Year 4 National Curriculum Mathematics Scope and Sequence

YEAR 4 - 2011 MATHS SCOPE AND SEQUENCE FOR ST ANTHONY’S (Adapted from the Australian Curriculum + Eva Devries scope and sequence.)

Year 4 National Curriculum Mathematics Scope and Sequence

NUMBER & ALGEBRA

• working with numbers from 99, 999 to tenths

• counting in whole numbers, decimals and fractions

• applying knowledge of counting patterns with smaller numbers to large whole numbers and decimals

• ask questions involving counting sequences to tens of thousands

• use a number line (marked and unmarked) and hundreds board to assist with counting forwards and backwards to 99 999
• use and interpret number lines from a range of starting numbers to

• use mental groupings to count and to assist with estimating the number of items in large groups (make to 10, make to 100, 1 000 rounding and adjusting)

• use and interpret number boards from a range of starting numbers to assist with counting to 99 999
• use the constant function of a calculator and to create and identify the counting number pattern to 99 999

• count in common fractions (1/2 ¼, 1/3, 1/5, 1/10)and decimal fractions in appropriate contexts

• count in whole numbers – 1, 2, 5, 10, etc and identify the pattern of counting that occurs – if students can count in 5’s they should be able to count in 50’s (+ 1 zero), 500’s (+ 2 zeros), etc

• recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences

• identify multiples and factors using basic facts and extensions
• practise counting in multiples to 100 and then beyond so that students can quickly and accurately record the multiples – 3”s, 4’s, etc. This should also become a strategy that could be used for learning the multiplication tables
• use factor ‘trees’ as a visual tool to assist students in identifying the factors of numbers

NUMBER & ALGEBRA

• using the four operations with pairs of odd or even numbers or one odd and one even number, then using the relationships established to check the accuracy of calculations

• discussing and asking questions involving whole and decimal numbers

• explaining the position of any number on a number board in relation to other numbers

• ask questions involving two- three-, four – and 5-digit numbers
• explain the position of any number on a number board in relation to other numbers
• recognise and describe some subsets of numbers – eg. numbers ending in ‘5’, odd and even numbers
• use the four operations with pairs of odd or even numbers or one odd and one even, and identify the relationships between these numbers – eg. odd + odd will always = even
• interpret numerical information from factual texts
• place and justify 2- and 3-, 4- and 5- digit numbers in an appropriate position on a number line when none, some or all graduations have being identified
• deconstruct number boards to reinforce the link to number tracks and a linear model of numbers
• adjust numbers to 99 999 where appropriate in everyday situations – when people shop they might need to ensure they have enough money at the register so they use ‘adjusting numbers’ strategies to assist in quickly adding amounts
• compare whole numbers to 99 999 and numbers including one decimal place, as ‘greater than’, ‘less than’, ‘equal to’ , including using the symbols (> < =)
• place and justify common and decimal fractions in an appropriate position on a number line (1/2 ¼, 1/3, 1/5, 1/10)

NUMBER & ALGEBRA

• Representing and recording numbers to 99 999 including decimals using different combinations of ten thousands, thousands, ones, etc.

• reproducing five-digit numbers in words using their numerical representations, and vice versa

• recognising and demonstrating that the place-value pattern is built on the operations of multiplication or division of tens

• identify the number before and after a given number to 99 999 and expose students to ‘see’ that 100 000 is 10 ten thousands
• read, record, compare and order up to five-digit whole numbers
• represent and record numbers to 99 999, including decimals using different combinations of ten thousands, thousands, ones, etc. For example – 77 hundreds + 56 ones = 7, 756. Place value charts are an excellent tool for students to use when they begin to ‘solve’ the combinations
• read, record, compare and order common fractions
• make, name and record 2-, 3-, 4- and 5- digit numbers
• make the largest and smallest number given any five digits
• recognise the multiplicative and division nature of place value e.g. ones to tens is multiply by 10, tens to hundreds multiply by 10 and 100s to 10s, 100’s to tenths
• recognise the place value of each digit of a number to 99 999
• represent numbers to 99 999 including using place value materials, symbols, words and calculators
• represent numbers in expanded notation
  e.g. 9 675 = 9 000 + 600 + 70 + 5
• use number expanders to explain the component parts of 2, 3 ,4 and 5- digit numbers
• use numerals expanders to explain the component parts of tenths
• adjust numbers to the nearest 10, 100 or 1 000 when estimating or to assist with calculations

NUMBER & ALGEBRA

• Identifying, creating and solving addition and subtraction problems involving whole numbers with totals to 99 999 and decimals (in context to 2 places with same number of decimal places)

• selecting from a range of computation strategies and methods. Recall all addition and subtraction facts.

