The Mobius math curriculum is in line with what is typical for North American school boards. Topics are introduced, and then in subsequent grades, built upon. This repetition and return to foundations build strong mathematical reasoning skills. Below are the themes in each grade. Note that themes often continue for many years, so the theme will often contain material that is both well above and well below grade level.
The Mobius math curriculum is in line with what is typical for North American school boards. Topics are introduced, and then in subsequent grades, built upon. This repetition and return to foundations build strong mathematical reasoning skills. Note that themes often continue for many years, so the theme will often contain material that is both well above and well below grade level.
Focuses on basic addition and subtraction, number recognition up to 100, understanding place value, and solving simple word problems. Introduces concepts of time and money, and explores basic shapes and measurements to build a strong numerical foundation.
Develops addition and subtraction fluency, introduces basic multiplication and division, and strengthens understanding of place value. Explores simple fractions, measurement units, and geometric shapes. Emphasizes solving word problems and logical thinking to enhance mathematical reasoning.
Visual patterning involves identifying and extending patterns using shapes, colors, and objects. Key skills include recognizing sequences, predicting the next elements, and understanding the rules governing patterns. Mastery of visual patterning builds a strong foundation for logical thinking, problem-solving, and algebraic reasoning, as it helps students grasp the concept of regularity and structure, essential for advanced math topics like functions and sequences.
Addition and subtraction are fundamental operations that involve combining and removing quantities. Key skills include understanding number bonds, mastering basic facts, using place value, and applying strategies for regrouping. Mastery of addition and subtraction builds a foundation for arithmetic fluency, critical thinking, and problem-solving, essential for advanced topics like multiplication, division, algebra, and practical applications in everyday life and various academic disciplines.
Builds on multi-digit multiplication and division, deepens understanding of fractions and decimals, and introduces geometry concepts like angles, lines, and symmetry. Focuses on solving multi-step word problems and understanding factors and multiples for number theory foundations.
Emphasizes mastery of multiplication and division facts, introduces fractions as parts of a whole, and explores concepts of area and perimeter. Strengthens skills in addition and subtraction with larger numbers and begins simple data interpretation and representation.
Number patterns involve recognizing and extending sequences of numbers based on specific rules. Key skills include identifying arithmetic and geometric patterns, predicting subsequent numbers, and understanding the relationships between numbers. Mastery of number patterns builds a strong foundation for logical reasoning, problem-solving, and algebraic thinking, essential for advanced topics like functions, series, and mathematical modeling in higher-level mathematics.
Coin math involves using coins to teach counting, addition, and subtraction. Key skills include recognizing coin values, making change, and performing basic arithmetic operations with money. Mastery of coin math builds a strong foundation for financial literacy, helping students understand real-world transactions, budgeting, and saving. It also reinforces number sense and prepares students for more complex mathematical concepts involving decimals and percentages.
Multiplication and division involve combining equal groups and splitting quantities into equal parts. Key skills include understanding multiplication tables, performing multi-digit operations, and grasping the relationship between multiplication and division. Mastery of these operations builds a foundation for arithmetic fluency, problem-solving, and higher-level math topics like fractions, decimals, algebra, and real-world applications in finance, measurement, and data analysis.
Base ten blocks are visual tools that help students understand place value and arithmetic operations. Key skills include recognizing units, rods, flats, and cubes, representing numbers, and performing addition and subtraction with regrouping. Mastery of base ten blocks builds a strong foundation for understanding the decimal system, essential for more advanced math topics such as multiplication, division, and decimal operations.
Graphing and data involve collecting, organizing, and visually representing information using charts and graphs. Key skills include interpreting bar graphs, line plots, and pie charts, as well as understanding mean, median, and mode. Mastery of graphing and data builds a foundation for statistical reasoning, critical thinking, and data analysis, essential for advanced topics like probability, algebra, and real-world decision-making in various fields.
Picture numbers use visual representations to help students understand numerical concepts. Key skills include recognizing and interpreting pictures as quantities, comparing sizes, and performing basic arithmetic operations visually. Mastery of picture numbers builds a strong foundation for developing number sense, fostering comprehension of abstract mathematical concepts, and easing the transition to symbolic math, essential for advanced topics like algebra and geometry.
