Curriculum & Standards Framework

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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:
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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
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compare and order common fractions with related denominators
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locate fractions on a number line and use it to count in fractional steps
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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:
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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:
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automatically recall and use multiplication and division facts up to 10 × 10
automatically recall and use simple common fraction addition and subtraction
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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:
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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:
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use front-end estimation to check computations
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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:
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4.2
MANUC402
Use written methods to multiply and divide whole numbers. This is evident when
the student is able to:
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4.3
MANUC403
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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:
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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
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it. This is evident when the student is able to:
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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:
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4.2
MANUP402
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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
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Year 7 benchmark: continue, create and describe number patterns involving
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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:
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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
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construct and verify number sentences (e.g. write a number sentence with two
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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.
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