Topic 5.1.1 Place Value to Hundreds of Thousands Strand: Number and Algebra Sub-strand: Number and Place Value Recommended teaching time: 2 weeks Mapping to F–10 curriculum in Victoria Content descriptions Recognise, represent and order numbers to at least tens of thousands Achievement standard (excerpt in bold) Level 4 Level 5 Level 6 Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students solve simple purchasing problems with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in Students solve simple problems involving the four operations using a range of strategies including digital technology. They estimate to check the reasonableness of answers and approximate answers by rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students order decimals and unit fractions and locate them on a number line. Students add and subtract fractions Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. They solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts. Students locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the
Assessment ideas Students read, write, order and represent numbers to at least hundreds of thousands; they identify numbers 100 more and 100 less, 1000 more and 1000 less and bridge over to the next or the last 100 or 1000; they round off numbers to the nearest 100, 1000 or 10 000. Resources AMSI (also available in ) NLVM Illuminations Notes Topic 5.1.2 Developing a Place Value Understanding of Decimal Numbers Strand: Number and Algebra Sub-strand: Fractions and Decimals Recommended teaching time: 2 weeks Mapping to F–10 curriculum in Victoria Content descriptions Recognise that the place value system can be extended beyond hundredths Compare, order and represent decimals Achievement standard (excerpt in bold) Level 4 Level 5 Level 6 Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students solve simple purchasing problems with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in familiar contexts and make connections between fractions and decimal notations Students solve simple problems involving the four operations using a range of strategies including digital technology. They estimate to check the reasonableness of answers and approximate answers by rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students order decimals and unit fractions and locate them on a number line. Students add and subtract fractions with the same denominator. They find unknown quantities in number sentences Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. They solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts. Students locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology. They make connections between the powers of 10 and the multiplication and division of
with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in familiar contexts and make connections between fractions and decimal notations up to two decimal places. Students identify unknown quantities in number sentences. They use the properties of odd and even numbers and describe number patterns resulting from multiplication. Students continue number sequences involving multiples of single-digit numbers and unit fractions, and locate them on a number line. order decimals and unit fractions and locate them on a number line. Students add and subtract fractions with the same denominator. They find unknown quantities in number sentences and continue patterns by adding or subtracting fractions and decimals. line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology. They make connections between the powers of 10 and the multiplication and division of decimals. Students add, subtract and multiply decimals and divide decimals where the result is rational. Students write number sentences using brackets and order of operations, and specify rules used to generate sequences involving whole numbers, fractions and decimals. They use ordered pairs of integers to represent coordinates of points and locate a point in any one of the four quadrants on the Cartesian plane. Activities Proficiencies Describing, continuing and creating increasing and decreasing patterns with fractions, decimals and whole numbers Forming generalisations or ‘rules’ to describe patterns Finding the unknown term in a pattern or equation Exploring the relationships between addition and subtraction Manipulating sets of numbers using a given rule, for example, if a number is even halve it; if a number is odd, subtract 1 then halve it Fluency through recognising the repeated nature of pattern Understanding the relationships between the four operations Problem solving to find the unknown term in a pattern or equation using strategies such as inverse operations Reasoning through forming generalisations about patterns Considering different levels of student ability Level 4 Students who are working at this level could: Explore and describe number patterns resulting from performing multiplication. Level 6 Students who are working at this level could: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence.
List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions Recognise that probabilities range from 0 to 1 Achievement standard (excerpt in bold) Level 4 Level 5 Level 6 Students describe different methods for data collection and representation, and evaluate their effectiveness. They construct data displays from given or collected data, with and without the use of digital technology. Students list the probabilities of everyday events. They identify dependent and independent events. Students pose questions to gather data and construct various displays appropriate for the data, with and without the use of digital technology. They compare and interpret different data sets. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities as a number from 0 to 1. Students interpret and compare a variety of data displays, including displays for two categorical variables. They analyse and evaluate data from secondary sources. Students compare observed and expected frequencies of events, including those where outcomes of trials are generated with the use of digital technology. They specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages. Activities Proficiencies Quantify the chance of an event occurring Investigate all the possible outcomes of an event and describing the chance of each outcome occurring Conduct fair tests or experiments including adequate sample sizes and controlling variables Link chance to fractions and using the language of probability such as “blue has a one in three chance of being selected” Investigate the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1 Fluency in listing possible outcomes from a chance experiment as fractions Understanding through using fractions to represent probabilities Problem solving by investigating chance through experiments Reasoning through interpreting results of chance experiments Considering different levels Level 4 Students who are working at this level could: Describe possible everyday events and order their chances of occurring. Level 6 Students who are working at this level could: Compare observed frequencies across experiments with expected frequencies (e.g. coin tosses). Assessment ideas Students: Are given a bag of coloured lollies or counters and asked to write the fraction expressing the chance of each colour being drawn out; students are then asked to make a coloured spinner that simulates this same chance. Resources
FUSE Illuminations Adjustable Spinner AMSI Notes Topic 5.2.7 Financial Plans and Budgets Strand: Number and Algebra Sub-strand: Money and Financial Mathematics Recommended teaching time: 2 weeks Mapping to F–10 curriculum in Victoria Content descriptions Create simple financial plans Achievement standard (excerpt in bold) Level 4 Level 5 Level 6 Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies Students solve simple problems involving the four operations using a range of strategies including digital Students recognise the properties of prime, composite, square and triangular numbers and determine