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How to learn Grade 5: Mathematics

Saskatchewan curriculum: Mathematics, Grade 5

0 of 39 concepts ready to learn · Markdown, for your AI

1. Statistics and Probability - Goals: Number Sense, Logical Thinking, Mathematics as a Human Endeavour · Describe, compare, predict, and test the likelihood of outcomes in probability situations.

  1. The Probability Scale: 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
  2. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
  3. Likelihood Language: Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible
  4. Ordering Likelihoods: Compare the likelihood of different events and order them from least to most likely — including situations with unequal outcomes such as a bag with more of one colour than another, or a spinner with sections of different sizes — and explain reasoning using informal language

2. Statistics and Probability - Goals: Number Sense, Logical Thinking, Mathematics as a Human Endeavour · Construct and interpret double bar graphs to draw conclusions.

  1. Reading and Comparing Bar Graphs: Solve comparison, sum, and difference problems using information presented in a bar graph

3. Statistics and Probability - Goals: Number Sense, Logical Thinking, Mathematics as a Human Endeavour · Differentiate between first-hand and second-hand data.

  1. Reading tables: Complete, read, and interpret information in tables, including timetables
  2. Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

4. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Identify, create, and analyze single transformations of 2-D shapes (with and without the use

  1. Coordinate Transformations: 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

5. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Identify and sort quadrilaterals, including: rectangles, squares, trapezoids, parallelograms

  1. Classifying shapes by properties: Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties
  2. Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

6. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes that

  1. Lines, Rays & Angles: Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures
  2. 3-D shapes (age 11+): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections

7. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Demonstrate understanding of capacity by: • describing the relationship between mL and L • se

  1. Estimating volume: Estimate volume of cuboids using 1 cm³ blocks; estimate capacity of containers using water
  2. Unit Conversions: Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate
  3. Measuring length (age 10+): Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units

8. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Demonstrate an understanding of volume by: selecting and justifying referents for cm³ or m³ u

  1. Counting Unit Cubes: Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units
  2. Estimating answers (age 10+): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)

9. Shape and Space - Goals: Spatial Sense, Logical Thinking, Number Sense, Mathematics as a Human Endeavour · Design and construct different rectangles given either perimeter or area, or both (whole numb

  1. Perimeter (age 10+): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically
  2. Understanding angles (age 9+): Use the properties of rectangles to deduce related facts and find missing lengths and angles

10. Patterns and Relations · Write, solve, and verify solutions of single-variable, one-step equations with whole number coefficients and whole number solutions.

  1. Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

11. Patterns and Relations · Represent, analyse, and apply patterns using mathematical language and notation.

  1. Number Pattern Relationships: Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane

12. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate an understanding of addition and subtraction of decimals (limited to thousandths).

  1. Adding and subtracting (age 10+): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why, with numbers up to 10,000,000 and decimals
  2. Tenths (age 9+): Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035)
  3. Reading and writing numbers (age 10+): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning
  4. Rounding Answers: Solve problems which require answers to be rounded to specified degrees of accuracy

13. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate understanding of decimals to thousandths by: • describing and representing • relating to f

  1. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  2. Fractions on a number line: 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
  3. Decimal & Percent Notation: 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
  4. Decimals for Tenths & Hundredths: Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)
  5. Reading Decimal Places: Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)
  6. Decimals and fractions (age 10+): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts

14. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate an understanding of fractions by using concrete and pictorial representations to: create s

  1. Understanding fractions (age 9+): Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly explain errors or alternative methods
  2. Dividing fractions (unit fractions): 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

15. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Develop and apply personal strategies for estimation and computation including: • front-end rounding •

  1. Constructing mathematical arguments: 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

16. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Demonstrate, with and without concrete materials, an understanding of division (3-digit by 1-digit) an

  1. Division with remainders: Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation

17. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Analyze models of, develop strategies for, and carry out multiplication of whole numbers.

  1. Reasoning with Equivalences: Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms
  2. Long multiplication: Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models

18. Number - Goals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human Endeavour · Represent, compare, and describe whole numbers to 1 000 000 within the contexts of place value and the

  1. Reading and writing numbers (age 9+): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
  2. Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations