**Rules, expectations and presentation **

# Maths Curriculum

## Year 3

#### Week 1

#### Week 2

**Number and Place Value**

- To recognise the place value of each digit in a three digit number
- To write numbers up to a 1000 using digits
- To write numbers up to a 1000 using words
- To use part, part whole to partition numbers in different ways
- MM To identify what odd or even number comes after a given number e.g. What odd number comes before 301? What are the next four even numbers after 196?

#### Week 3

**Addition**

- To use a number line for addition with partitioning
- To add three digit numbers with no regrouping
- To add three digit numbers with regrouping in the ones place value column
- To add three digit numbers regrouping in the tens and one’s place value columns
- MM To count on in multiples of 4 using number bonds. Adding 4 is the same as adding 3 then 1 or 2 then 2 or 1 then 3

#### Week 4

**Subtraction**

- To count back to find the difference using a number line
- To subtract three digit numbers with no exchanging
- To subtract three digit numbers with exchanging from tens to one’s
- To subtract three digit numbers with exchanging across all place value columns
- MM To count on in multiples of 8. Show how to use number bonds to help. Adding 8 is same as adding 7 then 1 or 6 then 2 or 5 then 3 or 4 then 4 or vice versa

#### Week 5

**Multiplication**

- To use number bonds to identify factors and products knowing what are factors and products – E.g. 5 x 4 = 20, so 4 x 5 = 20
- To recognise how place value changes with multiplying by 10
- To demonstrate two digit by one digit multiplication using the grid method
- To demonstrate two digits by one digit multiplication moving from grid method to expanded multiplication
- MM To count in multiples of 50

#### Week 6

**Division**

- To use number bonds to identify factors, multiples and products. Use multiples of 2, 3, 4, 5, 8 and 10
- To recognise how place value changes when dividing by 10
- To divide a two digit number by a one digit number (No remainders)
- To divide a two digit by a one digit number with some remainders
- MM To count in multiples of 100

#### Week 7

**Fractions**

- To identify unit fractions of objects, shapes and length
- To identify non-unit fractions of objects, shapes and length
- To compare fractions that share the same denominator
- To order fractions in ascending and descending order with same denominator
- MM To count forwards and backwards by 10

#### Week 8

**Measurement Time**** **

- To explain each roman numerals up to 20
- To tell and write the time from analogue clocks
- To tell and write the time from digital clocks
- To match and convert between digital and analogue clocks
- MM To count forwards backwards by 100

#### Week 1

**Measure**

- To recognise tenths arise from dividing an object into ten equal parts
- To count up and down in tenths
- To recognise equivalent fractions
- To calculate fractions of a quantity

#### Week 2

**Geometry – Shape**

- To identify horizontal, vertical lines and pairs of perpendicular and parallel lines
- To identify different types of angle
- To describe the properties of 2-D shapes
- To draw a range of 2-D shapes
- MM To identify the next number in a sequence

#### Week 3

**Statistics**

- To interpret data presented in a table
- To interpret data presented in a pictogram
- To interpret data presented in a bar chart
- To classify shapes, numbers and objects into a Venn diagram
- MM To calculate quickly pairs of multiples of 5 that total 100

#### Week 4

**Measurement – ****Length and Mass**

- To measure and compare lengths in m, cm and mm (using rulers or tapes)
- To measure and compare mass in kg and g
- To convert between units of length – m, cm and mm
- To convert between units of mass – kg and grams
- MM To add pairs of multiples of 100 that make 1000 as well as cross 1000

#### Week 5

**Measurement – ****Volume capacity**

- To measure and compare volume and capacity
- To convert between units of volume and capacity
- To solve capacity problems using both addition and subtraction
- To use multiplication and division to scale by integers – context volume and capacity See Y3 PA maths for examples
- MM To add 3 digit numbers and one using number bond facts e.g. 482 + 9 = 480 + 8 + 1 or 611 + 7 = 611 + 4 + 3

#### Week 6

**Number and place value**

- To compare three digit numbers
- To order three digit numbers in ascending and descending order
- To identify, draw and estimate amounts on a number line
- To round numbers to the nearest 10 or 100 using a number line
- MM To subtract 3 digit numbers and ones using number bond facts e.g. 345 – 7 = 345 – 5 – 2. 518 – 9 = 518 – 8 – 1

#### Week 7

__Measurement – ____Four Operations__

- To solve measurement problems using both addition and subtraction in the context of length
- To use multiplication and division to scale by integers – context length
- To solve measurement problems using both addition and subtraction in the context of mass
- To use multiplication and division to scale by integers – context mass
- MM To add and subtract 3 digit numbers and ones using number bond facts

#### Week 1

**Addition and subtraction **

Model estimation throughout the two weeks to build on the first lesson

- To use estimation to check the accuracy of addition and subtraction
- To use the inverse to check calculation
- To add three digit numbers regrouping across all place value columns
- To subtract three digit numbers exchanging across all place value columns
- MM – To add two digit multiple of tens to three digit numbers e.g. 285 + 9. First 85 + 9, which is like 85 +5 + 4. So 285 + 9 = 294

#### Week 2

**Addition and subtraction**

- To develop and recognise patterns in addition
- To develop and recognise patterns in subtraction
- To use addition and subtraction to solve one step word problems
- To use addition and subtraction to solve one and two step word problems
- MM – To subtract two digit multiple of tens from three digit numbers. Make links to number bonds. e.g. 260 -80 is like 26 – 8 or 26 – 6 – 2 therefore 260 – 80 = 180

#### Week 3

**Multiplication**__ __

- To identify factors of numbers up to 50
- To recognise how place value changes when multiplying and dividing by 10
- To carry out short multiplication (expanded method)
- To carry out short multiplication with regrouping (moving away from expanded)
- MM – To add multiples of one hundred from three digit numbers

#### Week 4

**Division**

- To divide a two digit by a one digit number with remainders and exchanging in the ones column e.g. 82 divide by 4
- To divide two digits by a one digit number with remainders and exchanging in multiple place value columns. e.g. 57 divide by 3
- To solve measuring and scaling problems (multiplication and division)
- To solve one step multiplication and division word problems
- MM – To subtract multiples of one hundred from three digit numbers

