year 4 - norfolk&suffolk hub · pdf fileyear 4 for more information and to make a booking ...

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Year 4

Big idea 1: Count, compare and order numbers (up to 1 000, including negative numbers)

Fluency Reasoning Problem solving

Exemplification of fluency

• Count in multiples of 6, 7, 9, 25, 1000

• Count backwards through zero to include negative numbers

• Represent numbers in different ways (include different representations – Roman numerals and other historical representation linked to topic, abacus, base ten etc.)

• Round any number to the nearest 10, 100, 1000, including decimals to 1 d.p. to nearest whole number and justify

Exemplification of reasoning

• Say whether a particular number will be reached if a sequence continues

• Make the largest/smallest possible number using three or four digits

• Order groups of numbers from smallest to largest

• Suggest a number that comes between two given numbers

• Say what number will be in a particular position in a sequence e.g. 10

th number

Exemplification of problem solving

• Say whether a particular number will occur in a given sequence

• Recognise and describe patterns in sequences of numbers

• Order a set of weights, where the size of some is given in grams and others in kilograms

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Year 4

Possible activities to exemplify fluency

• Count on in 9s from 23

• Count back in 25s from 650

• Say what temperature is 7 degrees colder than 4

• Round the different decimal numbers made by rolling two dice to the nearest whole number Source: NRICH – ‘Round the Dice Decimals’ activity

• Can count on in 25s from 50. Circle the numbers that will be in the sequence: 990, 550,125, 755,150

Source: NCETM Mastery Booklet

• Draw 302 on an abacus with three spikes

Possible activities to exemplify reasoning

• Will 46 be in the sequence of numbers made by counting up in 6s from 10? Why or why not?

• Use the 4 digits 1, 7, 3 and 0 to make the smallest possible number and the largest possible number Source: NCETM Mastery Booklet

• Given Egyptian symbols for 1 and 10 and 100, work out the value of some Egyptian numbers

Possible activities to exemplify problem solving

• Say what could be the lowest possible number of pounds saved if an amount is, say, £300 rounded to the nearest hundred

• Aim to make the largest number possible by rolling a dice and deciding which place of your number to put the number you rolled Source: NRICH – ‘Nice or Nasty’ game

• Interpret positions on a number scale extending below 0

Year 4

• Use cards 1, 4, 6 and decimal point to make a number between 4.1 and 4.61

• Given the sequence 20,30,40, 50, what will the nineteenth number in the sequence be? What will the hundredth number be?

Big idea 2: Recognise and use the positional, additive and multiplicative aspects of place value (4 digit numbers and decimals up to 2 decimal places)

• Divide 1 and 2 digit numbers by 10 and 100 and recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10, representing these as decimals

• Say how many tens is equal to a given number of hundreds

• Understand that in the number 3652 we can find the multiplicative place value of each digit by multiplying each digit by the column it is in e.g. 3 x 1000 = 3000

• Recognise the additive place value of each digit so when the individual values of the digits are added together they total the whole number

• Understand the positional place

value of each digit

• Justify answers in terms of place value

• Convince a friend of the value of each digit in integers and decimal numbers

• Explain why 23.4 x 10 = 234 and not 23.40

• Solve problems which involve converting between different units, including metric units and time

• Represent problems using apparatus to

organise thinking

Big idea 2: Recognise and use the positional, additive and multiplicative aspects of place value (4 digit numbers and decimals up to 2 decimal places)

• Match numbers with the same value represented in different ways

• Complete missing number

calculations involving division by 10

or 100

Source: KS2 SAT

• Explain why 53 hundreds has the same value as 530 000 hundredths

• Solve problems involving conversions between metres and centimetres

• Work systematically using place value to find different ways to represent 5600

e.g. 5.6 x 1000, 56 x 100, 560 x 10

Big idea 3: Develop number sense to support mental calculation

• Reorders calculations to do them more easily

• Round calculations to do an easier one mentally and then adjust the answer e.g. 29 x 3 = (30 x 3) - 3 = 87

• Use jottings when needed

• Use known facts to work out

unknown facts

• Discuss which method is easier

• Explain how a calculation can be more easily worked out by adjusting the numbers

• Use the relevant vocabulary when calculating

mentally

• Choose operations and efficient calculation strategies to solve problems

• Find multiple solutions to a problem

• Explore different ways of solving a

problem

Big idea 3: Develop number sense to support mental calculation

• Work out the cost of 4 DVDs at

£6.99 each by calculating 4 x £7

and adjusting by 4p

• Justify whether it is easier to calculate the

cost of 4 DVDs at £6.99 each by calculating 4

x £7 and adjusting by 4p or by a standard

written method

• How many calculations can you think of

with the answer 30?

