then advancing to more complex shapes such as circles, enhancing understanding of area calculations using formulas and calculators. Next, the unit concentrates on calculating the surface area of different prisms, ranging from rectangular to triangular, incrementally challenging students to handle more complex 3D shapes. Furthermore, the unit deepens geometric understanding by involving students in exercises counting the edges, faces, and vertices of various 3D shapes—both from shapes to properties and vice versa. This reinforces knowledge of 3D forms and develops spatial visualization and geometric analysis skills, essential for mastering the geometry involved in calculating areas and understanding 3D properties.

Skills you will learn include:

This math unit begins by introducing students to the concept of volume through practical examples, starting with counting blocks to determine the volume of rectangular prisms. The unit progresses to calculating the volumes of more complex prisms, such as triangular and pentagonal prisms, enhancing learners' understanding of volume calculation in diverse three-dimensional shapes. Alongside volume, the unit delves into the geometric properties of various 3D shapes, challenging students to identify and count edges, vertices, and faces. These exercises develop spatial visualization and geometric analysis skills that are fundamental for understanding surface areas and the structural elements of three-dimensional objects. Towards the end of the unit, the focus shifts slightly to include surface area calculations, starting with the basics like the area of a circle and then a right triangle, applying these principles within the context of broader geometric studies.

Skills you will learn include:

This math unit starts with a focus on understanding and manipulating equivalent ratios in practical contexts such as adjusting recipe quantities with whole numbers. It then progresses to solving similar problems involving decimals, emphasizing precision in calculation. As the unit develops, students also learn to handle ratios using fractions, both expanding and shrinking recipes, which enhances their skills in fraction operations and understanding proportions in real-life applications. The unit further advances to solving problems using non-integer multiples for scaling recipes, applying these concepts in more complex scenarios with both decimals and fractions. Students are also introduced to unit rates, where they calculate and compare unit prices in real-world shopping scenarios, utilizing both decimals and fractions. This section of the unit sharpens their practical mathematical skills, especially in financial literacy. Overall, the unit evolves from basic ratio and proportion manipulations to more intricate applications, preparing students to utilize these concepts adeptly in daily situations and complex mathematical contexts.

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 begins by introducing learners to the metric system and its measurement units, focusing initially on understanding and converting metric prefixes and their abbreviations. Students start with basic exercises that match numeric factors to metric abbreviations and progress to more complex conversions involving metric volume units with decimals. They also learn to compare the size of common metric prefixes to identify which represents a larger value. Further into the unit, students apply their understanding of metric conversions to real-life scenarios using map scales. They practice converting map scales into real-world distances, which involves recognizing different metric units such as kilometers, hectometers, and decameters, and calculating the actual distance from a map measurement. The unit advances to interpreting and applying different scales on maps to solve problems that involve converting measurements to various metric units. Through step-by-step progression, students also revisit and deepen their understanding of metric volume measurements, enhancing their skills in precision and decimal manipulation within the metric system. Lastly, the unit consolidates the ability to convert metric prefixes to their corresponding power of ten, ensuring a comprehensive grasp of the metric conversion process.

Skills you will learn include:

This math unit begins by developing students’ ability to recognize and complete arithmetic number patterns, both increasing and decreasing, to enhance logical reasoning and pattern recognition skills. The unit progresses to more complex geometric patterns, where students identify missing terms, practicing multiplication sequences and progression analysis. Shifting focus to series and summation, the unit introduces expressing and calculating sums of integer series, moving from simple addition to formal summation notation and back, thoroughly engaging students in understanding and applying summation in various contexts. Towards the end of the unit, the focus shifts to applying these skills in different contexts: formulating the first terms from equations for arithmetic sequences, identifying sequence types from initial terms, and solving problems involving exponents, specifically identifying ones-digit patterns in powers. This progression finely intertwines pattern recognition, arithmetic operations, series, and exponentiation to build comprehensive numerical and algebraic skills.

Skills you will learn include:

This math unit progressively introduces and develops students' understanding and skills in handling negative integers through a variety of operations using number lines and arithmetic calculations. Initially, students practice identifying and locating negative integers on number lines, gradually moving to interpret these visual representations by plotting points and matching them with given integers. The unit then advances into operations, beginning with single-step additions and subtractions of negative integers depicted through movements on number lines. Students learn to translate these movements into proper addition and subtraction equations. Further, the complexity increases as they delve deeper into subtraction exercises, strengthening their familiarity and computational skills with negative values through multiple practice problems. The final segments of the unit introduce and practice the division of negative integers, reinforcing understanding of division rules with negatives and solidifying the concepts needed to handle various combinations of positive and negative integers effectively.

Skills you will learn include:

This math unit begins with the basics of long division without remainders, focusing on two-digit dividends divided by single-digit divisors. Students start by mastering the process of performing exact divisions that yield whole numbers, establishing a strong foundation in division skills. The unit progresses to introduce remainders in division, first with similar two-digit by one-digit scenarios, and then advancing to more complex three-digit by one-digit equations, enhancing their problem-solving skills and understanding of division concepts. Further complexity is added by involving three-digit dividends with single and later two-digit divisors, navigating both no remainder and remainder scenarios. The unit also integrates related skills such as identifying missing values in multiplication and division equations, which deepens students' arithmetic comprehension and inverse operation skills. By the end of the unit, students are adept at handling various types of division equations, including long division with larger numbers and successfully calculating and interpreting remainders in diverse numerical contexts.

