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Curriculum & Standards Framework MATHEMATICS Level 4: Number – Learning Outcomes & Indicators At Level 4 the student is able to: Numbers, counting and numeration 4.1 MANUN401 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. This is evident when the student is able to: 4.2 read, say, write, compare and order whole numbers to 7 digits and numbers with decimal fractions to three decimal places. Year 7 benchmark: read, write, compare and order whole numbers to 7 digits and numbers with decimal fractions to two decimal places compare and order decimal fractions with unequal numbers of places (e.g. 3.05, 3.001, 4.4, 3.12) represent the structure of whole numbers to 7 digits and decimal numbers to 3 decimal places (e.g. 5634.657 = (5 × 1000) + (6 × 100) + (3 × 10) + (4 × 1) + Year 7 benchmark: use place-value knowledge to model different representations of whole numbers to 7 digits and decimal numbers to 2 decimal places (e.g. recognise that the price of a computer may be expressed as either one thousand eight hundred dollars or eighteen hundred dollars; a height of 154 cm can be recorded as 1.54 m) count in decimal fractional amounts (e.g. 0.3, 0.6, 0.9, 1.2, and so on) interpret negative whole numbers and locate them on a scale (e.g. – 5oC on a temperature scale). Compare and order common fractions. This is evident when the student is able to: MANUN402 compare and order common fractions with related denominators locate fractions on a number line and use it to count in fractional steps Year 7 benchmark: read, name, write and compare simple common fractions (limited to halves, thirds, quarters, fifths, eighths and tenths) and recognise simple equivalent fractions, decimals and percentages written in different forms (e.g. recognise that 25% off means 1/4 off the price; place 1/3, 1/8, 1/5, 1/10 on a number line). Office of Learning and Teaching, DE&T. 4.3 MANUN403 Rename common fractions as decimals and percentages. This is evident when the student is able to: convert a simple common fraction to a decimal and vice versa convert a simple common fraction to a percentage and vice versa Mental computation and estimation 4.1 MANUM401 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. This is evident when the student is able to: automatically recall and use multiplication and division facts up to 10 × 10 automatically recall and use simple common fraction addition and subtraction facts automatically recall frequently used common fraction, decimal and percentage equivalences 4.2 MANUM402 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. This is evident when the student is able to: 4.3 MANUM403 add and subtract mentally by rounding to the nearest 10 (e.g. 53 cm + 38 cm; think 53 and 40, take 2: $75 – $18; think 75 subtract 20, add 2) use place-value to extend multiplication and division facts (e.g. 70 m x 50 m; think 7 tens by 5 tens is 35 hundreds: how many 50 g in 450 g? Think 45 divided by 5) use number properties to generate multiples quickly (e.g. 12 by 5 equals 6 by 10, 7 twelves equals 7 tens and 7 twos). use number properties to calculate mentally with fractions Use estimation strategies to check the results of written or calculator computations. This is evident when the student is able to: use front-end estimation to check computations round decimals to the nearest whole number to check a computation (e.g. 8.6 × Office of Learning and Teaching, DE&T. 3.1 is around 9 × 3). Computation and applying number 4.1 MANUC401 Use written methods to add and subtract decimal numbers. This is evident when the student is able to: 4.2 MANUC402 Use written methods to multiply and divide whole numbers. This is evident when the student is able to: 4.3 MANUC403 MANUC404 multiply whole numbers by 2-digit whole numbers without using a calculator divide whole numbers by 1-digit whole numbers without using a calculator and check the answer using multiplication Year 7 benchmark: estimate and calculate using addition, subtraction, multiplication and division, using a variety of strategies, including: mental methods where the numbers are appropriate and manageable (e.g. 47 + 29, $2 – 65c, 3 muesli bars at 80c each); written methods: addition and subtraction (i.e. whole numbers and money and measurements to two decimal places); multiplication (i.e. 3-digit by 1-digit whole numbers); division (i.e. 3digit by 1-digit whole numbers); calculator methods where the numbers are outside mental and written limits specified above. compare various paper-and-pencil methods for ease and efficiency (e.g. lattice multiplication and the long multiplication algorithm). Use models to illustrate the four operations with common fractions, and develop written methods for carrying out these operations. This is evident when the student is able to: 4.4 