Squares and square roots involve understanding the multiplication of a number by itself and finding the original number from its square. Key skills include recognizing perfect squares, calculating squares and square roots, and using estimation for non-perfect squares. Mastery of these concepts builds a foundation for advanced topics like exponents, algebra, and geometry, essential for higher-level math, problem-solving, and various scientific applications.
Telling time involves reading clocks and understanding the passage of time. Key skills include recognizing hours and minutes, using analog and digital clocks, and calculating elapsed time. Mastery of telling time builds a foundation for time management, scheduling, and understanding time-related concepts in daily life. It is essential for developing punctuality, planning skills, and preparing for more complex topics like time zones and historical timelines.
Geometry of 2D shapes involves understanding and analyzing flat figures like circles, triangles, and rectangles. Key skills include identifying shapes, calculating perimeter and area, and recognizing properties like angles and symmetry. Mastery of 2D geometry builds a foundation for spatial reasoning, problem-solving, and more advanced topics such as 3D geometry, trigonometry, and geometric proofs, essential for higher-level math and various real-world applications.
The Pythagorean Theorem involves understanding the relationship between the sides of a right triangle. Key skills include calculating the lengths of sides using the formula a^2 + b^2 = c^2, identifying right triangles, and applying the theorem to solve problems. Mastery of the Pythagorean Theorem builds a foundation for advanced topics in geometry, trigonometry, and algebra, essential for higher-level math, physics, engineering, and real-world applications.
Negative integers involve understanding and working with numbers less than zero. Key skills include recognizing negative numbers, performing operations like addition, subtraction, multiplication, and division with negative integers, and plotting them on a number line. Mastery of negative integers builds a foundation for advanced topics such as algebra, coordinate geometry, and calculus, essential for higher-level math, science, finance, and various real-world applications.
Measurement units involve understanding and using standard units to measure length, weight, volume, and time. Key skills include converting between units (e.g., centimeters to meters, grams to kilograms), estimating measurements, and using appropriate tools. Mastery of measurement units builds a foundation for practical applications in everyday life, science, and engineering, essential for higher-level math topics like geometry, physics, and data analysis.
Cartesian coordinates involve using a grid system to locate points with pairs of numbers (x, y). Key skills include plotting points, understanding the x-axis and y-axis, and identifying the coordinates of points on a graph. Mastery of Cartesian coordinates builds a foundation for understanding graphing, geometry, and algebra, essential for advanced topics like linear equations, graphing functions, and spatial reasoning in higher-level math and science.
Area and perimeter involve measuring the surface and boundary of 2D shapes. Key skills include calculating the area and perimeter of rectangles, squares, triangles, and other polygons. Mastery of these concepts builds a foundation for spatial reasoning, geometry, and problem-solving, essential for advanced topics like volume, surface area, and trigonometry, as well as practical applications in architecture, engineering, and everyday life.
Decimals represent fractions written in a base-ten system. Key skills include understanding place value, converting between fractions and decimals, and performing operations like addition, subtraction, multiplication, and division with decimals. Mastery of decimals builds a foundation for advanced topics such as percentages, scientific notation, and algebra, essential for higher-level math, financial literacy, and practical applications in measurement, data analysis, and everyday transactions.
Numbers and place value involve understanding the value of digits based on their position within a number. Key skills include recognizing and writing numbers, comparing and ordering them, and understanding the base-ten system. Mastery of place value builds a foundation for arithmetic operations, number sense, and more advanced topics like decimals, fractions, and algebra, essential for higher-level math and practical problem-solving in everyday life.
Fractions represent parts of a whole. Key skills include understanding numerator and denominator, comparing and simplifying fractions, and performing operations like addition, subtraction, multiplication, and division with fractions. Mastery of fractions builds a foundation for advanced math topics such as decimals, percentages, ratios, and algebra, essential for higher-level math, real-world problem-solving, and various applications in science, engineering, and everyday life.
Fraction multiplication and division involve multiplying and dividing fractions and mixed numbers. Key skills include understanding reciprocal relationships, simplifying fractions, and applying cross-multiplication. Mastery of these operations builds a foundation for advanced math topics like ratios, proportions, algebra, and real-world problem-solving in fields such as science, engineering, and finance. It enhances numerical fluency and deepens understanding of fractional relationships and operations.
Factors and primes involve identifying the divisors of numbers and recognizing prime numbers. Key skills include determining factor pairs, understanding prime factorization, and using the greatest common factor (GCF) and least common multiple (LCM). Mastery of these concepts builds a foundation for advanced topics such as algebra, number theory, and problem-solving, essential for higher-level math, cryptography, and various scientific and real-world applications.
Slope and linear equations involve understanding the rate of change and the relationship between variables in a straight line. Key skills include calculating slope, graphing linear equations, and interpreting the y-intercept. Mastery of these concepts builds a foundation for advanced topics such as algebra, coordinate geometry, and calculus, essential for higher-level math, physics, engineering, and various real-world applications in data analysis and economics.
Strengthens skills in working with fractions and decimals, including addition, subtraction, multiplication, and division. Introduces volume, explores more complex geometrical shapes, and begins basic algebraic thinking with simple expressions and equations. Emphasizes problem-solving and critical thinking.
Focuses on ratios and proportional relationships, introduces the concept of negative numbers, and begins formal algebraic thinking with variables and expressions. Explores data analysis, statistical measures, and basic geometry, including area, surface area, and volume of shapes.
Emphasizes properties and relations of points, lines, surfaces, and solids, explores geometric proofs, and introduces basic trigonometry. Covers congruence, similarity, transformations, and the relationships between geometric shapes to develop spatial reasoning and logical thinking.
Radicals involve understanding the concept of square roots and higher-order roots. Key skills include simplifying radical expressions, performing operations with radicals, and rationalizing denominators. Mastery of radicals builds a foundation for advanced topics such as algebra, geometry, and calculus, essential for higher-level math, physics, and engineering. It enhances problem-solving abilities and prepares students for complex equations and real-world applications involving roots and exponents.
Trigonometry basics involve understanding the relationships between the angles and sides of right triangles. Key skills include learning sine, cosine, and tangent ratios, calculating side lengths and angles, and applying the Pythagorean theorem. Mastery of these concepts builds a foundation for advanced topics such as advanced trigonometry, calculus, and physics, essential for higher-level math, engineering, architecture, and various scientific applications.
Algebra basics involve understanding and using variables to represent numbers and relationships. Key skills include solving simple equations, understanding expressions, and using the properties of operations. Mastery of algebra basics builds a foundation for advanced topics such as linear equations, polynomials, and functions, essential for higher-level math, science, and engineering. It enhances logical thinking, problem-solving abilities, and prepares students for complex mathematical concepts.
Statistics involves understanding measures of central tendency: mean, median, and mode. Key skills include calculating these measures, interpreting data sets, and analyzing data distribution. Mastery of statistics builds a foundation for advanced topics such as probability, data analysis, and inferential statistics, essential for higher-level math, science, and real-world applications in fields like economics, sociology, and everyday decision-making. It enhances critical thinking and data literacy.
Speed, distance, and time involves understanding the relationships between these variables. Key skills include using the formula speed=distance/time, solving problems involving these concepts, and converting units. Mastery of speed, distance, and time builds a foundation for advanced topics such as physics, algebra, and calculus, essential for higher-level math, engineering, and real-world applications in travel, sports, and logistics.
Order of operations involves following specific rules to solve expressions accurately. Key skills include understanding and applying the BEDMAS rules (Brackets, Exponents, Division and Multiplication, Addition and Subtraction). Mastery of the order of operations builds a foundation for advanced topics such as algebra, calculus, and complex problem-solving, essential for higher-level math, science, and everyday applications in logical and systematic thinking.
Geometry of 3D shapes involves understanding and analyzing solid figures like cubes, spheres, and cylinders. Key skills include identifying 3D shapes, calculating volume and surface area, and recognizing properties like edges, faces, and vertices. Mastery of 3D geometry builds a foundation for advanced topics such as trigonometry, calculus, and spatial reasoning, essential for higher-level math, engineering, architecture, and various scientific applications.