Big idea 4: Add and subtract numbers, recognising that they are inverse operations (up to 4 digits and decimals with up to 2 decimal places)

• Use various formal, informal and mental methods

• Use inverse operations (solve missing number problems and check answers)

• Understand and use commutativity and associativity in addition and subtraction

• Decide on which operations and methods to use and why

• Use the mathematical language for addition and subtraction

• Use rounding and approximation to estimate answers and make decisions

• Solve addition and subtraction two step problems in context

• Choose and use appropriate operations and strategies

• Use different representations to understand and solve problems e.g. Bar Model

• Choose an efficient method to calculate an answer depending on the numbers involved, for example, a mental method utilising adjustment to add or subtract 998, rather than a written method

• Use inverse operations to check answers

• Write families of related number

statements

• Work out missing numbers from calculations which have some digits missing

• Reason about the value of missing digits

• Interpret different representations of a calculation when solving it

• Identify the order of calculations needed to tackle a multi-step problem

• Work backwards from an answer by applying inverse operations to find the starting point of a sequence of calculations

• Visualise problems to work out how to tackle them

• Use understanding of inverse

operations to solve missing box

problems

• Reason and explain why one calculation must give a larger, smaller or identical answer to another calculation

• Apply understanding of calculations crossing place value boundaries to solve ‘missing digit’ calculations

• Explain why one method is better than another

• Give examples where particular methods would be most appropriate

Big idea 5: Multiply and divide numbers, recognising that they are inverse operations (up to 3 digits by 1 digit and knowing multiplication and division facts up to 12 x 12)

• Recall number facts to 12 x 12

• Use patterns, place value, factor pairs and commutativity in mental calculations

• Use distributive law, for example, 8x12 = (8x10) + (8x2) and associative law, for example (2 x 3) x 4 = 2 x (3 x 4) Another example: 2 x 6 x 5 = 10 x 6 = 60

• Relate areas to arrays and

multiplication/ division

• Use apparatus and pictures to explain thinking

• Prove why one multiplication calculation gives the same answer as another one

• Explain how knowing one fact can help derive a related one

• Explain how to find the area of a rectangle with reference to arrays

• Solve problems in context including multiplying and adding including using distributive law

• Systematically use correspondence between objects such as number of choices of a meal to find all possibilities

• Solve problems on integer scaling using

multiplication and division

• Match calculations with answers

• Complete multiplication grids presented in different ways

• Complete calculations with missing numbers

• Combine knowledge of multiplication facts with knowledge of doubling and halving to quickly derive related facts

Source: DFES

• Use distributive property of multiplication

Source: DFES

• Apply properties of multiplication to say whether calculations are correct or not

• Use patterns observed in sequences of

multiples to solve problems

• Interpret question using appropriate visualisation

• Use self-correcting flashcards to learn, practise and improve speed with multiplication facts

Source: DFES

• Use games to practise and develop fluency

Source: DFES

• Complete empty boxes in multiplication grids

• Apply knowledge of multiplication facts to related calculations

• Demonstrate commutative property of multiplication

Source: KS2 SAT

• Can represent multiplications as arrays

Source: DFES

Big idea 6: Use algebra to express patterns and generalisations in mathematics

• Understand and use the equals sign as the balance of an equation

• Recognise symbols/ letters can represent numbers

• Use mathematical representations

to notice, continue and generate

patterns

• Give another example and another and another

• Use mathematical vocabulary to generalise

• Express a rule to describe a sequence

• Solve missing term problems

• Solve multi-step problems involving equivalence and more than one missing number, such as

6 x ? = ? – 2

• Understand that perimeter can be

expressed algebraically as 2(a+b)

where a and b are the dimensions in the

same unit

Big idea 6: Use algebra to express patterns and generalisations in mathematics

• 14 + 13 = 30 - c

• Explain what happens when two odd

numbers are added

• How long could the sides of a rectangle

be, if it has the same perimeter as a

square with sides 6cm?

Big idea 7(a): Recognise fractions and decimals of shapes, objects and quantities (unit and non-unit fractions, including tenths and hundredths)

• Recognise and show using diagrams, families of equivalent fractions and decimals (¼, ½, ¾)

• Round decimals (1d.p.) to nearest whole number

• Represent fractions and decimals in a variety of ways and contexts

• Apply knowledge of factors and

multiples to recognise and simplify

equivalent fractions

• Explain the relationship between non-unit fractions and multiplication and division of quantities (emphasis on tenths and hundredths)

• Use fraction vocabulary

• Conjecture about patterns in families of equivalent fractions

• Solve problems involving non-unit fractions

• Work systematically to find families of

equivalent fractions

• Use bars and fraction walls to find equivalent fractions

• Interpret diagrams in different ways to visualise equivalent fractions

• Know the equivalence of fractions and decimals

• Demonstrate knowledge of unit and non-unit fractions of money

Source: DFES

• Explain fractions in terms of related division and multiplication facts

• Explain how different representations of fractions are the same or different

• Visualise ‘the whole’ from seeing part

• Work systematically to find fractions

equivalent to

• Represent the whole when given part

• Find non-unit fractions when in context of recipe

Source: NCETM Mastery Booklet •

• Position numbers on a number line

• ‘Fractional Wall’ activity

Source: NRICH

• Explain which is more: 6 items shared between 8 people or 9 items shared between 12 people