Skills you will learn include:

This math unit begins with understanding the concept of perimeter through calculating missing side lengths of rectangles using given perimeters and side ratios. It progresses into more complex scenarios where students solve for side lengths with variables and fractional ratios. As the unit advances, the focus shifts toward the area of a rectangle, starting with exercises that require finding a side length given the area and one dimension, escalating to solving with the sides represented as variables and ratios, including fractions. Towards the latter part of the unit, practical applications are introduced where students calculate how many tiles are needed to cover an area, enhancing their understanding of the relationship between area, length, and width. The unit culminates with comprehensive exercises that integrate both perimeter and area calculations to determine rectangle dimensions, thereby reinforcing the students' abilities to apply conceptual and practical understanding of these geometric properties in various contexts.

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 progresses through a sequence of skills centered around the concept of prime factorization and finding the Greatest Common Factor (GCF). It begins with learning to factor numbers into primes up to four factors and advances into practical applications using Venn diagrams to visually identify common factors. Initial worksheets guide students through identifying the GCF of two numbers using these diagrams, progressing to more complex scenarios involving three numbers. The unit then explores multiple-choice problem settings where students have to select the GCF from given options, first with pairs and later with sets of three numbers. It further deepens the understanding of prime factorization by enabling students to determine if a number is a factor of another or both, using factor values or variables represented in factorized form. The concluding topics solidify the students' ability to recognize and use prime factorization and the GCF concept in various mathematical contexts, providing a foundational skill set for more advanced mathematical studies.

Skills you will learn include:

This math unit guides students through the process of dividing fractions in various forms, starting with basic fractional concepts and progressing to more complex operations. Initially, the unit introduces students to the concept of dividing simple fractions by whole numbers, using visual aids to help understand and formulate the process. This progresses into translating these visual representations into mathematical equations and vice versa. As students become more comfortable with simple fractions, the unit introduces division involving improper fractions, mixed numbers, and the relationship between division and multiplication by emphasizing the conversion of division into equivalent multiplication expressions and not simplifying results to focus on the mechanics of division. The unit steadily builds from foundational skills to more advanced operations where students divide whole numbers by mixed and improper fractions, further reinforcing understanding by moving from nonsimplified answers to complete simplification, thus enhancing students’ ability to manipulate and simplify fractional expressions in diverse mathematical scenarios.

Skills you will learn include:

This math unit begins by introducing students to the basic geometry of circles, focusing initially on calculating the circumference using the diameter and the radius. It then advances to include calculations involving a calculator and understanding the mathematical constant Pi (π), which is integral to circle geometry. As the unit progresses, the emphasis shifts towards the more complex area calculations of a circle, starting from using either its diameter or radius. Here, students learn to express these areas in terms of pi, furthering their application of pi in practical scenarios. The exercises evolve from employing basic formulas to more demanding tasks that require estimating and approximating pi, both with and without the use of calculators. This progression not only strengthens their operational skills but also deepens their understanding of how circle measurements relate to real-world applications, thus providing a comprehensive overview of circle geometry.

Skills you will learn include:

This math unit begins with students identifying types of triangles based on side lengths and progresses to more complex geometrical analysis, including the calculation and application of angle relationships. Initially, students classify triangles as equilateral, isosceles, or scalene. They move on to calculating and understanding the sum of interior angles in various polygons, applying this understanding specifically to triangle geometry. As the unit progresses, the focus shifts to solving for missing angles in triangles using algebraic equations, building on the triangle angle sum property. Subsequently, students examine the properties of isosceles and equilateral triangles, learning to deduce angles and side lengths based on given information. The unit culminates in applying these concepts to scalene triangles, enriching students' overall understanding of how side lengths and angles interrelate in different triangle types. This comprehensive approach helps students solidify their understanding of triangle geometry within broader geometrical contexts.

Skills you will learn include:

This math unit revolves around the application and mastery of percentages, starting from basic operations with decimals and percent calculations, and progressing to practical financial applications. Initially, students practice multiplying decimal tenths by tens to grasp decimal operations. The unit then delves into percentage calculations, beginning with simpler tasks such as determining what percentage one number is of another using 10% and 5% increments. As proficiency develops, students engage in calculating exact percentages of numbers even in 1% increments. The unit advances to applying these percentage skills to real-world scenarios involving percentage growth, reduction, and changes in numbers, emphasizing multiple real-life applications including financial scenarios like money growth and reductions. Operating primarily in 5% and 10% multiples, it gradually guides students through increasingly complex percentage problems, enhancing their computational abilities and preparing them for diverse practical applications of percentage calculations in everyday life.

Skills you will learn include:

This math unit begins with developing an understanding of determining the ones digit in products and exponents, starting with calculations involving small bases and progressively tackling larger bases and exponent values. Initially, students practice recognizing cyclical patterns of ones digits in small numbers raised to multiple powers. The unit progresses to include larger base numbers, where students continue to discern ones digit patterns through repeated multiplication and exponentiation, moving towards understanding the effects of varying power sizes on the final digits. Midway through the unit, the focus shifts towards prime factorization. Here, skills are honed in identifying whether an integer is a factor of another, using prime factorization to understand and check commonality between numbers, leading to an appreciation of greatest common factors. Concluding topics return to digit solving but with increased complexity: students work with both large and small exponents, exploring how exponent multiplication affects the ones digit when the exponents are identical or different. These exercises deepen conceptual understanding of patterns in ones digits within the framework of modular arithmetic and number theory, solidifying students' skills in pattern recognition and exponent manipulation.

