NUMBER PROCESSES
Forward Number Word Sequence (FNWS)Emergent FNWS
Produce FNWS up to ten
Produce FNWS up to ‘ten’ from a given number (drops back to one)
Produce FNWS up to ‘ten’ from a given number. Can produce number word after. (without dropping back)
Produce FNWS from ‘one’ to ‘twenty’. Can produce the number word after without dropping back.
Produce FNWS from ‘one’ to ‘thirty’. Can produce the number word after without dropping back.
Produce FNWS from ‘one’ to ‘one hundred’. Can produce the number word after without dropping back.
Can count in 10s.
Can count in 10s on and off the decade.
Can count in 1s and 10s on and off the decade.
Can count in 1s and 10s on and off the decade beyond 100.
Can count in 1s and 10s and 100s from a given number.
Can count in 1s and 10s and 100s and 1000s from a given number
Backward Number Word Sequence (BNWS)
Emergent BNWS
Produce BNWS from ‘ten’ to ‘one’
Produce BNWS from ‘ten’ to ‘one’ from a given number (drops back to one)
Produce BNWS from ‘ten’ to ‘one’ from a given number. Produce number word before. (without dropping back)
Produce BNWS from ‘twenty’ to ‘one’ from a given number. Produce number word before. (without dropping back)
Produce BNWS from ‘thirty’ to ‘one’ from a given number. Produce number word before. (without dropping back)
Produce BNWS from ‘hundred’ to ‘one’. Can produce the number word before without dropping back.
Can count backwards in 10s.
Can count backwards in 10s on and off the decade.
Can count backwards in 1s and 10s on and off the decade.
Can count backwards in 1s and 10s on and off the decade beyond 100.
Can count backwards in 1s and 10s and 100s from a given number.
Can count backwards in 1s and 10s and 100s and 1000s from a given number.
Understanding Numerals
Can identify some numerals in the range ‘1’ to ‘10’
Can identify and sequence numerals in the range ‘1’ to ‘10’
Can identify and sequence numerals in the range ‘1’ to ‘20
Can identify and sequence numerals in the range ‘1’ to ‘30’
Can identify and sequence numerals in the range ‘1’ to ‘100’
Can determine the value of each digit within ‘one hundred’ . e.g. 56 is 5 tens and 6 ones or 56 ones.
Can identify and sequence numerals in the range ‘1’ to ‘100’ and beyond.
Can determine the value of each digit within ‘one thousand’ . e.g. 362 is 3 hundreds, 6 tens and 2 ones, or 36 tens and 2 ones or 362 ones.
Can determine the value of each digit beyond ‘one thousand’ .
Can determine the value of each digit beyond ‘one thousand’ .
Can determine the value of each digit for numerals up to eight digit numerals
Can understand how numbers extend to numbers less than 0. Can add negative and positive numbers to an empty number line where 0 is clearly marked.
Can relate negative numbers to real life contexts e.g. temperature, money, coordinates
. / Can extend range of numbers to powers e.g. cubes (X3) and square roots (√)
Can convert to and from scientific notation for large and small numbers e.g 352000000 is 3.52 x 108 1.7x10-4 is 0.00017
Temporal Patterns
Can make a given number of sounds/movements (e.g. jump 3 times)
Can identify the number of sounds/movements (e.g. how many times did I clap?)
Finger Patterns
Can build finger patterns by 1s
Can throw finger patterns 1-5
Can throw finger patterns 1-10
Uses 5 plus finger patterns
Uses doubles finger patterns
Can structure numbers by using 0, 5 and 10
Can throw finger patterns 1-10
Number Structures
Counts domino patterns in 1s
Can identify domino patterns
Counts tens frames in 1s
Identify ten frames
Understands and Uses 5-plus patterns
Understands and Uses doubles
Can structure numbers by using 0, 5 and 10
Can structure numbers to 20 in a variety of ways.
Can structure numbers to 100 using tens and ones.
Can structure numbers to 100 in a variety of ways. (e.g. 32 is 3 tens and 2 ones, 2 more than 30, 20+12, 35-3, 8 less than 40, etc.)
Can structure numbers to 1000 through hundreds and decades.
(e.g. 376+84=380+80 or 456+4 or 376+24+60 or 376+4+20+60=460)
Can structure numbers beyond 1000.
Addition and Subtraction
Count perceived items. This may involve seeing, hearing and feeling items.
Can count 2 or more perceived collections together. This may involve seeing, hearing and feeling items.
Can count on rather than count from ‘one’ to solve addition and missing addend tasks (for example, 6+[ ] =9).
Use a count-down-from strategy to solve removed items tasks (for example (17-3 as 16, 15, 14 – answer 14)
Use a count-down-to to solve missing subtrahend tasks (for example, 15 – [ ]=11) and written tasks such as 17-14 (16, 15, 14 – answer 3).
Can choose the more efficient from count-down-from and count-down-to strategies.
Can use understanding of number structures to develop and explain a range of non-count-by-ones strategies such as:
- compensation
- using a known result
- adding to ten
- commutativity,
- subtraction as the inverse of addition
- awareness of the ‘ten’ in a teen number.
Can use their understanding of number structures to develop and explain their own range of non-count-by-ones strategies to solve tasks within 100.
Can use both mental strategies and algorithms. Can choose the most efficient method for the problem given.
Can use understanding of number structures to develop and explain own range of non-count-by-ones strategies to solve tasks within 1000. Can use both mental strategies and algorithms. Can choose the most efficient method for the problem given.
Can use understanding of number structures to develop and explain own range of non-count-by-ones strategies to solve tasks beyond 1000. Can use both mental strategies and algorithms. Can choose the most efficient method for the problem given.
Can use understanding of positive and negative numbers in problem solving contexts.
Multiplication and Division
Can use perceptual counting (i.e. by ones) to establish the numerosity of a collection of equal groups,.
Can share items into groups of a given size (quotitive sharing),
Can share items into a given number of groups.
Can use an (early) multiplicative counting strategy to count visible items arranged in equal groups.
Can use an (early) multiplicative counting strategy to count items arranged in equal groups in cases where the individual items are not visible.
Can use an (early) multiplicative counting strategy to count items arranged in equal groups in cases where the individual items and groups are not visible.
Can count composite units (e.g. 3,6,9) in repeated addition and subtraction Can use the composite unit a specified number of times.
Can count groups and share groups in 2s
Can count groups and share groups in 3s
Can count groups and share groups in 4s
Can count groups and share groups in 5s
Can count groups and share groups in 6s
Can count groups and share groups in 7s
Can count groups and share groups in 8s
Can count groups and share groups in 9s
Can count groups and share groups in10s
Can regard both the number in each group and the number of groups as a composite unit. Can immediately recall or quickly derive many of the basic facts for multiplication and division.
x2 x3 x4 x5 x6 x7 x8 x9 x10
Can identify the multiples and factors of numbers from familiar times tables. E.g. 14 is a multiple of 7 and 7 is a factor of 14
Can use understanding of number structures and equal groups to develop and explain own range of strategies for multiplying and dividing of tens and ones by a single digit. (e.g. 32x4, 56÷4, 34÷7)
Can use understanding of number structures and equal groups to develop and explain own range of strategies for multiplying and dividing by tens and ones. (e.g. 32x32, 84÷12, 87÷16)
Can apply knowledge of equal shares to simplify fractions.
Can apply the rule that a negative multiplied by a positive equals a negative
Can apply the rule that a negative multiplied by a negative equals a positive
Can use understanding of positive and negative numbers in problem solving contexts.
Can use understanding of number structures and equal groups to solve a range of problems.
I can apply my understanding of factors to investigate and identify when a number is prime (link to Sieve of Eratosthenes)
Can evaluate a whole number power mentally or by using technology.
Can describe the advantage of writing numbers as a whole number power
Estimating and Rounding
Five-wise
Can round to the nearest 10
Can round to the nearest 100
Can round to the nearest 1000
Can round to the nearest whole number
Can round to the nearest 1 decimal place
Can round any number a required number of decimal places e.g. money to 2d.p, volume to 3d.p
Can round a given number of significant figures (e.g. 57329 rounded to 3 s.f is 57300, 0.25943 to 2 s.f is 0.26)
Order of operations
Can apply BODMAS to calculations
Brackets Of(to the power of) Division Multiplication Addition Subtraction
Vocabulary
odd and even numbers
Vocabulary for addition – plus, add, sum, total, altogether…
Vocabulary for subtraction – take away, subtract, difference, minus…
Vocabulary for multiplication – multiply, product, times…
Vocabulary for division – divide, share, group…
Whole numbers and fractions (rational numbers)
Factors and multiples
Integers (Positive and negative whole numbers)
Rational Numbers (any number that can be expressed as a fraction)
Index (power)
Prime numbers (a number with exactly two factors: 1 and itself)
Prime factors
Understanding Fractions and Decimals
Can share items by sorting them in equal groups
A whole object can be shared into parts
Can share an object by cutting it into equal parts
A fraction is a part of the whole amount
A fraction is an equal sharing of the whole amount
Halving the whole amount will give you two equal parts/shares
The bottom number in a fraction is called the denominator and tells us how many shares there are.
The top number in a fraction is called the numerator and tells us how many equal parts of the whole should be considered
Can describe why one half is written as ½
Two equal halves make a whole
½ can have the value 0.5 and can be put on the number line halfway between 0 and 1.
Can put simple fractions on an empty number line.
Can match fractions that have the same value and put them on an empty number line.
Can describe equivalent fractions
I can understand different kinds of fractions. e.g. proper fraction, improper fraction, equivalent and mixed numbers.
I can interpret a fraction and make a pictorial representation of it.
Can find the half of the whole amount by dividing it by 2.
To find the quarter of the whole amount we divide it by 4.
Can use the denominator to calculate the simple fraction of a quantity e.g ¼ of 40 is 40 divided by 4, ½ of 84 is 84 divided by 2 = 42
Can simplify fractions
I can calculate the fraction of whole amounts by using my knowledge of fractional notation, division and multiplication. e.g. ¾ of 100 is 100 divided by 4, then multiplied by 3 = 75.
Understand decimals as special fractions.
Can write any fraction as a decimal fraction. E.g 2/5 = 2 divided by 5 = 0.4
Understand that 1/10 of 1 is 0.1 (1 divided by 10)
Understand that 1/100 of 1 is 0.01 (1 divided by 100)
Can understand the value of each digit in a decimal number e.g 56.38 (8 represents 8 hundredths)
Can place decimals on a number line.
Understands that a percentage is a fraction with the denominator of 100.
Can equate decimals and percentages.
Can describe the link between fractions, decimal fractions and percentages.
Can use understanding of the link between fractions and percentages to calculate the percentage of a quantity.
e.g. 50% of 60 is the same as half of 60 = 30
75% of 60 is the same as ¾ of 60 …=45
30% of 200 is 200 divided by 100, then multiplied by 30= 60
Can calculate the percentage of given quantity
Can apply my knowledge of fractions, decimal fractions and percentages to solve related problems e.g. comparing shop discounts.
Can write a whole or mixed number as top-heavy fraction.
Can convert between whole or mixed numbers, and fractions.
Understanding Ratio
Understands that quantities can be compared. This can be written as a ratio e.g 1:4, 9:6
Can use understanding of ratio to increase/decrease proportionally. e.g 1:415:60 9:63:2
Can apply knowledge of ratio and proportion to real life situations.
Addition and Subtraction of Decimal Fractions
Can use their understanding of decimal fractions to develop and explain their own range of strategies to solve tasks up to 2 decimal places.
Can use mental strategies, algorithms and calculators. Can choose the most efficient method for the problem given.
Can use their understanding decimal fractions to develop and explain their own range of strategies to solve tasks.
Can use mental strategies, algorithms and calculators. Can choose the most efficient method for the problem given.
Addition and Subtraction of Fractions
Can describe equivalent fractions
Be able to find a common denominator for given fractions and rewrite as equivalent fractions
Be able to add and subtract fractions by using equivalent fractions.
Multiplication of Decimal Fractions
Can use their understanding of decimal fractions to develop and explain their own range of strategies to solve tasks up to 2 decimal places.
Can use mental strategies, algorithms and calculators. Can choose the most efficient method for the problem given.
Can use their understanding decimal fractions to develop and explain their own range of strategies to solve tasks.
Can use mental strategies, algorithms and calculators. Can choose the most efficient method for the problem given.
Vocabulary
Whole numbers and fractions (rational numbers)
Numerator and denominator
Recurring decimals
Expressions and Equations (algebra)
recognise, discuss, duplicate, extend and create simple numeric and non-numeric patterns
recognise simple rules in context e.g. getting bigger by 1
Recognise and use the (=) sign .
Understand that symbols can be used to represent quantities
Extend create and explain the rules for a repeating patterns and simple number sequences.
Understand commutative and associative properties and use them to simplify calculations.
e.g 3+5=5+3
5+3+7=(7+3)+5=
Understand and use the facts that add and subtract, multiply and divide are inverse processes.
Find the missing numbers in statements where symbols are used for unknown numbers or operators (e.g. 4+=5 or what is the value of , 45=9 what is )
Understand that (=) signifies balance/equality in a number sentence.
Understand and use symbols such as (), () , ()
Understand and use symbols such as (), () , ()
Understand number patterns involving the four operations (+) (-) (x) ()
Understand and use function machines and the associated relationship between input and output values
explain in words the rule that has generated a number pattern.
Understand that these rules can be represented by letters, symbols and graphs.
Understand and apply the concept of variables where letters and symbols represent numbers, in appropriate contexts. e.g. science and technology
Understand and use distributive properties
e.g. 2x27= (2x20) = (2x7)
723= (603)+(123)
extend their understanding of ‘balance ‘ by adding, subtracting, multiplying or dividing similarly on both sides on a number sentence or equation.
Substitute values into formulae
Form and solve simple expressions, equations and inequalities
Solve simple equations with variable on one side of the equal sign involving very simple single or double operations. E.g. x-4=7, 2n+3=9
Solve simple inequations (e.g. x-4>7)
Can collect like terms e.g. 5x-3+6x+7=11x+4 7b3 –(4b3–6b)=3b3+6b
Multiply expressions 3×y×y=3y2 (3y)2=3y×3y=9y2
Evaluate simple expressions by substitution e.g 2ab+4c a=3, b=5, c=-6 (observing rules of BODMAS)
Can collect like terms e.g. 5x-3+6x+7=11x+4 7b3 –(4b3–6b)=3b3+6b
Multiply expressions 3×y×y=3y2 (3y)2=3y×3y=9y2
construct algebraic equations to express problems we want to solve.
create a simple formula to describe how one quantity relates to one or more other quantities contained in a:
- diagram
- table
- statement
Patterns
Colour and shape patterns
copy a pattern or sequencecontinue a patterns or sequence
describe simple patterns or sequences
create simple patterns or sequences
describe patterns in the environment
Simple counting patterns
continue repeating pattern or sequence
describe repeating patterns or sequences
create repeating patterns or sequences
identify patterns in the environment
Explain the rule for simple counting patterns
Continue simple number sequences
1.3.5.7.9
8+0=8, 7+1=8, 6+2=8 etc
Can distinguish between odd and even numbers
Can copy and continue more complex sequences with shapes or numbers.
Create patterns by rotating a shape (use a template or computer turtle graphics)
Continue and describe more complex sequences (e.g. 1, 1, 2, 3, 5, 8, 13…)
Work with patterns and relationships: within and among multiplication tables (e.g. the link between the 3 and the 9 times tables)
Explain the rule used to generate a sequence and apply it to extend the pattern
Investigate Square Numbers: 1,4,9,16, (adding on in consecutive odd numbers) and link with diagrams.
Investigate Triangular Numbers: 1,3,6,10 (adding on consecutive numbers) and link with diagrams.
The values within a sequence are called terms
The values in a sequence are called terms
We use n to describe the position of a term in the sequence for example n=2 gives the second term
The formula for the general term or nth term allows us to
- Generate the sequence
- Find the value of a specific term in a sequence
- E.g. 4n-3 generates the sequence 1,5,9,13,17…
All terms in the sequence are connected by the same rule
The rule for a linear sequence is of the form:
an +/- b
Given a linear sequence we construct a table of values to help us determine its rule
The constant difference of a linear sequence is its multiplier
The correction number, b, is what we add or take away to get from the number in the times table to the term in the sequence
When we know a and b we can write the rule for a linear sequence e.g. 2n+5
Money
Recognising Money
Recognise coins: 1p 2p, 5p 10p 20p 50p £1 £2
Recognise Notes £1 £5, £10 £20 £50 £100
Using Money
Exchange coins to buy things: 1p 2p, 5p 10p 20p 50p £1 £2
Use a combination of coins or notes to buy things in whole pence or pounds:
up to 5p up to 10p up to 20p,
up to 50p up to 100p
up to £1 up to £2 up to £5
up to £10 up to £50 up to £100
beyond £100
Use a combination of coins and notes to buy things in pounds and pence.
up to £1 up to £2 up to £5
up to £10 up to £50 up to £100
beyond £100
Work out change from 10p
Work out change from 20p
Work out change from 50p