• counting on or back,
• breaking one or more numbers into place value or other compatible parts, working with the parts and putting these parts back together
• using doubling and / or halving
• adjusting one or both numbers and where necessary compensating for the adjustments – eg. 400 – 199 (adjust 199 to 200 by adding 1 and then find answer and – 1
• using place value knowledge – eg. when recording the algorithm the ‘houses’ are recorded underneath each other; eg. taking a 100 will affect the hundred and possibly the thousand digit as well; x and ÷ by multiples of ten means moving digits up or down depending if it’s x or÷
• use and record methods (student-generated and traditional) to add and subtract whole numbers to 99 999 e.g. on empty number lines
• use calculators for computations to 99 999 and interpreting the display
• use and record methods (student-generated and traditional) to add and subtract decimals fractions to one place with the same number of places
• align places and including zeros when using traditional written methods to add and subtract whole numbers and decimals to one place
• using written methods — with whole numbers up to five digits, where regrouping/trading is required including money

• solve addition and subtraction algorithms involving regrouping and trading

NUMBER & ALGEBRA

• Identifying, creating and solving addition and subtraction problems involving whole numbers with totals to 99 999 and decimals (in context to 2 places with same number of decimal places)

• selecting from a range of computation strategies and methods. Recall all addition and subtraction facts.

• determine whether a problem needs addition or subtraction to be solved
• explain whether an exact or approximate answer is best suited to a situation
• select and use mental, written or calculator methods to solve addition and subtraction problems
• solve one and two-step word problems involving whole numbers, money and measures in familiar contexts
• check the reasonableness of a solution to a problem by relating it to the original problem
• reflect on own method of a solution for a problem, considering whether the method can be improved
• apply the inverse relationship of addition and subtraction to check solutions
• record addition and subtraction equations ( number sentences) using drawings, tables, numbers, words and symbols and combinations of these
• explain what strategy was used for the addition and subtraction computation

NUMBER & ALGEBRA

• using known multiplication facts to calculate related division facts

• recall multiplication facts 1s, 2s, 4s, 8s and 5s to  10 including zero facts
• determine remaining number facts (3s, 6s, 7s, 9s ) to x 10 using these strategies: doubles, skip counting, turn around
• extend known facts where the numbers are manageable e.g. 2 × 3 = 6 therefore 2 × 30 = 60
• use place value knowledge to extend number facts
• recall division facts related to known multiplication facts for 1s, 2s, 4s, 5s, 8s, 10’s
• determine remaining division facts(3s,6s 7s,9s)
• recognise the inverse relationship between multiplication and division to provide students with a strategy to generate division facts –

• determine remaining number facts (3s, 6s, 7s, 9s ) to x 10 using these strategies: - doubles, skip counting, turnarounds, inverse multiplication
• relate multiplication and division facts to at least 10x10

NUMBER & ALGEBRA

• using known facts and strategies, such as commutativity, doubling and halving for multiplication, and connecting division to multiplication when there is no remainder

• use mental and/or written methods where appropriate for multiplication and division (single whole number multipliers and divisors) for 1s, 2s, 4s, 5s , 8s
• use calculators for multiplication computations beyond the basic facts to

• use calculators for division computations where is divisor is a factor of the dividend
• identify multiples on a hundreds chart
• use a calculator to generate a multiplication table
• determine extensions of multiplication and division facts such as 4 × 2 is 8 so 4 x 20 is 80
• determine whether a problem needs multiplication or division to be solved
• select and use mental, written or calculator strategies to solve multiplication and division problems
• pose and solve multiplication and division problems involving numbers up to 5-digit and numbers including decimals
• explain whether an exact or approximate answer is best suited to a situation
• apply the inverse relationship of multiplication and division to check answers
• interpret and record the display when using a calculator to multiply and divide whole numbers and decimal fractions
• explain the relationship between subtraction and division as repeated subtraction
• explain the relationship between addition and multiplication as repeated subtraction