Skills you will learn include:

This math unit begins with basic skills, teaching students to identify points on a Cartesian grid using positive coordinates. They then progress to applying geometric concepts such as the calculation of line lengths to determine missing coordinates. As the unit advances, learners explore the area calculations of geometric figures like rectangles, right triangles, and parallelograms positioned in the first quadrant of the grid. Subsequently, the unit introduces more complex scenarios that incorporate the determination of missing coordinates based on the area of acute triangles and the perimeter of rectangles using only positive values. Eventually, the unit extends these principles by including negative coordinate values, challenging students to apply their skills in more diverse scenarios. This gradual increase in complexity enables students to develop proficiency in manipulating the Cartesian grid to solve various geometric problems involving area and perimeter calculations and enhances their spatial and logical reasoning skills.

Skills you will learn include:

This math unit begins by helping students understand and use the Pythagorean theorem for calculating hypotenuse and other side lengths of right triangles using radical values. It progressively teaches them to solve Pythagorean equations from provided values or squares, initially focusing on radical forms and later introducing decimals for more complexity. As students move through the unit, they practice basic algebraic manipulations including solving for missing values and computing square roots from equation formats. The unit also strengthens foundational understanding of squares and square roots, starting from identifying perfect squares and approximating square roots, which serves as an essential precursor to effectively applying the Pythagorean theorem. This progression not only enhances students' abilities in handling equations and geometric concepts but also bolsters their number sense and estimation skills, fundamental to more advanced mathematical topics.

Skills you will learn include:

This math unit begins by building foundational skills in multiplying decimal numbers by powers of ten, progressing to involve more complex scenarios like handling different decimal places and incorporating negative powers. It further delves into the practical application of scientific notation, starting with conversions from scientific to standard form, both without decimal places and progressing to one and two decimal places, enhancing precision. The unit then reverses the process, teaching students to convert small decimals into scientific notation for different decimal precision levels. As the unit advances, it integrates more demanding multiplication tasks involving numbers in scientific notation, requiring students to apply their understandings of exponent rules and decimal shifts. This culminates in sophisticated operations involving the multiplication of decimal numbers representing both the tenths and hundredths by whole numbers or powers of ten, significantly sharpening precision and efficiency in handling complex numerical transformations. The unit closes with a focused practice on multiplying powers of ten within scientific notation, reinforcing the rules of exponents effectively.

Skills you will learn include:

This math unit starts with basic geometry concepts, initially focusing on the estimation and calculation of angles formed by various lines. It progresses from estimating angles in reverse and calculating complementary angles that sum up to 90 or 180 degrees, to more complex problems involving identification and calculations related to intersecting, parallel, and perpendicular lines. As the unit advances, students are tasked with identifying relationships between lines and solving for unknown angles in geometrical setups involving crossing lines, both parallel and perpendicular. They refine their understanding of angles in different contexts, including naming and calculating degrees in triangles and other formations. The unit also helps students apply these skills in practical scenarios involving diagrams, fostering a deeper understanding of geometry and its applications.

Skills you will learn include:

This math unit begins with an exploration of simple interest, where students first learn to calculate interest using principal, rate, and time. This skill is expanded upon by solving for different variables such as principal and rate based on given values of interest and other factors. As the unit progresses, students also learn to determine the time required to earn a specified amount of interest. These initial topics set a strong foundation in understanding how interest accumulates in financial contexts. Later, the unit shifts focus to the growth and reduction of money through percentage calculations. Students practice calculating the final amount of money after applying percentage increases and decreases in specific multiples (10% and 5%), considering various financial scenarios including tips, interest growth, taxes, and discounts. This transition from simple interest calculations to broader percentage manipulations allows students to apply their mathematical understanding in diverse and practical financial situations. This progression enhances their capability to handle real-life financial tasks efficiently.

Skills you will learn include:

This math unit starts with teaching students the fundamentals of prime factorization, enabling them to break down numbers into their prime components using factor trees. As students advance, they explore Venn diagrams to grasp the relationship between different sets of numbers, primarily focusing on identifying common and distinct factors. The unit progresses to more complex applications by teaching how to utilize these factorizations to find the lowest common multiple (LCM) of two and eventually three numbers. This skill is fundamental in solving problems involving the LCM in both numerical and variable formats, enhancing students' understanding of divisibility, multiples, and their practical applications in different scenarios. Through a repetitive, yet increasingly challenging set of exercises, students strengthen their factoring skills and apply these in diverse contexts, including populating Venn diagrams correctly and determining multiplicity from algebraic expressions. This structured progression is vital for mastering the essentials of number theory related to factors and multiples.

Skills you will learn include:

This math unit develops skills around advanced fraction addition and subtraction, especially focusing on problems involving fractions with different denominators. It starts with simpler fraction addition tasks, guiding students on how to set up and solve problems where two fractions have different denominators, progressing towards advanced simplification of answers. As the unit progresses, students also encounter subtraction problems requiring a similar approach of finding a common denominator, but with added complexity in terms of simplifying results and not simplifying results to enhance understanding. Furthermore, the unit evolves to dealing with missing values in equations, challenging students to determine the missing fraction to balance addition or subtraction equations. This applies to simple fractions and mixed fractions, progressively building problem-solving skills and a deep understanding of fraction operations with varied complexity and context.