#### Week 5

**Fractions**

- To compare fractions with different denominators
- To order fractions with different denominators
- To add like fractions
- To subtract like fractions
- MM – To use partitioning to add three and two digit numbers. e.g.55 + 37 = 55 + 30 + 7

#### Week 6

**Fractions**

- To identify non-unit fractions of objects, shapes and length
- To recognise equivalent fractions
- To calculate fractions of a quantity
- To solve one and two step problems involving fractions
- MM – To use partitioning subtract three and two digit numbers. e.g. 365 – 42 is 60 – 40 and 5 – 2 giving an answer of 323

#### Week 1

**Geometry – ****Shape**

- To construct 3-D shapes using modelling materials
- To recognise 3-D shapes in different orientations
- To recognise angles as a description of a turn
- To identify and describe symmetrical and non-symmetrical polygons ad polyhedral

#### Week 2

**Statistics**

- To solve one and two step problems using data recorded in a table
- To solve one and two step problems using data recorded in bar charts
- To solve one and two step problems using data recorded in pictograms
- To organise shapes, numbers and objects into a Carroll diagram
- MM – To add and subtract two and three digits that bridge through multiples of 10 and 100. e.g. 57 + 13 = 57 + 3 + 10 or 342 – 8 = 342 – 2 – 6

#### Week 3

**Measurement – ****Money**

- To recognise and use coins and notes to compare amounts (Will involve converting between pounds and pence)
- To select different combinations of coins to make the same amounts of money e.g. What is the smallest number of coins I could use to make 80p? I have 5 coins that make £1.35. What could they be?
- To solve money problems that involves finding the total
- To calculate the change given in £ and p
- MM – To use compensation when adding and subtracting – E.g. 53 + 11 = 53 + 10 + 1 or 70 – 9 = 70 – 10 + 1

#### Week 4

**Measurement – ****Time**

- To tell and write the time in both analogue and digital clocks
- To identify the number of days in each month, years and leap year. Teach pupils knuckle trick for remembering
- To compare times in seconds, minutes and hours
- To calculate and compare duration of events
- MM – To identify doubles of multiples of 5. e.g. 30 + 30 or 85 + 85

#### Week 5

**Number and Place Value**

- To count up and down in 10 and 100
- To write numbers as words and vice versa
- To compare and order a three digit numbers
- To solve a range of number and place value problems
- MM – To add using near doubles e.g. 19 + 20 = 20 + 20 – 1

#### Week 6

**Four Operations – Context Measurement**

- To measure and calculate perimeter of 2-D shapes
- To recognise the place value of different measures
- To convert between different units of measure
- To identify fractions of measures

#### Week 1

**Addition and subtraction**__ __

- To use estimation when solving three digit addition and subtraction with regrouping/ exchanging
- To solve missing number addition and subtraction word problems
- To use reasoning to explain misconceptions in addition and subtract column method
- To solve one and two step addition and subtraction word problems
- MM To subtract numbers that are close together using counting on e.g. 500 – 488 = 488 + 12

#### Week 2

**Multiplication and division**

- To use estimation when solving three digit by one digit short multiplication (no expanded)
- To use estimation when solving bus stop division (including remainders)
- To solve one and two step multiplication and division problems
- To demonstrate when to round up or down depending on context when multiplying and dividing
- MM To multiply a number by 10 or 100

#### Week 3

**Multiplication and division**** **

- To use distributive property strategy to divide ‘friendly’ numbers
- To solve missing number multiplication and division problems
- To use reasoning to explain misconceptions in multiplication and division column method
- MM To divide a number by 10 or 100

#### Week 4

**Fractions**** **

- To count up and down in halves, quarters and thirds, identifying missing fractions on a number line or in a sequence
- To identify fractions that are between two numbers e.g. What fraction is half way between 3 and 4? What fraction is in between 5 and 5 and 1/2? What fractions could be between 7 and 8?
- To recognise equivalent fractions
- To compare and order fractions
- MM To use times table facts to multiply mentally

#### Week 5

**Fractions**

- To identify unit and non-fractions of objects, shapes and length
- To add and subtract like fractions
- To calculation fractions of a quantity
- To solve a range of problems involving fractions
- MM To use times table facts to divide mentally

#### Week 6

**Geometry – ****Shape**

- To identify horizontal, vertical lines and pairs of perpendicular and parallel lines
- To identify different types of angle
- To identify lines of symmetry in regular and irregular 2-D shapes
- To measure and calculate perimeter of 2-D shapes

- MM To double and halve two and three digit numbers

#### Week 1

**Geometry – ****Position and Direction**

- To describe the position on a 2-D grid as coordinates
- To describe movements of coordinates on a grid as translations (left, right, up and down/ NSEW)
- To plot specific points on a quadrant
- To draw simple symmetric patterns and shapes across a mirror line

#### Week 2

**Measurement – ****Money**

- To select different combinations of coins to make the same amounts of money e.g. What is the smallest number of coins I could use to make 80p? I have 5 coins that make £1.35. What could they be?
- To solve money problems that involves finding the total
- To calculate the change given in £ and p
- To solve a range of one and two step word problems involving money
- MM To multiply by 4 and 8 using doubling

#### Week 3

**Measurement – ****Length, Mass and Volume**

- To measure and compare lengths in m, cm and mm (using rulers or tapes)
- To measure and compare volume and capacity
- To convert between units of length, mass and volume
- MM To divide by 4 and 8 using halving

#### Week 4

**Measurement – ****Length, Mass and Volume**

- To recognise the place value of different measures, see Y3 PA maths number and place value for examples
- To calculate fractions of measures, see Y3 PA maths for example
- To solve addition and subtraction problems in the context of LMV
- To use multiplication and division to scale by integers – context LMV

#### Week 5

**Statistics**

- To record and interpret data in a table (Pupils put their own/class / given data into a bar chart)
- To record and interpret data in a bar chart (Pupils put their own/ class/ given data into a bar chart)
- To record and interpret data in a pictogram (Pupils put their own/ class/given data into a bar chart)
- To record and interpret data in a Carroll Diagram (Pupils put their own/ class/given data into a bar chart)
- MM To multiply two digit by one digit numbers mentally using partitioning

#### Week 6

**Measurement – ****Time**

- To compare time written in both analogue and digital clocks
- To convert between the days months and years
- To convert between time in seconds, minutes and hours
- To calculate and compare duration of events
- MM To state own date of birth and calculate who is older and younger

#### Autumn 1

- Number and place value
- Addition
- Subtraction
- Multiplication
- Division
- Fractions
- Time

#### Autumn 2

- Fractions
- Geometry – shape
- Statistics
- Length and mass
- Volume and capacity
- Number and place value
- Four operations in the context of problem solving

#### Spring 1

- Addition and subtraction
- Multiplication
- Division
- Fractions

#### Spring 2

- Geometry – shape
- Statistics
- Money
- Time
- Number and place value
- Four operations in the context of measurement

#### Summer 1

- Addition and subtraction
- Multiplication and division
- Fractions
- Geometry – shape

#### Summer 2

- Geometry – position and direction
- Money
- Length, Mass & Volume
- Statistics
- Time

## Year 4

#### Week 1

**Rules, Systems, Expectations**

#### Week 2

**Number and Place Value**

- To recognise the place value of each digit in a four digit number
- To write numbers beyond a 1000 using digits and words
- To calculate 10, 100 or 1000 more or less than any given number
- To compare and order numbers beyond 1000
- MM To count in multiples of 6,7 and 9

#### Week 3

**Addition and Subtraction**

- To add four digit numbers with no regouping
- To subtract four digit numbers with no exchanging
- To add four digits numbers with regrouping in one or two place value columns
- To subtract four digit numbers with exchanging in one or two place value columns
- MM To add and subtract multiples of ten mentally

#### Week 4

**Addition and subtraction**

- To add four digit numbers with regrouping in multiple place value columns
- To subtract with numbers that have zero in multiple place value colums. E.g. 5000 – 374
- To add decimals up to two decimal places
- To subtract decimals up to two decimal places
- MM To add and subtract using partioning

#### Week 5

**Multiplication**

- To multiply by 10, 100 and 1000
- To multiply three digit numbers by a one digit number using short multiplication
- To multiply two digit by two digit numbers
- To recognise factor pairs of a number
- MM To recognise what happens when multiplying and dividing by 1 and 0

#### Week 6

**Division**

- To use number bonds to identify factor and products (solving missing number sentences)
- To divide by 10, 100 and 1000
- To divide a two digit number using short division (including remainders, no exchanging)
- To divide three digit numbers using short division, including exchanging and remainders
- MM To use times table facts to multiply and divide mentally

#### Week 7

**Fractions and Decimals**

- To use factors and mulitples to recognise equivlant fractions
- To simplify fractions
- To compare fractions
- To calculate fractions of amounts
- MM To count forwards or backwards in steps of fractions

#### Week 8

**Measurement – Time**

- To tell and write the time on an analogue clock
- To convert time between analogue and digital clocks
- To convert between hours, minutes and seconds
- To convert between days, weeks, months and years
- MM To identify how many days are in each month of the year

#### Week 1

**Fractions and decimals**

- To add like fractions
- To subtract like fractions
- To recognise and write decimal equivalents of tenths
- To compare and order decimals up to 2DP

#### Week 2

**Geometry – Shape**

- To classify a range of regular and irregular polygons
- To classify different triangles
- To classify different quadrilaterals
- To identify lines of symmetry in 2-D shapes presented in different orientations
- MM To subtract mentally using counting

#### Week 3

**Statistics**

- To interpret data recorded in a table
- To interpret and present data in a bar chart
- To interpret and present data in a pictogram
- To intrepret and present data on a time graph
- MM To use time table facts to multiply and divide mentally

#### Week 4

**Measurement Length and Mass**

- MM – To multiply and divide by 10, 100 and 1000
- To estimate, compare and calculate measures using rulers or tapes
- To convert between different units of length
- To read analogue and digital scales to find the mass of an object
- To convert between different units of mass

#### Week 5

**Measurement – Volume and Capacity**

- To solve four operation problems that involve length and mass
- To estimate, compare and measure the capacity and volume using intervals
- To convert between litres and millilitres
- To solve four operation problems that involve volume and capacity
- MM To estimate a range of measures

#### Week 6

**Measurement – Perimeter and Area**

- To calculate the perimeter of rectangles and squares
- To calculate the area of a shapes by counting the number of squares
- To calculate the area of squares and rectangles
- To make comparisons betweent the perimter and area
- MM To identify different shapes and their properties

#### Week 7

**Four Operations Context of Problem Solving MWV**

- To add and subtract four digit numbers where there is re-grouping in multiple place value columns Look back at measure section
- To multiply three digits by a one digit number (short multiplication)
- To multiply two digit by two digit numbers (short multiplication)
- To divide three digit by one digit numbers including remainders and exchanging – Look back at measure section
- MM to identify pairs of multiples of 50 that total 1000

#### Week 1

**Number and Place Value**

- To compare and order numbers beyond 1000
- To round any number to the nearest 10, 100 and 1000
- To estimate and round numbers in the context on measurement
- To identify and count in negative numbers
- MM To count in multiples of 25 and 1000

#### Week 2

**Addition and Subtraction**

- To use the inverse to check addition and subtraction calculations
- To use estimation to check addition and subtraction with regrouping/exchanging
- To solve one step addition and subtraction word problems
- To solve multi-step addition and subtraction word problems
- MM To add or subtract three or more numbers mentally using re-ordering e.g. 5 + 8 + 15 + 32.= (32+8) + (5+15) Encourage use of number bonds to add/subtract ‘easier’ numbers first

#### Week 3

**Multiplication and Division**

- To multiply two digit by two digit numbers
- To multiply decimals
- To divide a three digit number by a one digit number
- To solve one and two step word multiplication and division problems
- MM To multiply together 3 numbers using times table facts

#### Week 4

**Fractions and Decimals**

- To round decimal numbers to the nearest whole number
- To recognise and write decimal equivalents of hundredths
- To recognise and write decimal equivalents of halves and quarters
- To solve four operation one and two step word problems with fractions and decimals
- MM To identify factor pairs of any number up to 100

#### Week 5

**Fractions and Decimals**

- To add and subtract like fractions
- To calculate fractions of amounts
- To compare and order fractions on a numberline with varied and missing intervals
- To compare and order decimals on a numberline going through 0, with varied and missing intervals
- MM To recognise the value of each digit from 10,000s to 1/100ths

#### Week 6

**Geometry – Position and Direction**

- To recognise positions on a 2-D grid
- To plot points on a coordinate grid
- To describe movements between positions as translations
- To draw shapes on a coordinate grid
- MM To recognise that a right angle is a 90 degree turn, two make a half turn, 3 make 3/4 turn and four make a complete turn

#### Week 1

**Geometry – Shape**

- To identify acute, obtuse and right angles
- To classify and compare angles
- To draw reflections in order to create a symmetric shape
- To compare and classify geometric shapes based on their properties (faces, vertices and edges)

#### Week 2

**Measurement – Money**

- To estimate and compare amounts of money
- To calculate change in pounds and pence
- To multiply and divide in the context of money
- To solve a range of money problems in the context of four operations
- MM To convert pounds into pence and vice versa

#### Week 3

**Measurement – Time**

- To solve problems converting hours, minutes and seconds
- To solve problems converting years months, weeks and days
- To calculate and compare time duration of events
- To calculate time durations that pass through the hour
- MM To use knowledge of No of days in months to solve a range of problems . e.g. Jan went swimming on Wednesday 14th Jan. He went swimming exactly 4 weeks later. What was the date? The pool closed on Friday 20th March. It opened on Friday 10th April. How long had it been closed?

#### Week 4

**Statistics**

- To solve problems related to data recorded in a table
- To solve problems with bar charts
- To solve problems related to pictograms
- To solve problems related to time graphs
- MM To calculate mentally one fact: (91-25=□) and then state the other three related facts

#### Week 5

**Measurement – Length/Mass/Capacity**

- To multiply and divide by 10, 100 and 1000. Particular when product is a decimal number
- To convert between units of measurement across length, mass and capacity
- To solve a range of one step word problems based on measurement
- To solve a range of two step word problems based on measurement
- MM To extend and explain number sequences (48, 41, 34, 27…) including those that continue beyond zero (5, 1, -3…)

#### Week 6

**Measurement – Perimeter and Area**

- To find the perimeter of rectangles and squares
- To find the area of a shapes by counting the number of squares
- To find the area of squares and rectangles
- To make comparisons between the perimeter and area

#### Week 1

**Number and Place Value**

- To distinguish between use Roman numerals
- To count forwards and backwards in negative numbers
- To explain the place value of decimals
- To solve a range of problems involving number and place value
- MM To calculate 10, 100 or 1000 more or less than a given number

#### Week 2

**Addition and Subtraction **

- To solve missing number addition and subtraction problems, including decimals
- To identify and explain misconceptions in addition and subtraction working out, including decimals
- To solve a range of addition and subtraction one and two step word problems
- MM To add and subtract using compensating – E.g. 38 +69 =38 + 70 – 1. 405 – 298 = 405 – 300 +2. – Extra materials needed
- MM – To add using near doubles- extra materials required – e.g. 38 + 35 = Double 35 + 3. 1.5 + 1.6 = Double 1.5 + 0.1 or Double 1.6 – 0.1

#### Week 3

**Multiplication and Division**

- To use the distributive law
- To use associative law to multiply three numbers
- To solve one and two step problems using scaling
- MM To use doubling and halving facts to solve multiplication and division mentally. e.g. 36 x 50 = 36 x 100 divided by 2. 1/4 of 64 = half of half of 64. 60 x 4 = 60 x 2 x 2

#### Week 4

**Fractions and Decimals**

- To use common factors and multiples to find equivalent fractions
- To add and subtract fractions
- To calculate fractions of amounts, as well as the total when you know the fraction. e.g. If 1/4 = 30 than the total must be 120
- To identify fraction and decimal equivalents across tenths and hundredths, including numbers above 1
- MM To count forwards and backwards in decimals

#### Week 5

**Fractions and Decimals**

- To identify decimal equivalents of common fractions e.g. 1/2, 1/3, 1/4, 1/5, 1/8, 1/10. If I know 1/3 is 0.333… then I know 2/3 is…
- To compare and order multiple fractions by finding their decimal equivalents.- e.g. 1/4, 4/10, 65/100 and 1/2
- To solve a range of one step word problems involving fractions and decimals. Encourage annotation or visual aids like bars
- To solve a range of two step word problems involving fractions and decimals. Encourage annotation or visual aids like bars
- MM To round an decimal up to two DP to the nearest whole number

#### Week 6

**Geometry – Position and Direction **

- To reflect shapes across a quadrant
- To plot points on a coordinate grid
- To describe movements between positions as translations
- To draw shapes on a coordinate grid
- MM To solve a range of problems involving quarter/half/ 3/4/full turns. e.g. If it s 3 o clock, how many degrees will the minute hand turn if the time is 3:45? Mr Webster stands on the spot and turns 720 degrees. How many turns has he completed? Vary the context but time makes sense

#### Week 1

**Four Operations Money**

- To estimate and compare money
- To calculate change in pounds and pence when buying with a range of amounts including notes £10/£20/£50
- To multiply and divide using money
- To solve a range of money problems in the context of four operations

#### Week 2

**Geometry – Shape**

- To identify, classify and compare angles
- To compare and classify a range of regular and irregular polygons
- To classify different triangles and quadrilaterals
- To compare and classify geometric shapes based on their properties
- MM To identify pairs of parallel and perpendicular lines with shapes and rays

#### Week 3

**Four Operations**

- To solve missing number problems related to multiplying by one and two digits- extra materials required
- To solve missing number problems related to short division
- To identify and explain misconceptions in multiplying by one and two digits
- To identify and explain misonceptions in bus stop division
- MM To use times table facts to multiply and divide mentally

#### Week 4

**Time**

- To tell and convert the time between analogue and digital clocks
- To convert between a range of units of time. Seconds, minutes, hours, days, months, weeks and years
- To calcuate time durations that pass through the hour
- To solve a range of time problems that require the four operations
- Review of all concepts

#### Week 5

**Statistics**

- To interpret and present data on a line graph – Pupils draw and produce their own line graph based on data given to them
- To interpret and present data in a bar chart. Pupils draw and produce their own bar chart based on data given to them
- To interpret and present data in a pictogram. Pupils produce their own pictogram based on a data given to them
- To interpret and record data into a Venn diagram
- To interpret and record data into a Carroll diagram

#### Week 6

**Four Operations**

- To solve a range of four operation problems on length, mass and volume
- To solve a range of four operation fraction and decimal problems
- To solve a range of number and place value problems
- To solve a range of perimeter and area problems
- To solve a range of shape problems

#### Autumn 1

- Number and place value
- Addition and subtraction
- Multiplication
- Division
- Fractions and decimals
- Time

#### Autumn 2

- Fractions and decimals
- Geometry – shape
- Statistics
- Length and mass
- Volume and capacity
- Perimeter and area
- Four operations in the context of problem solving

#### Spring 1

- Number and place value
- Addition and subtraction
- Multiplication
- Division
- Fractions and decimals
- Position and direction

#### Spring 2

- Geometry – shape
- Money
- Time
- Statistics
- Length, mass and capacity
- Perimeter and area

#### Summer 1

- Number and place value
- Addition and subtraction
- Multiplication and division
- Fractions and decimals
- Position and direction

#### Summer 2

- Money
- Shape
- Four operations
- Time
- Statistics
- Four operations

## Year 5

#### Week 1

**Presentation, times tables rockstars**

**Arithmetic introduction**

#### Week 2

**Number and Place Value**

- To recognise the place value of each digit in a six digit number
- To represent 6 digit numbers in words or digits
- To compare & order numbers beyond 100,000
- To round numbers to the nearest 10, 100, 1000 , 10,000 and 100,000
- MM To calculate 10,000 and 100,000 more/less than any six digit number

#### Week 3

**Addition and Subtraction **

Estimation should be happening throughout the week

- To round off numbers to estimate the answer for addition and subtraction. E.g. 1296 +2508 rounded is approx. equal to 1300 +2500 = 3800
- To add five digit numbers (regrouping in the 1000s, 100s, 10s and 1s)
- To subtract five digit+ numbers (exchanging in the 1000s, 100s, 10s and 1s)
- To solve one and two step word problems involving addition and subtraction
- MM To add and subtract multiple numbers efficiently using re-ordering. – Extra materials required – E.g. 25 + 36 + 75 = 75 + 25 + 36

#### Week 4

**Multiplication and Division**

- To multiply whole numbers & decimals numbers by 10, 100, 1000
- To divide whole numbers and decimal numbers by 10, 100 and 1000
- To multiply numbers up to four digits by a one digit number
- To divide numbers up to four digits by a one digit number, interpreting the remainders
- MM To add multiples of 100 and 1000 using knowledge of place value

#### Week 5

**France residential and Harvest Festival rehearsal**

#### Week 6

**Multiplication and Division**

- To identify common factors of two numbers
- To multiply numbers up to four digits by a two digit number
- To solve word problems involving multiplication and division
- To identify prime numbers and prime factors
- MM To subtract multiples of 100 and 1000 using knowledge of place value

#### Week 7

**Four Operations**

- To identify and explain common misconceptions in column addition and subtraction opportunity to practise both before correcting misconceptions)
- To solve a range of multi-step problems involving addition and subtraction
- To identify and explain common misconceptions in multiplication and division written methods
- To solve a range of word problems involving multiplication and division
- MM To add and subtract whole numbers mentally using partitioning

#### Week 8

**Measurement Time**

- To solve problems involving converting units of time (Seconds, minutes, hours and days)
- To solve problems involving converting units of time (days, hours, week and years) (Show trick for knowing which months are 31 days using knuckles)
- To calculate time duration problems that pass through the hour
- To solve a range of time measurement problems
- MM To convert between analogue and digital clocks Year 4 objective in PA maths

#### Week 1

**Fractions, Decimals and Percentages**

- To identify equivalent fractions (including tenths and hundredths)
- To compare and order fractions (whose denominators are multiples of the same number)
- To calculate fractions of numbers and quantities
- MM – To calculate sixths by halving thirds, eighths by halving quarters and tenths by halving fifths and twentieths by halving tenths

#### Week 2

**Fractions, Decimals and Percentages**

- To convert mixed numbers to improper fractions (and back)
- To read and write decimal numbers as fractions
- To convert fractions to percentages. Getting fractions into decimal fractions (e.g. over 10 or 100)
- To identify percentage and decimal equivalents
- MM – To add and subtract whole numbers when bridging through multiples of 10 e.g. 575 + 28 = 575 + 25 + 3

#### Week 3

**Geometry – Properties of Shape**

- To sort regular and irregular polygons
- To estimate and compare angles
- To compare angles
- To identify missing angles
- MM – To identify angles at a point and one whole turn

#### Week 4

**Measurement – Length and Mass**

- To convert between different units of metric measure
- To use all four operations to solve problems involving length
- To solve four operation problems involving mass
- To measure and draw lines and shapes to the nearest mm
- MM – To examine the quantity of objects (e.g. coins a jar, grapes in a bowl etc.) and make a reasonable estimate

#### Week 5

**Measurement – Volume and Capacity**

- To solve problems involving converting units of measurement
- To estimate and measure capacity
- To estimate and measure volume
- To use approximate equivalences between metric and imperial units
- MM – To order units of measurement in ascending and descending order. E.g. 1100g 1kg, 0.95kg, 900g

#### Week 6

**Measurement – Area and Perimeter**

- To measure and calculate the perimeter of composite rectilinear shapes
- To calculate and compare the area of rectangles (cm² and m²)
- To estimate the area of irregular shape
- To solve missing measure questions when presented algebraically
- MM – To calculate the difference by counting up through the next multiple of 10, 100 or 1000

#### Week 7

**Statistics**

- To solve comparison problems using information in a line graph
- To solve sum problems using information in a line graph
- To solve difference problems using information in a line graph
- To complete, read and interpret information in tables
- MM – To identify what to add to a decimal with a units and tenths to make the next highest whole number e.g. 8.25 + ? = 9

#### Week 1

**Number and Place Value**

- To identify the term-to-term rule
- To interpret negative numbers
- To count in steps of powers of 10 up to 1 000 000
- To read Roman numerals
- MM To add and subtract using compensating e.g. 138 + 69 = 138 +70 – 1

#### Week 2

**Addition and Subtraction**

- To add and subtract decimal numbers up to two decimal places
- To identify the missing value in addition and subtraction problems
- To solve a range of addition and subtraction problems (put some problems in the context of measurement to recap last term)
- To add and subtract negative numbers
- MM To add using near doubles e.g. 160 + 170 = 160 doubled + 10 or 150 doubled + 30