add and subtract decimal numbers with equal numbers of decimal places without using a calculator explain the role of place-value in the written methods chosen to add and subtract add and subtract fractions with small related denominators (e.g. fifths and tenths) and record these using understood written methods use appropriate models to represent products and quotients of simple fractions (e.g. half of half a pie, how many half pizzas in three pizzas?) find fractional parts of discrete collections and quantities recognise the relationship between division and fractions and interpret a remainder when dividing by a whole number Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve Office of Learning and Teaching, DE&T. it. This is evident when the student is able to: select the relevant information to solve a problem or carry out a practical task and determine whether additional information is required Year 7 benchmark: recognise and use inverse relationships between addition and subtraction, and multiplication and division, different division formats, simple ratios and computational skills to solve practical problems set in familiar contexts (e.g. I’ve got 32 391 points and the record is 35 374 so I need about 3000 points more to beat the record on this computer game; a recipe for 8 people takes 2 cups of flour so for 4 people it will need 1 cup) restate verbally expressed problems symbolically in terms of the operation needed describe situations which may be represented by given symbolically expressed number sentences use a calculator and its memory facility to solve problems involving a sequence of operations on decimal numbers, interpreting remainders, negative numbers and overflow displays operate with negative whole numbers in everyday situations (e.g. the temperature at Mount Hotham dropped 6oC from 3oC). Number patterns and relationships 4.1 MANUP401 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. This is evident when the student is able to: 4.2 MANUP402 use rules which involve a combination of operations to generate a sequence (e.g. start with 4, multiply the previous term by 2.5 and subtract 4) describe and test a rule which produces a given number sequence Year 7 benchmark: continue, create and describe number patterns involving whole numbers, fractions and decimals (e.g. count by thirds continue the number pattern 123, 132, 141, 150 … ; use the rule ‘double and add 3’ to create a set of numbers) describe and verify rules for number sequences which relate each element to the previous element or elements (e.g. next term in a Fibonacci sequence) and each element to its position in the sequence (e.g. tenth term of 1, 4, 9, 16, 25, …). Specify multiples and factors of whole numbers. This is evident when the student is able to: generate and recognise multiples of whole numbers find and use factors of whole numbers (e.g. to multiply by 15, multiply by 3 then by 5) define and identify prime numbers. Office of Learning and Teaching, DE&T. 4.3 Construct, verify and complete number sentences involving the four operations, brackets, decimal numbers and fractions. This is evident when the student is able to: MANUP403 construct and verify number sentences (e.g. write a number sentence with two operations and the number ) complete number sentences (e.g. complete 16 = . . × (. . + . .)) solve number puzzles expressed in words or with missing numbers (e.g. I’m thinking of a number, if I multiply it by 6 and add 3, I get 33). Victorian Essential Learning Standards (VELS) MATHEMATICS Number Level 4 At Level 4, students comprehend the size and order of small numbers (to thousandths) and large numbers (to millions). They model integers (positive and negative whole numbers and zero), common fractions and decimals. They place integers, decimals and common fractions on a number line. They create sets of number multiples to find the lowest common multiple of the numbers. They interpret numbers and their factors in terms of the area and dimensions of rectangular arrays (for example, the factors of 12 can be found by making rectangles of dimensions 1 × 12, 2 × 6, and 3 × 4). Students identify square, prime and composite numbers. They create factor sets (for example, using factor trees) and identify the highest common factor of two or more numbers. They recognise and calculate simple powers of whole numbers (for example, 24 = 16). Students use decimals, ratios and percentages to find equivalent representations of common fractions (for example, 3/4 = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8). They explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers). They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money. They use estimates for computations and apply criteria to determine if estimates are reasonable or not. Office of Learning and Teaching, DE&T.