How to learn Year 5: Mathematics

Victorian Curriculum and VCE (VCAA): Mathematics, Year 5

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1. Statistics and Probability

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
Probability as a Fraction: Describe the probability of simple equally-likely outcomes using unit fractions: the probability of rolling a 6 on a fair die is 1/6, flipping heads is 1/2, picking one specific colour from three equally represented colours is 1/3; place these fractional probabilities on a 0-to-1 probability scale
The 0-to-1 Probability Scale: 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. Measurement and Geometry

Measuring angles: Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure
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
Nets of 3-D Shapes: Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net
12-hour and 24-hour time: Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks
Angles in triangles (age 11+): 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
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

3. Number and Algebra

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
Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
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
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
Choosing Maths Tools: Select and use tools and representations strategically: choose between mental methods, formal written methods, algebraic approaches, coordinate grids, and technology based on the demands of the problem
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
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
Estimation to check answers to calculations: Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Factors, multiples, and primes: 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