#### Week 3

**Multiplication and Division**

- To multiply four digits by one and two digit numbers
- To divide four digit numbers by a one digit number including interpreting remainders
- To multiply and divide whole numbers by 10, 100 and 1000
- To use the distributive property strategy to divide ‘friendly’ numbers
- MM To derive quickly related facts e.g. 150-80 = 70, 1500-800 = 700, 1.5-0.8 = 0.7

#### Week 4

**Fractions, Decimals and Percentages**

- To add and subtract fractions with denominators that are multiples of the same number
- To multiply fractions and mixed numbers by a whole number
- To identify equivalent fractions, decimals and percentages
- To solve problems with percentages
- MM To identify a number that sits halfway between two numbers e.g. (2743 + 2831)/2

#### Week 5

**Fractions, Decimals and Percentages**

- To add and subtract decimals numbers less than one e.g. 0.08 + 0.26
- To multiply decimals less than one by 10, 100 and 1000 (e.g. 0.45 x 100 = 45)
- To round decimals
- To solve problems with decimals

- MM To recognise that knowing a fact such as 136+319=455 makes it possible to find 455-318 and 455-137

#### Week 6

**Measurement – ****Money and Time**

- To use multiplication and division to inter scale and calculate changing rates
- To add, subtract, multiply and divide in the context of converting money (show conversion in preparation for problem solving next day) e.g. £15.54 = 1554p. 1554 x 3 =6216, which means 15.54 x 4 = £62.16
- To solve problems involving money
- To read and solve problems using timetables
- MM To mentally add and subtract tenths, and one-digit whole numbers and tenths e.g. 1.4 + 0.7 = 1.4 + 0.6 + 0.1

#### Week 1

**Four Operations Conversion**

- To use number bonds to for factor and products to identify missing factors (using fractions and decimals) See Y5 PA maths for example of triangles
- To solve conversion word problems involving addition and subtraction
- To recognise and use square numbers
- To identify the lowest common multiples between two numbers

#### Week 2

**Geometry – ****Position and direction**

- To describe and plot points across one and two quadrants
- To describe and plot points across all four quadrants
- To translate the position of a shape on one quadrant
- To reflect the position of a shape across a mirror line
- MM To estimate, compare and identify angles e.g. obtuse, acute, reflect, right angle

#### Week 3

**Geometry – ****Properties of shape**

- To identify and describe diagonal and parallel lines
- To identify 3-D shapes from 2-D representations
- To solve problems using nets
- To identify missing angles and lengths
- MM To use times table facts to solve multiplication problems mentally

#### Week 4

__Fractions, Decimals and Percentages__

- To compare and order decimals and decimal numbers up to 3D
- To compare and order fractions
- To convert mixed numbers to improper fractions (and back)
- To find fractions of amounts
- MM To use knowledge of factors to solve division mentally

#### Week 5

**Addition and Subtraction**

- To identify misconceptions in column method decimal addition and subtraction
- To add and subtract fractions, including improper fractions and mixed numbers
- To identify when is most effective to use mental or written strategies for addition and subtraction
- To solve a range of one and two step problems
- MM To calculate the rise and fall in temperature using both positive and negative integers

#### Week 6

**Multiplication and Division**

- To identify all the factor pairs of a number, as well as common factor pairs
- To identify composite (non-prime) numbers See Y5 PA maths
- To establish whether a number up to 100 is a prime number
- To identify when is most effective to use mental or written strategies for multiplication and division

#### Week 1

**Number and Place Value**

- To identify the value of each digit in a decimal number up to 3DP
- To calculate the term-to-term rule in linear sequences that involve fractions or decimals
- To round whole and decimal numbers
- To solve problems involving number
- MM To recognise that 1 square metre = 10 000 cm² and that 1 square cm = 100mm²

#### Week 2

**Measurement – ****Area, Perimeter and Volume**

- To compare the perimeter and area of rectangles
- To solve the perimeter and area of composite rectilinear shapes
- To solve volume problems based on 3-D shapes
- To review my knowledge of area, perimeter and volume
- MM To convert fluently between all units of time. Seconds, minutes, hours, days, weeks, months

#### Week 3

**Statistics**

- To solve a variety of problems using information in a line graph
- To complete, read and interpret information in tables
- To solve problems involving time tables
- MM – To multiply mentally using partitioning

#### Week 4

**Measurement – ****Length, Mass, Capacity and Money**

- To convert between different units of metric measure
- To use approximate equivalences between metric and imperial units
- To solve a range of problems on mass, volume and length
- To solve a range of problems involving time and money
- MM To use knowledge of times tables to divide mentally

#### Week 5

**Fractions, Decimals and Percentages**

- To interpret non-integer answers to division by expressing results in different ways
- To convert decimal fractions into decimals
- To count in decimals
- To multiply fractions and mixed numbers by a whole number
- MM – To identify a decimal fraction between 2 numbers (between 41 and 42)

#### Week 6

**Geometry – ****Position and Direction**

- To reflect the position of a shape in all four quadrants
- To translate the position of a shape in all four quadrants
- To draw and plot data across four quadrants
- To plot shapes across four quadrants Consider questions where coordinates are missing and pupils use dimensions of shape to complete or finding missing coordinates when they only know one or two coordinates of a shape
- MM To double using known facts e.g. Double 79 = Double 70 + double 9

#### Week 1

**Fractions, Decimals and Percentages**

- To solve problems with fractions
- To review my knowledge of FDP

*Focus on what has been hard to teach, hard to learn in FDP across the year *

#### Week 2

**Number and Place Value**

- To solve problems involving roman numerals
- To solve problems involving common factors, prime factors and LCM
- To review my knowledge of number and place value
- To review my knowledge of number and place value
- MM To multiply by 5 and 50. Equivalent to multiply by 10 or 100 and then dividing by two

#### Week 3

**Four Operations**

- To recognise cubed numbers
- To apply distributive law
- To solve division problems with decimals (use place value counters if needed)
- To solve a range of four operation word problems. Still check for fluency of formal written methods
- MM To multiply numbers with a 1 or 9 in the units column effectively e.g. 13 x 19 = (13 x 20) – 13. Or 22 x 21 = (22 x 20 ) + 22

#### Week 4

**Geometry – Combined**

- To compare angles
- To measure angles using a protractor
- To draw angles using a protractor
- To identify missing angles across a range of problems

