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How to learn Grade 5: Mathematics

Manitoba curriculum: Mathematics, Grade 5

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1. Statistics and Probability

  1. Likelihood Language: Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible
  2. 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
  3. Reading and Comparing Bar Graphs: Solve comparison, sum, and difference problems using information presented in a bar graph

2. Shape and Space

  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
  2. 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
  3. 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
  4. 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
  5. Estimating volume: Estimate volume of cuboids using 1 cm³ blocks; estimate capacity of containers using water
  6. 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)
  7. 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. Perimeter (age 10+): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically

3. Patterns and Relations

  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
  2. Shape patterns: Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

4. Number

  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. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  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. 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)
  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
  7. 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
  8. Adding Fractions (Unlike Denominators): Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
  9. Division with remainders (age 10+): Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate
  10. Dividing by two-digit numbers: Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context
  11. 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
  12. Mental multiplication and division (age 9+): Multiply and divide numbers mentally drawing upon known facts, including related facts and place-value adjustments
  13. Estimating by rounding: Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values
  14. 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