# Grade 6: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 39 concepts ready. In the app: https://ai.page/roadmap/ca-sk-grade-6 Part of: [Saskatchewan: Mathematics](https://ai.page/roadmap/ca-sk.md) Goal: Saskatchewan curriculum: Mathematics, Grade 6 ## 1. Statistics and Probability - Goals: Spatial Sense, Number Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate understanding of probability by: determining sample space, differentia - [The Probability Scale](https://ai.page/c/the-probability-scale/index.md): Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability - [The 0-to-1 Probability Scale](https://ai.page/c/the-0-to-1-probability-scale/index.md): Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages ## 2. Statistics and Probability - Goals: Spatial Sense, Number Sense, Logical Thinking, Mathematics as a Human Endeavour · Extend understanding of data analysis to include: line graphs, graphs of discrete - [Line graphs (age 10+)](https://ai.page/c/line-graphs-age-10/index.md): Interpret and construct pie charts and line graphs; use these to solve problems - [Statistical Analysis Vocabulary](https://ai.page/c/statistical-analysis-vocabulary/index.md): Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes ## 3. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Demonstrate understanding of single, and combinations of, transformations of 2-D shapes (with - [Coordinate Transformations](https://ai.page/c/coordinate-transformations/index.md): Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original ## 4. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Demonstrate understanding of the first quadrant of the Cartesian plane and ordered pairs with - [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context ## 5. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Demonstrate understanding of regular and irregular polygons including: classifying types of t - [Regular and irregular polygons](https://ai.page/c/regular-and-irregular-polygons/index.md): Distinguish between regular and irregular polygons based on reasoning about equal sides and equal angles - [Types of angles (age 11+)](https://ai.page/c/types-of-angles-age-11/index.md): Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons ## 6. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Extend and apply understanding of perimeter of polygons, area of rectangles, and volume of ri - [Perimeter (age 10+)](https://ai.page/c/perimeter-age-10/index.md): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically - [Angles in triangles (age 11+)](https://ai.page/c/angles-in-triangles-age-11/index.md): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning ## 7. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Demonstrate understanding of angles including: identifying examples, classifying angles, esti - [Understanding angles (age 10+)](https://ai.page/c/understanding-angles-age-10/index.md): Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties - [Understanding angles (age 11+)](https://ai.page/c/understanding-angles-age-11/index.md): Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems - [Angles in triangles (age 10+)](https://ai.page/c/angles-in-triangles-age-10/index.md): Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties - [What Is an Angle?](https://ai.page/c/what-is-an-angle/index.md): Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes - [Measuring angles](https://ai.page/c/measuring-angles/index.md): Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure - [Measuring angles (age 11+)](https://ai.page/c/measuring-angles-age-11/index.md): Draw and measure line segments and angles accurately using ruler and protractor, and interpret scale drawings to extract real measurements - [Constructing mathematical arguments](https://ai.page/c/constructing-mathematical-arguments/index.md): Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches - [Estimating Angles](https://ai.page/c/estimating-angles/index.md): Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size ## 8. Patterns and Relationships - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Extend understanding of patterns and relationships by using expressions and equati - [Expressions & Equations Vocabulary](https://ai.page/c/expressions-and-equations-vocabulary/index.md): Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign) - [Number Pattern Relationships](https://ai.page/c/number-pattern-relationships/index.md): Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane ## 9. Patterns and Relationships - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Extend understanding of preservation of equality concretely, pictorially, physical - [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-maths/index.md): Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations - [Proportion](https://ai.page/c/proportion/index.md): Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations ## 10. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate an understanding of ratio concretely, pictorially, and symbolically. - [Ratio Notation](https://ai.page/c/ratio-notation/index.md): Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations - [Percentages (age 9+)](https://ai.page/c/percentages-age-9/index.md): Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole) ## 11. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Extend understanding of fractions to improper fractions and mixed numbers. - [Mixed numbers and improper fractions](https://ai.page/c/mixed-numbers-and-improper-fractions/index.md): Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5) - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-3/index.md): Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line - [Fractions of a whole (age 10+)](https://ai.page/c/fractions-of-a-whole-age-10/index.md): Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers - [Dividing fractions (unit fractions)](https://ai.page/c/dividing-fractions-unit-fractions/index.md): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result ## 12. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate understanding of integers concretely, pictorially, and symbolically. - [Number Sets & Infinity](https://ai.page/c/number-sets-and-infinity/index.md): Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances ## 13. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate understanding of percent (limited to whole numbers to 100) concretely, pictorially, and sy - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% - [Decimal & Percent Notation](https://ai.page/c/decimal-and-percent-notation/index.md): Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value ## 14. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Extend understanding of multiplication and division to decimals (1-digit whole number multipliers and - [Division with Decimals](https://ai.page/c/division-with-decimals/index.md): Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers ## 15. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate understanding of the order of operations on whole numbers (excluding exponents) with and w - [Order of operations (age 10+)](https://ai.page/c/order-of-operations-age-10/index.md): Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structure to solve proportion problems efficiently ## 16. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate understanding of factors and multiples (concretely, pictorially, and symbolically) includi - [Factors, multiples, and primes](https://ai.page/c/factors-multiples-and-primes/index.md): Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems - [Prime numbers](https://ai.page/c/prime-numbers/index.md): Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19 ## 17. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate understanding of place value including: greater than one million and less than one thousan - [Reading and writing numbers (age 10+)](https://ai.page/c/reading-and-writing-numbers-age-10/index.md): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning - [Place Value Problem-Solving](https://ai.page/c/place-value-problem-solving/index.md): Solve number and practical problems involving place value with increasingly large positive numbers ## Health: 0 of 100 Of its 39 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - The Probability Scale has no explanation yet - Experimental probability has no explanation yet - The 0-to-1 Probability Scale has no explanation yet - Line graphs (age 10+) has no explanation yet - Statistical Analysis Vocabulary has no explanation yet - Coordinate Transformations has no explanation yet - Plotting points in the first quadrant has no explanation yet - Regular and irregular polygons has no explanation yet - Types of angles (age 11+) has no explanation yet - Perimeter (age 10+) has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Understanding angles (age 10+) has no explanation yet - Understanding angles (age 11+) has no explanation yet - Angles in triangles (age 10+) has no explanation yet - What Is an Angle? has no explanation yet - Measuring angles has no explanation yet - Measuring angles (age 11+) has no explanation yet - Constructing mathematical arguments has no explanation yet - Estimating Angles has no explanation yet - Expressions & Equations Vocabulary has no explanation yet - Number Pattern Relationships has no explanation yet - Numbers on a number line has no explanation yet - Proportion has no explanation yet - Ratio Notation comes before Factors, multiples, and primes, which it needs - Ratio Notation has no explanation yet - Percentages (age 9+) has no explanation yet - Mixed numbers and improper fractions has no explanation yet - Fractions on a number line has no explanation yet - Fractions of a whole (age 10+) has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Number Sets & Infinity has no explanation yet - Positive and Negative Numbers has no explanation yet - Percentages as Fractions has no explanation yet - Decimal & Percent Notation has no explanation yet - Division with Decimals has no explanation yet - Order of operations (age 10+) has no explanation yet - Factors, multiples, and primes has no explanation yet - Prime numbers has no explanation yet - Reading and writing numbers (age 10+) has no explanation yet - Place Value Problem-Solving has no explanation yet Credit: The structure of Saskatchewan curriculum: Mathematics (https://curriculum.gov.sk.ca/CurriculumHome?id=153); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.