Skills you will learn include:

This math unit begins with foundational skills in recognizing and computing perfect squares within numerical sequences. Students first practice identifying missing squares from sequences and then apply similar skills to determine the closest perfect square below a specific number. The unit progresses to locating the nearest perfect square above given numbers, further reinforcing these basic concepts. As students advance through the unit, the focus shifts to more complex tasks involving approximation techniques. They learn to approximate non-whole numbers to their squared values, identifying perfect squares immediately above and below these approximations. The unit then moves to deeper analysis, where students approximate square roots to the nearest whole integers. They practice bracketing square roots of numbers between two consecutive integers, enhancing their ability to estimate and understand square roots relative to whole numbers. Overall, the unit develops from fundamental recognition of perfect squares to more sophisticated approximation of square roots, forming a comprehensive approach to understanding squares and roots in mathematical sequences.

Skills you will learn include:

This math unit begins with enhancing students' understanding of basic division by powers of ten, emphasizing the adjustment of decimal places when dealing with positive integers. Progressing deeper into the unit, students learn to handle divisions involving decimals and negative powers of ten, further challenging their ability to manipulate decimal values effectively. Fractional representations of division are introduced to solidify comprehension of decimal interactions. Later, the unit transitions into long division where the results are decimals, aiming to solidify manual calculation skills and precision with remainders. Pivoting towards scientific notation, students then practice multiplying decimals by powers of ten, preparing them for converting numbers in scientific notation to standard decimal forms. This gradually escalates in complexity from zero to two decimal places, enhancing students' accuracy and understanding of scaling numbers by powers of ten. The unit culminates with exercises on dividing whole numbers by decimal tenths, reinforcing a comprehensive grasp of decimal division concepts throughout various practical scenarios.

Skills you will learn include:

This math unit begins with learning the basics of adding mixed fractions with different denominators without simplification, progressing to mastering the addition with one or two denominators changed. Students first focus on the mechanics of fraction addition, then move towards adding and subtracting fractions with varying complexities, including finding and adjusting to common denominators without initially simplifying the results. As the unit progresses, students learn to simplify their answers post-addition and subtraction, enhancing their skills in reducing fractions to their simplest form. Further into the unit, subtraction of mixed fractions is introduced, where students continue to work on problem setup and simplification. They also tackle more complex problems that involve finding missing values in addition and subtraction equations, illustrating a deepened understanding of fraction operations and the importance of denominator alignment. This sequence strengthens their ability to handle multiple aspects of fraction manipulation, culminating in a comprehensive grasp of adding and subtracting fractions with mixed numbers.

Skills you will learn include:

This math unit begins with prime factorization, teaching students to break down numbers into prime factors, which sets a solid foundation in understanding numbers' structural properties. The unit progresses to various aspects of factoring, such as transforming expressions from a factored form to a composite form and vice versa. These activities enhance students' fluency in manipulating expressions and deepen their understanding of the multiplication and division processes. As the unit advances, the focus shifts towards applying these factoring skills to simplify fractions, initially working with composite numbers and gradually moving towards more complex fractions. Through structured problem-solving, students learn to factorize both numerators and denominators, simplifying fractions to their most reduced forms. By the end of the unit, students are adept at simplifying multiplication and division of fractions through factorization, mastering a crucial aspect of algebraic manipulation and enhancing their overall mathematical problem-solving skills.

Skills you will learn include:

This math unit begins by developing students' understanding of exponent multiplication and division, especially focusing on operations involving negative exponents. Students first practice multiplying positive by negative exponents, followed by dividing negative exponents which lead into simplification tasks involving negative to negative and negative to positive exponential operations. The unit progresses to more complex applications of the exponent power laws, understanding different bases including variable, prime, and composite bases. Students engage with multiple exponent layers and practice resolving expressions where variables are raised to negative and fractional powers. This includes tasks like simplifying equations with bases raised to another power and calculating resultant exponents when similar terms are multiplied. Towards the end, students apply these exponent operations to solve for unknown exponents in algebraic expressions involving different types of bases and powers. They work on reducing complex exponential expressions and solving equations that equate expressions with variable and known powers, enhancing their exponent manipulation skills crucial for algebraic proficiency.

Skills you will learn include:

This math unit focuses on developing skills in unit conversions, beginning with simpler tasks using single ratios and progressing to more complex scenarios involving two ratios. Initially, students practice setting up and solving unit rate conversion problems with one ratio, learning how to handle different units such as yards per second and feet per second, and converting between time and length measurements. As they advance through the unit, they start dealing with real-world contexts, applying their conversion skills to practical situations involving speeds and distances. Towards the later part of the unit, the complexity increases as students work with two ratios in their conversions. They tackle more challenging exercises, which require understanding and setting up problems involving multiple units and steps, such as converting rates involving different measurements systems like feet per second into yards per minute. The unit culminates with students solving word problems that require applying dual ratios to find the correct answers, enhancing their ability to perform multidimensional analysis and proportional reasoning in practical scenarios.