#### Week 5

**Geometry – Continued**

- To review my knowledge of angles
- To compare, sort and describe regular and irregular polygons
- To identify a range of 3-D shapes
- To review my knowledge of reflection and translation
- MM To identify the difference between concave, convex and complex polygons. As well as shapes that are not polygons

*Focus on what has been hard to teach, hard to learn in geometry across the year *

#### Week 6

**Four Operations**

- To identify when is more appropriate to use mental addition and subtraction or a formal written method
- To identify and correct misconceptions when solving decimal addition and subtraction
- To identify when it is appropriate to use written or mental multiplication and division to solve a problem
- To identify and correct misconceptions when solving multiplication and division
- MM To count around a clock face in turns and degrees

#### Autumn 1

- Number and place value
- Addition and subtraction
- Multiplication and division
- Four operations
- Time

#### Autumn 2

- Fractions, decimals and percentages
- Properties of shapes
- Length and mass
- Volume and capacity
- Area and perimeter
- Statistics

#### Spring 1

- Number and place value
- Addition and subtraction
- Multiplication and division
- Fractions, decimals and percentages
- Money and time

#### Spring 2

- Four operations
- Position and direction
- Properties of shapes
- Fractions, decimals and percentages
- Addition and subtraction
- Multiplication and division

#### Summer 1

- Number and place value
- Area, perimeter and volume
- Statistics
- Length, mass, capacity and money
- Fractions, decimals and percentages
- Position and direction

#### Summer 2

- Fractions, decimals and percentages
- Number and place value
- Four operations
- Geometry combined
- Four operations

## Year 6

#### Week 1

**Rules, Expectations, Presentation, Times Tables Rock Stars**

**Arithmetic introduction**

#### Week 2

**Number and Place Value**

- To recognise the place value of numbers up to 7 digits
- To compare and order numbers up to 10,000,000
- To round any whole number
- To interpret negative numbers
- MM To calculate a 1000, 10,000 and 100,000 more or less than any 7 digit number

#### Week 3

**Addition and Subtraction**

- To use estimation to check answers to calculations
- To solve any addition and subtraction with numbers up to 2 decimal places
- To demonstrate the order of operations using brackets
- To systematically solve multi-step problems
- MM To order integers from smallest to largest crossing zero

#### Week 4

**Assessment Week**

** Multiplication and Division**

- Arithmetic Paper
- Reasoning Paper 1
- Reasoning Paper 2
- To multiply up to 4 digits by a two digit whole number
- To divide numbers up to 4 digits by 1 digit then 2 digit whole number using short division

#### Week 5

**Multiplication and Division**

- To interpret remainders as whole number remainders, fractions or rounding
- To multiply and divide with decimals
- To solve word problems involving multiplication and division
- MM To identify common factors and prime numbers
- MM To use re-ordering to effectively solve and addition and subtraction problems

#### Week 6

**Fractions, Decimals and Percentages**

- To compare and order fractions
- To add and subtract fractions with different denominators and mixed numbers
- To multiply and divide fractions with different denominators and mixed numbersTo calculate fractions of amounts
- MM To add and subtract four digit+ multiples of 10, 100 and 1000 using partitioning

#### Week 7

**Fractions, Decimals and Percentages**

- To use common factors to simply fractions
- To find percentage of amounts
- To calculate decimal and fraction equivalents
- To multiply and divide by powers of 10
- MM To add and subtract decimal fractions up to 2DP using partitioning. E.g. 2.77 – 0.45 = 2.77 – 0.4 – 0.05

#### Week 8

**Measurement – Area and Perimeter**

- To prove that shapes with the same area can have different perimeters
- To calculate the area of triangles
- To calculate the area of parallelograms
- To calculate and estimate the volume of cubes and cuboids
- MM To add and subtract using compensation

#### Week 1

**Number and Place Value**

- To identify decimals and other intervals on a number line
- To add and subtract negative numbers
- To round any decimal number up to 3DP
- MM To identify near doubles: 421 + 387 = 808

#### Week 2

**Geometry – ****Shape and angles**

- To compare and classify geometric shapes (2D)
- To compare and classify geometric shapes (3D)
- To identify missing angles in triangles and quadrilaterals
- To visualise a 3-D shape from its net
- MM To identify parallel, perpendicular and diagonal lines

#### Week 3

**Measurement – Length, Mass and Volume**

- To calculate, estimate and compare volume of cubes, cuboids and compound shapes
- To convert measures using decimal notation to 3DP
- To solve problems involving conversion and measure
- To convert between miles and KM and other scaled rates
- MM To calculate the difference by counting up through the next multiple of 10, 100 or 1000 e.g. 7000 – 3675 is 5 + 20 +300 = 3325

#### Week 4

**Measurement – Money, Time and Temperature**

- To solve problems involving converting units of time
- To solve time duration problems using four operations
- To solve problems involving money using the four
- To add and subtract positive negative integers in the context of temperature
- MM To identify what to add to a decimal with units, 10ths and 100ths to make the next highest whole number or 10th

#### Week 5

**Statistics**

- To interpret and solve problems using line graphs
- To interpret and solve problems using pie charts
- To connect angles and percentages to pie charts
- To calculate and interpret the mean as the average
- MM To calculate alternative averages mentally

#### Week 6

**Fractions, Decimals and Percentages**

- To multiply and divide with decimals
- To identify percentage equivalents to decimal and fractions
- To solve a range of decimal, percentage and fraction word problems
- To solve fraction and percentage questions related to pie charts
- MM To multiply and divide decimal numbers by 10, 100 and 1000

#### Week 7

**Geometry – ****Position and Direction**

- To describe positions on all four quadrants
- To draw and plot shapes across all four quadrants
- To translate shapes across the coordinate plane
- To reflect shapes across the coordinate plane
- MM To multiply and divide whole numbers 10, 100 and 1000

#### Week 1

**Four Operations**

- To demonstrate the order of operations using brackets
- To use communitive, associate and distributive laws of multiplication
- To use the distributive property strategy
- To solve a range of four operation word problems
- MM To use times table facts to multiply mentally

#### Week 2

**Assessment Week and ****Four Operations**

- Arithmetic
- Reasoning 1
- Reasoning 2
- To identify common factors and multiples
- MM To use times table facts to divide mentally