Volume and surface area involve measuring the space inside 3D shapes and the total area covering their surfaces. Key skills include calculating the volume of cubes, rectangular prisms, and cylinders, and determining the surface area of these shapes. Mastery of these concepts builds a foundation for advanced topics like geometry, trigonometry, and calculus, essential for higher-level math, engineering, architecture, and various scientific applications.
Percentages represent parts per hundred and are used to describe proportions and compare quantities. Key skills include converting between fractions, decimals, and percentages, calculating percentage increases and decreases, and solving real-life problems involving discounts and interest rates. Mastery of percentages forms the foundation for advanced topics in algebra, statistics, and financial literacy, essential for understanding data analysis and practical financial decisions.
Polynomials involve expressions with multiple terms consisting of variables and coefficients. Key skills include adding, subtracting, multiplying, and factoring polynomials, as well as understanding degrees and terms. Mastery of polynomials builds a foundation for advanced topics such as algebra, calculus, and complex equations, essential for higher-level math, engineering, and various scientific applications. It enhances algebraic thinking and problem-solving abilities.
Geometry of circles involves understanding the properties and measurements of circles. Key skills include identifying parts of a circle (radius, diameter, circumference), calculating area and circumference, and understanding the relationship between radius and diameter. Mastery of circle geometry builds a foundation for advanced topics such as trigonometry, calculus, and coordinate geometry, essential for higher-level math, engineering, and various scientific applications.
Emphasizes solving linear equations and systems of equations, explores functions and their properties, and covers advanced geometry, including transformations and the Pythagorean Theorem. Prepares students for more advanced algebra with a focus on analytical thinking and problem-solving.
Develops understanding of algebraic expressions and linear equations, works with rational numbers and proportions, and introduces probability and statistics. Explores geometric concepts like scale drawings, circles, and three-dimensional figures to build a strong mathematical foundation.
Probability involves understanding the likelihood of events occurring. Key skills include calculating probabilities, using fractions and percentages to express probabilities, and understanding concepts like random events and outcomes. Mastery of probability builds a foundation for advanced topics such as statistics, data analysis, and risk assessment, essential for higher-level math, science, and real-world decision-making in fields like finance, engineering, and everyday life.
Focuses on understanding and applying linear equations, inequalities, and functions, introduces quadratic equations and basic polynomials. Explores real numbers, exponents, and radicals to build a foundation for advanced algebraic concepts and problem-solving skills.
Scientific notation involves expressing large or small numbers using powers of ten. Key skills include converting between standard and scientific notation, multiplying and dividing numbers in scientific notation, and understanding significant figures. Mastery of scientific notation builds a foundation for advanced topics like algebra, physics, and engineering, essential for higher-level math and science. It enhances precision and simplifies calculations involving very large or very small quantities.
Exponents represent repeated multiplication of a number by itself. Key skills include understanding base and exponent notation, applying exponent laws, and performing operations like multiplication and division with exponents. Mastery of exponents lays the foundation for advanced topics such as algebra, geometry, and calculus, enhancing logical thinking and problem-solving abilities essential for higher-level math and practical applications in science and finance.
Exponent multiplication and division involve using the laws of exponents to simplify expressions. Key skills include multiplying and dividing powers with the same base, understanding the properties of exponents, and simplifying expressions with exponents. Mastery of these skills builds a foundation for advanced topics such as algebra, polynomial operations, and scientific notation, essential for higher-level math, science, and engineering. It enhances problem-solving and algebraic thinking.
Geometry of triangles involves understanding the properties and types of triangles. Key skills include identifying different triangles (e.g., equilateral, isosceles, scalene), calculating area and perimeter, and understanding concepts like angles and congruence. Mastery of triangle geometry builds a foundation for advanced topics such as trigonometry, the Pythagorean theorem, and geometric proofs, essential for higher-level math, engineering, and various scientific applications.
Rates and ratios explores the relationships between multiple items. Key skills include calculating ratios from parts, finding equivalent ratios, using a known ratio to calculate a quantity, and manipulating ratios with decimals and fractions. Mastery of rates and ratios builds a foundation for more advanced topics like speed, time, and distance, as well as advance math topics like trigonometry.