Skills you will learn include:

This math unit begins by teaching students how to calculate the area of circle sectors using fractional parts and then transitions to angle-based methods. Initially, students learn to calculate both exact areas and those rounded to the nearest integer using the sector's fraction of a circle or the given central angle. As the unit progresses, the focus shifts to more complex figures such as the 'circle donut', where students find either the inner or outer radius given other dimensions. Advanced topics cover converting given sector information into other properties like fractional coverage, sector angles, or arc lengths. Moving from specific area calculations to deducing other sector characteristics, learners deepen their understanding of the relationships between different properties of circle sectors. This helps in developing a comprehensive skill set in circle geometry, enhancing spatial reasoning and problem-solving abilities within the context of circle sectors and their broader geometric implications.

Skills you will learn include:

This math unit progresses from fundamental understanding of number patterns to applications involving algebraic expressions and sequences. Initially, students work with polynomial and arithmetic sequences, identifying specific terms or missing values, which strengthens their grasp of polynomial sequences and decreasing arithmetic patterns. The unit evolves to cover geometric sequences, allowing students to discern multiplication patterns. As the unit progresses, there's a significant shift towards understanding and applying exponents, particularly in identifying units digits of large numbers raised to powers, fostering skills in recognizing patterns and predicting behavior in exponentiation. Further developing their skills related to sequences, students learn to express sums of series using summation notation, transitioning from basic addition to more complex algebraic representations. They also work on determining the sums of integers from 1 to N and convert summation notation to expanded addition. Moreover, towards the latter part of the unit, students deal with interpreting and creating rules for arithmetic sequences, amplifying their algebraic thinking and application skills. Understanding the structure and rules of decreasing arithmetic patterns through equations refines their ability to apply mathematical operations and recognize patterns within sets of numbers.

Skills you will learn include:

This math unit advances students' knowledge in the metric system, focusing on understanding the relationship between prefixes, exponents, and abbreviations for both extremely large and small measurements. Initially, students learn to convert metric prefixes into corresponding powers of ten and vice versa, beginning with larger units and then addressing smaller units. Their knowledge is then extended to associating these powers with standard metric abbreviations, facilitating precise unit identification based on scientific notation. Progressing further, students engage in converting between various metric length and mass units involving decimals, enhancing their practical and computational skills in unit conversion. The introduction of mnemonic devices aids in retaining and applying the concepts of powers and prefixes effectively, especially when dealing with very large or small magnitudes. Finally, the unit includes exercises that challenge students to compare and determine relative sizes of metric units, solidifying their understanding of the metric system's hierarchical structure. This comprehensive approach develops a thorough competency in metric measurements and conversions, vital for mathematical and scientific applications.

Skills you will learn include:

This math unit progresses through a focused study of three-dimensional (3D) geometry, beginning with the investigation of surface areas for various prisms and moving towards more complex geometrical calculations. Initially, students learn how to calculate the surface area of rectangular prisms by assessing individual block faces exposed on the outside. This foundational skill is deepened through the examination of edges, vertices, and faces on diverse 3D shapes, enhancing their ability to visualize and analyze geometric properties. The curriculum then advances to understanding nets of these shapes and applying learned concepts to calculate surface areas of cylinders and triangular prisms. Further, students explore formulas involving Pi, such as calculating the area and circumference of circles, intricately linking circle geometry with 3D contextual applications. Overall, this unit equips students with robust skills in visualizing, analyzing, and computing properties of various 3D objects, critical for comprehensive geometry education.

Skills you will learn include:

This math unit begins with foundational practices in the power laws of exponents, focusing initially on expressions where variables serve as the bases and are raised to positive powers. As students progress, they delve into more complex scenarios involving prime and composite bases, extending to situations with both positive and negative exponents, including fractional bases. The complexity increases as they engage in solving for unknown exponents in equations, where bases could be variable, known, or prime, and powers are further raised to another power. Throughout the unit, students hone skills in simplifying, multiplying, and manipulating expressions with exponents through a variety of problem settings, enhancing their proficiency in algebraic manipulation and understanding of exponent rules crucial for advanced mathematical concepts. The unit culminates in the application of these skills to solve for missing exponent values in expressions, demonstrating growth from basic exponentiation rules to solving complex exponential equations.

Skills you will learn include:

This math unit guides students from understanding prime factorization to mastering the identification and application of the Greatest Common Factor (GCF) across different numbers. Students begin with exercises that simplify numbers into their prime factors using factor trees, enhancing their initial familiarity with factorization. As the unit progresses, learners utilize Venn diagrams to visually identify common factors. This approach not only aids in finding the GCF for pairs and sets of three numbers by recognizing overlap in factors, but also challenges students to discern GCFs from more complex diagrams and factor relationships. Subsequently, the unit integrates the use of variables and algebraic expressions in factorization, deepening students' ability to work with abstract representations of numbers. By the end of the unit, students are adept at applying these skills to solve problems that require identifying the GCF and understanding the underlying factor relationships through both numerical calculations and visual aids. Thus, establishing a robust foundation in factorization that supports advanced mathematical concepts and problem-solving.

Skills you will learn include:

In this math unit, students progress through a sequence of topics that build foundational to advanced skills in algebra. The unit starts with basic skills such as expanding and simplifying algebraic expressions when multiplying a variable by a bracketed term, followed by solving linear equations with increasing complexity—from three to four terms. It then advances to manipulating algebraic fractions, where students solve and simplify equations that involve fractions with variables. The complexity in fraction manipulation progresses across orientations until students deal with comprehensive problems that require reducing fractions that involve variables to their simplest forms. Towards the end of the unit, the focus shifts to applying algebra in practical contexts using balance shapes. Students learn to analyze image-based problems and to use substitutions and subtraction to solve for the equations and answer visually represented through balance beams. This culminates in understanding complex ratios, substitutions, and algebraic manipulations through symbolic and visual interpretations, rounding out their algebraic skills with both numerical and real-world problem-solving abilities.