• explain what strategy was used for the multiplication and division computation

NUMBER & ALGEBRA

• exploring the relationship between families of fractions (halves, quarters and eighths or thirds and sixths) by folding a series of paper strips to construct a fraction wall

• converting mixed numbers to improper fractions and vice versa

• investigating the use of fractions and sharing as a way of managing Country: for example taking no more than half the eggs from a nest to protect future bird populations

• explain and demonstrate that the denominators of fractions represent the number of equal pieces into which the whole was divided
• recognise that the larger the denominator of a fraction, the smaller the fraction
• represent fractions (halves, thirds, quarters, fifths, eighths and tenths) in different ways (area, linear and set models)
• read and record common fractions (1/2 (halves), 1/3 (thirds), 1/4, 1/5, 1/8 and 1/10)
• recognise that a unit fraction (i.e. one in the numerator) e.g. 1/5, is the amount represented by one of five equal parts
• interpret the numerator and denominator of a fraction
• e.g. 3/8 means 3 of 8 equal parts
• explain that a common fraction is a ‘number’ and has a position on the number line (linear model)
• use the halving strategy to model halves, quarters and eighths (area model)
• identify related common fractions (halves, quarters and eighths; fifths and tenths) using materials, folding and diagrams
• count forwards and backwards using common fractions and counting beyond one e.g. 2/3 , 3/3, 4/3 or 2/3, 1, 1 1/3
• locate common fractions (1/2, 1/3, 1/4, 1/5, 1/8 and 1/10) on a marked and unmarked number line (linear model) including improper fraction and mixed numbers
• use numbers lines that go beyond 1
• use number lines with different starting points e.g. 2 ½ , 8/4
• rename 2/2, 4/4, 8/8 as 1
• rename mixed numbers as improper fractions and convert mixed numbers to improper fractions and vice versa

• fraction involves ‘equal parts’ illustrated by area models and parts of a collection
• fraction as an operator (of 20 = 10)
• fraction as a number on a number line
• fractions and decimals are representations of the same number.

NUMBER & ALGEBRA

• using division by 10 to extend the place-value system

• using knowledge of fractions to establish equivalences between fractions and decimal notation

• read and record decimals in context to one place e.g. 2.5 is the same as ‘two whole and five-tenths’
• recognise the decimal point as marking the end of the whole number representation and the beginning of the decimal representation
• recognise the multiplicative nature of place value e.g. ones to tenths is divide by 10
• recognise place value of each digit of a number including ten thousands, thousands, hundreds, tens, ones, tenths, hundredths
• compare and classify decimal numbers as ‘smaller than 1’, ‘and ‘greater than 1
• compare decimal numbers using place value
• count forwards (to ten) and backwards (to zero) using tenths
• counting on and back by decimal fractions (tenths) starting from any number
• identifying the number before and after a given number, decimals to 2 places in context
• express and interpret tenths as decimals e.g. 1/10 = 0.1 and vice versa and hundredths as decimals e.g. 1/100 = 0.01
• compare and order decimal numbers (tenths & hundredths) and justify decisions by using a number line
• explain that when a whole is divided into 10 equal parts, these parts are called ’tenths’ and when a whole is divided into 100 equal parts, these parts are called hundredths

NUMBER & ALGEBRA

• using division by 10 to extend the place-value system

• using knowledge of fractions to establish equivalences between fractions and decimal notation

• explain the connection between one-tenth (& one-hundredth) as a common fraction and one-tenth as a decimal fraction
• describe the place-value of digits in numbers to 99 999 including decimals to 2 places in context using a number expander
• compare and order decimals with the same number of decimal places (to 2 decimal places) on number line
• record and interpret numbers expressed as decimals in terms of wholes and parts e.g. 4.5m is half way between 4m and 5m, it is 4 whole metres and half a metre
• check whether a calculation is reasonable by using an alternative method e.g. use a number line or calculator to show that ½ is the same as 0.5 and 5/10
• explain the relationship between fractions and decimals e.g. ½ is the same as 0.5 (1/2, ¼, 1/5 and 1/10)
• interpret and represent the number displayed on a calculator by rounding to one decimal place

NUMBER & ALGEBRA