#### Week 3

**Algebra**

- To use simple formula to generate, express and describe equivalent expressions
- To use simple formula to generate, express and describe equivalent expressions
- To use simple formula to generate, express and describe mathematical formula
- To use simple formula to generate, express and linear number sequence
- MM To solve mentally one fact 4.97-1.58 and then state three other related facts

#### Week 4

**Ratio**

- To use scale factors to solve problems involving shape
- To use knowledge of fractions and multiples to solve problems involved in unequal quantities
- To solve problems involving missing ratio
- To solve ratio problems that involve unequal sharing
- MM To use knowledge of number facts to prove exact multiples e.g. multiples of 100, 25, 10, 5. and 2

#### Week 5

**Four Operations**

- To solve a range of problems that involve FDP
- To solve a range of algebraic problems systematically
- To solve a range of multi-step word problem four operations
- To solve a range of ratio problems
- MM To use knowledge of number facts to prove exact multiples e.g. multiples of 3, 4, 6, 8 and 9

#### Week 6

**Fractions, Decimals and Percentages**

- To solve fraction of amounts problems when the total is unknown
- To compare and order fractions, decimals and percentages
- To compare percentages
- To solve a range of FDP word problems
- MM To use related facts to double and halve e.g. Double 277 = 400 +140 +14

#### Week 1

**Number and Place Value**

- To round any number any whole number or decimal number
- To interpret the remainder as a decimal, fraction or round
- To identify the term to term rule
- MM To identify multiples of numbers using doubling and halving e.g.14 x 5 = 14 x 10 divided by 2

#### Week 2

**Geometry – ****Shape and Angles**

- To demonstrate how to find the diameter and radius of a circle
- To identify and find missing angles
- To draw 2-D shapes given dimensions and angles
- To visualise patterns drawn on a 3-D shape and where it will occur
- MM To create the biggest/ smallest integer possible with a range of digits (i.e. 8 3 0 7 6 0 2)

#### Week 3

**Algebra**

- To identify missing numbers using algebra
- To identify two missing numbers using algebra
- To use simple formula to generate, express and describe mathematical formula
- To identify all the possibilities of combinations of two variables
- MM To calculate the squares of all numbers from 1×1 to 12×12 and look at other powers

#### Week 4

**Statistics**

- To solve problems using line graphs
- To solve problems using pie charts
- To calculate and interpret the mean as the average
- To solve a range of statistical problems
- MM To identify fractions that are bigger and smaller than others e.g. 9/14 is in between 4/7 and 5/7

#### Week 5

**Ratio**

- To solve ratio problems involving scaling
- To compare percentages
- To solve missing ratio and unequal sharing problems
- To solve a range of ratio problems
- MM To identify fractions that are bigger and smaller than decimal fractions e.g. 505/100 is in between 0.50 and 0.51

#### Week 6

**Four Operations**

- To solve a range of measurement conversion word problems
- To solve a range of shape and angle problems
- To solve a range of position and direction problems
- To identify common factors, multiples and prime numbers

#### Week 1

**Outcome**

- To solve four operation word problems
- To demonstrate the order of operations using brackets
- To solve four operation fraction problems
- To calculate fraction and percentage of amounts
- MM To explain the percentage equivalent to common fractions and vice versa

#### Week 2

**Outcome**

- To solve a range of area, perimeter and volume problems
- To solve a range of position and direction problems
- To solve a range of problems involving coordinates
- To solve a range of problems on 2-D shapes
- MM To explain the equivalent of one thousandth/100th/10th/quarter and half of 1km, 1kg, 1 litre in m, g and ml respectively

#### Week 3

**Outcome**

- To solve fraction, decimal and percentage word problems
- To solve a range of 3D shape problems
- To solve a range of ratio problems
- To round any whole or decimal (3DP) number

#### Week 4

**Outcome**

- To solve a range of algebraic problems
- To solve a range of missing angle problems
- To solve a range of conversion word problems
- To solve a range of statistics problems
- To explain 1/10 is divide by 10 and 10%, finding 25%, 50% etc.

#### Week 5

**SATs week**

#### Week 6

**Outcome**

- To solve a mathematical investigation
- To discover different types of numbers, including perfect numbers
- To solve number puzzles involving positive and negative numbers
- To rapidly recall of all multiplication tables up to 12 x 12 – Maths challenge
- To solve a mathematical investigation

#### Week 1

**Statistics**

- To read and interpret scales on a map
- To draw graphs with two relating variables
- To create a school population pyramid
- To solve a mathematical investigation

#### Week 2

**Geometry**

- To draw triangles accurately
- To draw a range of 2-D shapes
- To draw a range of circles
- To construct arcs and sectors
- To solve a mathematical investigation

#### Week 3

**Rhos y Gwaliau**

#### Week 4

**Algebra**

- To construct a graph from algebraic expressions
- To solve and simplify algebraic formula
- To interpret the square root
- To use unconventional methods to calculate the height of a building

#### Week 5

**Fractions, Decimals and Percentages**

- To construct a pie chart with multiple sectors
- To interpret binary numbers
- To solve problems that involve percentage and fractional increase and decreases
- To solve a mathematical investigation
- To solve a mathematical investigation

#### Week 6

**Number and Place Value**

- To solve problems involving both positive and negative numbers
- To solve a range of fraction, decimal and percentage problems
- To solve a range of problems involving number
- To solve a mathematical investigation
- To solve a mathematical investigation

#### Autumn 1

- Number and place value
- Addition and subtraction
- Multiplication and division
- Fractions, decimals and percentages
- Area and perimeter

#### Autumn 2

- Number and place value
- Shape and angles
- Length, Mass and Volume
- Money, time and temperature
- Statistics
- Fractions, decimals and percentages
- Position and direction

#### Spring 1

- Four operations
- Algebra
- Ratio
- Four operations
- Fractions, decimals and percentages

#### Spring 2

- Number and place value
- Shape and angles
- Algebra
- Statistics
- Ratio
- Four operations

#### Summer 1

- Recap previously taught concepts, considering hard to teach, hard to learn areas
- Fractions, decimals and percentages
- 2D and 3D shapes
- Problem solving
- Statistics
- Algebra, angles, length, mass and capacity

#### Summer 2

- Statistics
- Geometry
- Algebra
- Fractions, decimals and percentages
- Number and place value