Skills you will learn include:

This math unit begins by developing students' foundational understanding of circle geometry, starting with calculating the area of a circle using its radius and the value of π, and finding the radius from the diameter. Students initially perform these calculations manually, learning to express results in terms of π. The unit progresses to more complex applications involving areas and circumferences of circles with and without calculators. Subsequently, the unit advances to three-dimensional shapes, specifically focusing on cylinders. Students learn to calculate the volume of cylinders using given dimensions and progress to more challenging problems such as determining missing dimensions (radius, height, or side) from the volume and other known measurements. Understanding the relationships between dimensions and applying these in formulas is emphasized, alongside the use of π in calculations. Towards the end of the unit, students explore the spatial reasoning involved in identifying and describing nets of three-dimensional shapes, expanding their geometric insight into how 2D shapes can represent 3D objects, thus rounding out their understanding of geometry from basic area calculations to complex three-dimensional analysis.

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 guides students from basic to more complex applications of percentage calculations, starting with finding set multiples of percentages of a number and advancing towards applying percentages in realistic scenarios. It begins by familiarizing students with calculations of simple percentages (10% and 5% multiples) of given numbers to build foundational skills. As the unit progresses, the complexity increases as students learn to compute unknown quantities when one number is a defined percentage of another, utilizing real-world examples like calculating percentage increases or decreases. The unit further delves into scenarios involving financial contexts, emphasizing how percent changes affect money through calculations of percentage growth on investments or price reductions. Each step advances the learners’ ability to manipulate and understand percentages in various practical and everyday contexts, culminating in proficient application skills.

Skills you will learn include:

This math unit starts by introducing students to the basic concepts of the metric system, focusing on metric unit abbreviations and their corresponding powers of ten. Students learn to identify and match abbreviations to exponent values and to differentiate between very large and very small metric units. The unit progresses to more complex skills, such as using mnemonic devices to remember the order of metric prefixes for extremely small to extremely large units. Later, students practice converting numbers between normal and scientific notation, rounding to two decimal places, which is crucial for expressing large and small quantities succinctly. The unit then shifts to more applied skills, such as converting various metric units—length, volume, and mass—with a focus on precision and understanding of decimal placements in real-world contexts. These exercises are presented in multiple-choice format, enhancing students' understanding and mastery of metric unit conversions and the relationships among different units in a comprehensive, practical manner. Through these sequential topics, students build a strong foundation in both theoretical and practical aspects of the metric system and scientific notation.

Skills you will learn include:

This math unit begins by teaching students to calculate speed from distance and time with an emphasis on unit conversions, advancing to more complex scenarios involving calculating car speeds and travel times using clock times. Students progress to comparing travel times among different moving objects requiring unit conversions and applying these skills to return trip scenarios. The unit develops further by incorporating variables and changing units in problems that involve calculating time from distance and speed, as well as speed from distance and time intervals. Advanced topics include scenarios where two cars, traveling the same distance or duration at different speeds, require calculations to solve for unknown speeds using algebra. The unit peaks with problems that challenge students to determine which of two entities is faster or has traveled further, involving complex conversions between different units of distance and time, enhancing problem-solving skills, algebraic manipulations, and understanding relationships within speed, distance, and time contexts.

Skills you will learn include:

This math unit starts with foundational skills in understanding and calculating ratios, initially focusing on how to determine the total quantity from given subgroup ratios and how to use visual cues to calculate specific item counts based on visualized ratios. Progressively, the unit shifts towards more advanced applications of ratios in the context of trigonometry. Students practice solving for unknown lengths in geometric figures using basic trigonometric principles and ratio calculations, with exercises including parallel lines, right-angle line displays, and various triangular configurations. Towards the end of the unit, the focus shifts to practical applications of ratios and unit rates, where students calculate and compare unit prices and determine the best prices in decimal and fraction formats. This transition from basic to more complex applications provides students with a comprehensive understanding of ratio calculations and their practical implications in both geometric and everyday contexts.

Skills you will learn include:

This math unit starts with introducing students to using Cartesian grids to find missing coordinates based on the length of line segments with positive values, moving on to include negative coordinates, which adds complexity. The unit progresses from simple geometric reasoning to more complex problem-solving involving calculation of areas and perimeters of different shapes such as rectangles, right triangles, acute triangles, obtuse triangles, and parallelograms using known coordinates. As students advance, they solve for missing coordinates using given information about areas and perimeters, initially handling only positive and then including negative coordinate values. This math unit effectively builds from understanding basic Cartesian grid concepts and geometrical properties to applying these in solving increasingly complex problems, enhancing students' spatial reasoning, algebraic skills, and geometrical understanding for real-world and mathematical applications.