• Explain whether strategies to work out fractions are correct

• Recognise what fraction of a shape has been shaded

Source: KS2 SAT

• ‘In the Money’ activity

Source: NRICH

• ‘Red Balloons, Blue Balloons’ activity

Source: NRICH

Big idea 7(b): Calculate with fractions and decimals (add and subtract fractions with the same denominators and decimals to 2 decimal places)

• Calculate with fractions giving results greater than one whole

• Convert between mixed numbers and improper fractions

• Convert between fractions and decimal

• Find the effect of dividing a 1 or 2 digit number by 100

• Explain why multiplying by ten and multiplying again by ten is the same as multiplying by 100 (use a Gattegno chart)

• Explain what fraction needs to be added to any proper fraction to make a complete whole

• Use understanding of size of fractions to

convince a friend whether fraction additions

are correct or not

• Make connections between fractions of a length, of a shape and as a representation

• Solve simple money and measure

problems involving fractions and

decimals

Big idea 7(b): Calculate with fractions and decimals (add and subtract fractions with the same denominators and decimals to 2 decimal places)

• Represent addition and subtraction of fractions with the same denominator on diagrams and number lines

• Reason about pairs of fractions with a difference of one-eighth

• Use understanding of size of fractions to explain whether fraction additions are correct or not

• Work systematically to find all the possible subtractions involving sixths (proper fractions) that give an answer of one sixth

Big idea 8:

Choose, use and compare a variety of units of measure to an appropriate level of accuracy

• Use multiplication to convert from larger units to smaller units

• Read scales, interpreting unlabelled positions marked on the scale

• Choose appropriate equipment and units to make measurements of length, mass and capacity

• Read analogue and digital clocks

accurately

• Use knowledge of units to estimate mass, length and capacity in real life contexts

• Use the vocabulary associated with measures

• Reason about different scales

• Solve problems involving conversions between units

• Work logically to order a set of measures where conversion is needed

Big idea 8:

• Read scales, interpreting unlabelled positions marked on the scale

Source: DFES

• Interpreting unlabelled positions marked on a scale

• Solve problems involving conversions between metres and centimetres

• Order a set of weights, where the size of some is given in grams and others in kilograms

Big idea 8:

• Order a set of capacities, where some

are given as fractions of litres and

others in millilitres

Big idea 9:

Recognise and use the properties of shapes, including position and direction

• Use properties to describe shapes - include angles, regular/irregular and symmetry

• Complete a symmetric figure with respect to a specific line of symmetry, including outside shape

• Identify quadrilaterals and triangles, based on their properties

• Use coordinates to describe position

• Compare lengths and angles within shapes

• Use appropriate vocabulary, including isosceles, equilateral and scalene; parallelogram, rhombus, trapezium

• Reason about the size of a polygon from knowledge of its coordinates

• Explain why a shape is or is not a specific type based on its properties

• Solve problems involving translations

• Use knowledge of shape properties to solve problems

• Systematically sort shapes in logical ways

• Draw a shape from a description of its properties

Big idea 9:

• Choose a shape that matches its description

• Plot specified points to draw sides to complete a given polygon

• Name and match particular quadrilaterals and triangles to their images

• Say the coordinates of the point which will complete a given polygon

• Draw examples of different shapes and describe their properties

• Explain whether having four right angles means a rectangle is a regular shape

• Explain why a line is or is not a line of symmetry

• Work out the perimeter of a polygon, given its coordinates

• Put shapes in Venn diagrams and Carroll diagrams

• Draw shapes with specified properties

Big idea 9:

• Reason about the coordinates of a vertex using knowledge of the properties of a shape

Source: KS2 SAT

• ‘A Cartesian Puzzle’ activity

Source: NRICH

• Use a range of scales

• Read points on one axis that correspond to given measures on the other axis

• Represent data as graphs and charts

• Complete tables by reading graphs and charts

• Interpret tables of data to answer

questions

• Use the correct vocabulary associated with statistics

• Justify opinions about whether particular statements about a set of data are true or not

• Explain why one type of graph is more

appropriate than another

• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

• Use logic to make up a story to fit a line

Big idea 10:

Collect, organise and interpret data (discrete and continuous)

Big idea 10:

• Justify opinions about whether particular statements about a set of data are true or not

• Interpret graphs to solve problems

• Make up a story to fit a line graph

Big idea 10:

• Justify why one type of graph is more appropriate than another

rmatio

year 4 - norfolk&suffolk hub · pdf fileyear 4 for more information and to make a booking ...

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