Skills you will learn include:

This math unit begins by introducing students to the concept of calculating the area of a rectangle using given side ratios and area values. It progresses by incorporating variables and fractional values into these area calculations, enhancing students' algebraic understanding and proportional reasoning with increasingly complex problems. The unit also broadens to include practical applications such as tile coverage problems, where students calculate the number of tiles required based on area, fostering spatial reasoning and application of the area concepts in practical contexts. Transitioning from area-focused topics, the unit shifts to explore the perimeter of rectangles. Here, students apply their skills to find missing side lengths using given perimeters and side ratios, with a progression towards handling variables, algebraic expressions, and fractional side ratios. This segment similarly evolves to include real-world applications such as segment coverage, requiring students to calculate how many given segments are needed to match a rectangle's perimeter. Throughout, the unit strengthens problem-solving skills, logical reasoning, and basic algebra within geometric contexts.

Skills you will learn include:

This math unit progresses through various aspects of understanding and calculating the slope of a line, as well as deriving other line characteristics such as rise and run using the slope formula. Initially, the unit introduces the basic terms "rise" and "run" and the concept of slope by identifying these components on a graph. Students then learn to compute the slope using the rise over run formula expressed as an equation. Progressively, they apply this understanding to determine the rise and the run from known values of slope and one of the other variables. Through practice, the unit strengthens students' ability to manipulate and solve equations involving slope, rise, and run. Later, this evolves into more complex tasks where slope is calculated between specific points or derived from graphical representations, enhancing skills in interpreting and analyzing linear relationships by applying algebraic methods and critical thinking.

Skills you will learn include:

In this math unit, students begin by expanding and simplifying algebraic expressions focusing on multiplying bracketed terms with the same variable, setting a foundational understanding of polynomial operations. They then progress to evaluating algebraic expressions through variable substitution, dealing initially with simple and negative terms, and advancing to more complex situations involving squared terms and negative coefficients. The practice intensifies as students substitute values into multiple fractional squared and bracketed squared terms, reinforcing their capacity to manage and compute expressions under specified conditions. Further advancing their algebraic skills, students practice solving basic linear equations to isolate variables, first with two terms and progressing to three terms, enhancing their handling of various algebraic functions. The unit culminates with advanced algebra concepts where students translate balanced shapes into equations, focusing on establishing and solving ratios, and involves visual and analytical skills by substituting and subtracting to find solutions in complex algebraic contexts. This flow from foundational polynomial operations to complex variable substitution and application in real-world contexts challenges students to deepen their understanding and proficiency in algebra.

Skills you will learn include:

This math unit progressively builds upon understanding prime factorization and factoring skills through various applications. Initially, students apply prime factorization to verify if one number is a multiple of others. Enhancing this base, they tackle similar problems using variables as factors, exploring more complex algebraic expressions. The unit proceeds to deepen comprehension of factor trees, where students identify prime factors extensively. Advancing further, the unit focuses on utilizing Venn diagrams and low-tech visual aids to determine the Lowest Common Multiple (LCM) and understanding distinct prime factors when factoring multiple numbers simultaneously. By analyzing various populated and theoretical sets, learners systematically identify LCMs and distinguish necessary prime factors across different scenarios. Finally, the course engages students in implementing Venn diagrams to find distinct factors and the greatest common factors (GCF), alongside nurturing their capability to analyze factorization through multiple choice challenges and factor tree construction, solidifying their skills in handling complex factoring and number theory tasks.

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 begins by teaching students how to calculate the volume of various prisms and cylinders, using standard formulas for three-dimensional shapes. It progresses towards a deeper understanding of these shapes' geometric properties by involving learners in tasks that require counting edges, faces, and vertices of different 3D shapes. After grasping the identification and basic counting of geometrical features, the unit then evolves to more complex activities, requiring students to work reversely -- selecting the correct 3D shape based on described properties such as number of faces and vertices. Moving forward, the unit returns to volumetric calculations but increases in complexity as students must now also compute missing side dimensions from given volumes and other dimensions, fostering a comprehensive understanding of spatial reasoning and applications of volume formulas in real-world contexts. The progression ensures mastery from basic volume calculation through to intricate manipulation of geometrical formulas and spatial properties.

Skills you will learn include:

This math unit begins by developing students’ understanding of multiplication in scientific notation, starting with problems that include multiplying normalized numbers projected in zero decimal places up to handling numbers with one decimal place. As students progress, they engage in more complex multiplications involving decimals and different powers of ten within the scientific notation framework. The unit transitions into division, initially focusing on dividing large numbers by powers of ten and then diving deep into dividing numbers in scientific notation, with zero decimal places and normalized formats. Throughout, the exercises emphasize manipulation and understanding of powers of ten, both in multiplication and division, enhancing proficiency in handling very large or very small numbers efficiently. The comprehensive approach from basic to more intricate problems helps solidify students’ grasp of scientific notation in both contexts, crucial for their mathematical development.

Skills you will learn include:

This math unit emphasizes the systematic exploration and application of the Pythagorean theorem in various geometric contexts, developing from foundational identification to advanced problem-solving skills. Initially, students learn to identify parts of a right triangle—distinguishing between legs and the hypotenuse. Progressing through the unit, learners apply the Pythagorean theorem to compute areas of squares on the sides of triangles and solve for the lengths of missing sides using algebraic and radical expressions. Advanced worksheets focus on solving real-world problems, including calculating side lengths in decimal form and handling Pythagorean triplets, further solidifying their understanding of triangle properties. The exercises evolve from simple recognition tasks to complex applications, demonstrating fluency in algebraic manipulations and enhancing geometric comprehension through practical scenarios and radical calculations.

Skills you will learn include:

This math unit begins by introducing students to negative integers on a number line, starting with identifying and labeling positions and then progressing to using the number line for addition and subtraction of negative integers. As the unit advances, foundational skills in arithmetic operations with negative integers, such as multiplication and division, are developed. The exercises become more complex by requiring multiple operations with single and paired negative integers to solidify understanding and application of these concepts. The latter half of the unit shifts focus towards algebraic functions, starting with basic substitution of variables in simple and fractional terms involving negative integers. Students practice evaluating algebraic expressions by substituting specific integer values, including negatives, into equations and computing the results. The complexity increases as they deal with fractional terms, algebraic expressions involving power operations, and distributive properties to simplify expressions with bracketed terms and negative integers. This culminates in a comprehensive understanding of handling negative numbers within arithmetic and algebraic contexts.

Skills you will learn include:

In this math unit, students progressively develop their skills in understanding and solving problems related to speed, distance, and time. Initially, the unit introduces scenarios where students calculate time and speeds for trains passing platforms based on given distances and speeds. The complexity advances as students solve for unknown variables such as speeds and lengths using principles of relative motion and algebraic techniques. The problems escalate from straightforward applications to more complex situations, including comparisons between two cars traveling the same distance at different speeds or for the same time duration but at varied speeds. These excursions into comparative analysis refine students' abilities to manipulate and solve for unknown quantities within given constraints. Towards the latter part of the unit, the focus shifts to person-based movement scenarios within trains. Students apply their understanding to compute relative speeds and distances, such as determining a person's speed relative to the ground or solving for the train's length based on a person walking through it. Each topic deepens understanding of the relationships between speed, time, and distance, enhancing students' problem-solving skills within real-world motion contexts.

Skills you will learn include:

This math unit begins with teaching students prime factorization using factor trees, gradually advancing their skills in breaking down numbers into four and then three factors. The unit progresses into applications of these factorization skills, specifically focusing on simplifying fractions. Initially, students practice converting composite fractions to their simplest forms by canceling common factors. As their understanding deepens, they apply factorization to simplify multiplication and division of fractions, a step that involves more complex and comprehensive manipulations of fractional expressions using factoring techniques. Further into the unit, the emphasis shifts toward analytical skills involving factor comparison. Students compare factored numbers, analyzing expressions with exponents to determine relational values using comparison operators. These tasks reinforce their understanding of multiplication, division, exponents, and deepen their comparative reasoning skills with multiplicative expressions. Towards the end, learners engage in identifying large numbers factored into three components, demonstrating an understanding of number decomposition and exponent manipulation, necessary for advanced arithmetic and algebraic functions.

Skills you will learn include:

This math unit begins with understanding the basics of Cartesian grids, such as calculating straight-line distances and understanding directions between points using simple movements like right, left, up, and down. Students then progress to applying geometric concepts such as the Pythagorean Theorem to calculate the lengths of sides in right triangles, focusing initially on identifying and using labeled sides in equations, and gradually moving towards expressing these lengths as radicals and decimals. As the unit advances, the complexity increases, integrating skills to calculate distances and directions on Cartesian grids using angles, and interpreting these distances both numerically and as radicals. The practice evolves from straightforward distance calculation between two points directly along grid lines to determining distances and directions expressed as vectors and angles, further utilizing the Pythagorean Theorem implicitly to compute distances shown as square roots. Towards the end, students apply the distance formula extensively, calculating the distances as radicals and understanding deeper spatial relationships in two-dimensional space through various problems that contextualize theoretical coordinate geometry into practical scenarios. Overall, the unit builds from foundational grid navigation and basic geometric calculations to sophisticated applications of algebra in geometry, enhancing both spatial awareness and algebraic skills.

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 with introducing the fundamentals of Pythagorean triples and the application of the Pythagorean theorem to solve for missing hypotenuse lengths in triangles. As learners progress, they deepen their understanding by identifying sets of integer lengths that form Pythagorean triples and practicing calculations involving the theorem for missing sides as well as the hypotenuse in right triangles. These exercises strengthen skills in solving for unknowns using the properties of right triangles and similar triangles. The unit progresses into more complex scenarios, reinforcing students' ability to apply these geometric principles to solve real-world problems. Towards the end, the practice involves the identification and calculation of side lengths and hypotenuse in triangles represented with decimal values and as scaled triples, ultimately enhancing the learners' proficiency in practical applications and numerical computation within the context of geometry.

Skills you will learn include:

This math unit focuses on the foundational concepts and manipulation of exponents using the power law. Starting with basic problems, students practice solving for unknown exponents when dealing with equations involving prime and composite bases paired with variable and unknown powers. Initially, the tasks require simplifying expressions with exponents based on established power laws, such as \((b^n)^m = b^{n \cdot m}\). As the unit progresses, problems increase in complexity, including working with variable exponent bases, transitioning between different numeral bases (primarily base ten), and solving equations where both bases and exponents can be variables or constants. Towards the end of the unit, the focus shifts to more specific manipulation of power laws involving base ten. Here, students deal with scenarios requiring the conversion between different powers of ten while determining unknown exponents. This sequence reinforces a thorough understanding of exponent rules, essential for algebraic manipulations and higher mathematical concepts, setting a strong foundation in handling exponents in various mathematical contexts.

Skills you will learn include: