At St Michaels we follow the Primary Assertive Mentoring (PAM) approach, which involves individual target setting, tracking of progress and most importantly mentoring of children. Mentoring helps children to develop a growth mindset, so that children posses positive learning attitudes to help them achieve their next steps. The PAM approach encourages students to share their ideas and experiences, reflect upon similarity and differences in approaches and to respect that not everyone learns in the same way. Children are encouraged to work both independently and with others, using resources to support and develop their mathematical thinking.

Within year groups, children are grouped dependent upon their stage in development in mathematics. Stages run from zero to six and within each stage children will either be: emerging, developing, securing or mastering their understanding. Once children have mastered a stage, they are then ready to move on in the next stage of their learning. The stage children are working upon depends entirely on the needs of the learner.

Children working broadly inline with national expectations will be at:

- Stage 2/3
- Stage 3
- Stage 4
- Stage 4/5

__Stage 0__

*Number*

- Recognise some numerals of personal significance and numerals 1 to 5.
- Count up to three or four objects by saying one number name for each item.
- Count objects to 10, and beginning to count beyond 10.
- Count out up to six objects from a larger group.
- Select the correct numeral to represent 1 to 5, then 1 to 10 objects.
- Count an irregular arrangement of up to ten objects.
- Estimates objects check by counting them.
- Use the language of ‘more’ and ‘fewer’ to compare two sets of objects.
- Find the total numbers of items in two groups by counting all of them.
- Say the number that is one more than a given number.
- Find one more or one less from a group of up to five objects, then ten objects.

*Shape, Space and Measure*

- Use simple positional language such as ‘behind’ or ‘next to’.
- Beginning to talk about the shapes of everyday objects, e.g. ‘round’ and ‘tall’.
- Beginning to use mathematical names for ‘solid’ 3D shapes and ‘flat’ 2D shapes, and mathematical terms to describe shapes or to select a particular named shape.
- Order two or three items by length or height.
- Order two items by weight or capacity.
- Uses everyday language related to time.
- Beginning to use everyday language related to money.
- Order and sequence familiar events.

__Stage 1__

*Place Value *

- Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.
- Count, read and write numbers to 100 in numerals.
- Count in multiples of twos, fives and tens.
- Identify one more or less of a given number
- Identify and represent numbers using objects and pictorial representations including the number line, and use

the language of: equal to, more than, less than (fewer), most, least.

- Read and write numbers from 1 to 20 in numerals and words.

*Adding and Subtracting*

- Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs.
- Represent and use number bonds and related subtraction facts within 20.
- Add and subtract one-digit and two-digit numbers to 20, including zero.
- Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.

*Multiplication and Division*

- Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

*Fractions*

- Recognise, find and name a half as one of two equal parts of an object, shape or quantity.
- Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

*Measures *

- Compare, describe & solve practical problems for: lengths/heights; mass/weight; capacity/volume; time.
- Measure and begin to record the following: lengths/heights; mass/weight; capacity/volume; time (hours, minutes, and seconds).
- Recognise and know the value of different denominations of coins and notes.
- Sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening.
- Recognise and use language relating to dates, including days of the week, weeks, months and years.
- Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

*Geometry*

- Recognise and name common 2-D shapes (e.g. rectangles, circles and triangles) and 3-D shapes (e.g. cuboids (including cubes), pyramids and spheres).
- Describe position, directions and movements, including half, quarter and three-quarter turns.

__Stage 2__

*Place Value *

- Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward.
- Recognise the place value of each digit in a two-digit number (tens, ones).
- Identify, represent and estimate numbers using different representations, inc. the number line.
- Compare and order numbers from 0 up to 100; use <, > and = signs.
- Read and write numbers to at least 100 in numerals and in words.

*Adding and Subtracting*

- Solve addition and subtraction problems; apply knowledge of mental and written methods.
- Recall and use add and subtract facts to 20 fluently, and derive and use related facts up to 100.
- Add and subtract numbers including: a 2-digit no and 1s or 10s; two 2-digit numbers; adding three 1-digit numbers.
- Show that adding of two numbers can be done in any order and that subtraction cannot.
- Understand the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

*Multiplication and Division*

- Recall/ and use multiplication and division facts for the 2, 5 and 10 x tables, including recognising odd and even numbers.
- Calculate maths statements for multiplication and division; write them using the (×), (÷), (=) signs.
- Show that multiplication of two numbers can be done in any order and that division cannot.
- Solve multiplication and division problems using materials, repeated addition and mental methods.

*Fractions*

- Record, find, name and write fractions ??, ??, 2/4, ???
_{ }of a length, shape, set of objects or quantity. - Write simple fractions e.g. ?? of 6 = 3 and recognise the equivalence of 2/4 and ??.

*Measures *

- Choose/use stand units to est/measure m/cm, kg/g, °C, l/ml, to nearest unit, using rulers, scales etc
- Compare and order lengths, mass, volume/capacity and record the results using >, < and = .
- Record and use symbols for pounds (£) and pence (p); combine amounts to make a particular value.
- Solve simple problems (practical context) involving addition and subtraction of money, giving change.
- Compare and sequence intervals of time
- Tell and write the time to 5 min, inc ?? past/to and draw hands on a clock face to show these times.

*Geometry*

- Identify and describe the properties of 2D shapes, inc the no of sides and symmetry in a vertical line.
- Identify and describe the properties of 3D shapes, including the number of edges, vertices and faces.
- Identify 2D shapes on the surface of 3D shapes, e.g. a circle on a cylinder, a triangle on a pyramid.
- Compare and sort common 2D and 3D shapes and everyday objects.
- Order and arrange combinations of mathematical objects in patterns.
- Describe position, direction, and movement including rotation as a turn & in terms of right angles for ??, ??, & ??? turn.

*Statistics*

- Interpret and construct simple pictograms, tally charts, block diagrams and simple tables.
- Ask and answer questions by counting objects, sorting categories, totalling/paring categorical data.

__Stage 3__

*Place Value *

- Count from 0 in multiples of 4, 8, 50 and 100. Find 10 or 100 more or less than a given number.
- Recognise the place value of each digit in a three-digit number (hundreds, tens, ones).
- Compare and order numbers up to 1000.
- Read and write numbers up to 1000 in numerals and in words.
- Identify, represent and estimate numbers using different representations.
- Solve number problems and practical problems involving these ideas.

*Adding and Subtracting*

- Add and subtract numbers mentally, including: a 3-digit no and 1s, 10s, 100s.
- Add and subtract numbers with up to 3 digits, using formal written methods including columnar.
- Estimate the answer to a calculation and use inverse operations to check answers.
- Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

*Multiplication and Division*

- Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
- Calculate math statements (x and ÷) using known tables, inc 2-digit x 1-digit, (mental & written methods)
- Solve missing no problems involving x and ÷, including integer scaling & correspondence problems

*Fractions*

- Count up/down in 10ths; record 10ths arise from ÷ an object into 10 equal parts & ÷ 1-digit numbers by 10
- Recognise/find/write fractions of a discrete set of objects: unit/non-unit fractions (small denominators)
- Recognise/use fractions as numbers: unit fractions and non-unit fractions with small denominators
- Recognise and show, using diagrams, equivalent fractions with small denominators
- Add and subtract fractions with the same denominator within one whole (e.g. ??? + ?? = ???)
- Compare and order unit fractions, and fractions with the same denominators

*Measures *

- Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
- Measure the perimeter of simple 2-D shapes
- Add and subtract amounts of money to give change, using both £ and p in practical contexts
- Tell/write the time from an analogue clock, inc Roman numerals from I to XII, and 12hr/24hr clocks
- Estimate and read time to nearest min; record/compare in sec/min/hr. Use vocabulary am/pm, morning, noon
- Know the no of seconds in a minute and the number of days in each month, year and leap year

*Geometry*

- Draw 2D, make 3D shapes using modelling materials; record 3D shapes in different orientations
- Recognise that angles are a property of shape or a description of a turn
- Record 2 right angles = ??-turn, 3 = ??? turn, 4 = full turn. Identify angles greater or less than a right angle
- Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.

*Statistics*

- Interpret and present data using bar charts, pictograms and tables
- Solve 1 & 2-step questions (‘How many more/fewer?’) using information in bar charts, pictograms, tables.

__Stage 4__

*Place Value *

- Count in multiples of 6, 7, 9, 25 and 1000
- Find 1000 more or less than a given number. Round any number to the nearest 10, 100 or 1000
- Count backwards through zero to include negative numbers
- Recognise the place value of each digit in a 4-digit number (thousands, hundreds, tens, and ones)
- Read Roman numerals to 100 (I to C); know the numeral system changed to include zero and PV

*Adding and Subtracting*

- Add/sub up to 4 digits numbers using columnar addition and subtraction where appropriate
- Estimate and use inverse operations to check answers to a calculation
*Solve add/subtraction 2 step problems in contexts, deciding which operations and methods to use and why*

*Multiplication and Division*

- Recall multiplication and division facts for multiplication tables up to 12 × 12
- Recognise and use factor pairs and commutativity in mental calculations
- Multiply 2 and 3-digit numbers by a 1-digit number using formal written layout
- Problems using the distributive law to multiplication 2 digit by 1 digit, integer scaling and correspondence problems

*Fractions*

- Recognise and show, using diagrams, families of common equivalent fractions
- Count up/down in 100ths; recognise that 100ths arise when dividing by 100 and 10ths by 10
- Add and subtract fractions with the same denominator
- Write decimal equivalents of any number of 10ths or 100ths; and the decimal equivalents to ??, ?? and 3/4
- Divide a 1 or 2 digit no by 10 and 100, identify the value of the digits as units, 10ths and 100ths
- Round 1 decimal place no to nearest whole no. Measure/money problems with fractions and decimals

*Measures *

- Convert units of measure (e.g. km/m). Solve problems converting hrs/min; min/sec; years/months etc
- Calculate perimeter of a rectilinear figure in cm/m. Find area of rectilinear shapes by counting squares
- Estimate, compare and calculate different measures, including money in pounds and pence
- Read, write and convert time between analogue and digital 12 and 24-hour clocks

Geometry

- Classify geometric shapes, including quadrilaterals and triangles
**,**based on their properties and sizes - Identify acute and obtuse angles and compare and order angles up to two right angles by size
- Identify lines of symmetry in 2D shapes in different orientations
- Complete a simple symmetric figure with respect to a specific line of symmetry
- Describe coordinates in the 1
^{st}quadrant and translations of a given unit to the left/right, up/down - Plot specified points and draw sides to complete a given polygon

Statistics

- Interpret/present discrete/continuous data using graphical methods, inc bar charts/time graphs
- Solve comparison, sum and difference problems using info in bar charts, pictograms, tables etc

** **

__Stage 5__

*Place Value *

- PV to at least 1 000 000 and determine the value of each digit
- Count on or back in powers of 10. Round to the nearest 10, 100, 1000, 10 000 and 100 000
- Negative numbers in context, count on or back with positive and negative numbers through zero
- Read Roman numerals to 1000 (M) and recognise years written in Roman numerals

*Adding and Subtracting*

- Add/subtracting numbers with more than 4 digits, inc formal written methods (columnar add/sub)
- Add and subtract numbers mentally with increasingly large numbers
- Add/subtract multi-step problems in contexts, deciding which operations and methods to use and why

*Multiplication and Division*

- Identify multiples and factors, inc all factor pairs of a number, and common factors of two numbers
- Use the vocabulary of prime numbers, prime factors and composite numbers. Recall prime numbers up to 19
- Multiply and divide 4 digits by a 1 digit number using the formal written methods
- Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
- Recognise and use square numbers and cube numbers, and the notation for squared and cubed

*Fractions*

- Order, add, subtract fractions whose denominators are the same or multiples of the same number
- Name/write equivalent fractions of a given fractions, represented visually, including 10ths and 100ths
- Convert mixed numbers and improper fractions and write maths statements > 1 as a mixed number
- Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
- Round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
- Read, write, compare and solve problems involving number up to three decimal places
- Solve problems which require knowing % and decimal equivalents of ??, ??, ??, ?, ?

*Measures *

- Convert diff units of metric measure (e.g. km/m; cm/mm; g/kg; l/ml)
- Calculate perimeter of rectangles; area of squares/rectangles and estimate area of irregular shapes
- Estimate volume (e.g. using 1 cm blocks to build cubes/cuboids) and capacity (e.g. using water)
- Convert units of time. Use all 4 operations to solve problems involving measure using decimal notation

*Geometry*

- Identify 3D shapes, including cubes and other cuboids, from 2D representations
- Estimate/compare acute, obtuse and reflex angles. Draw given angles, measure them in degrees
- Identify: angles at a point and one whole turn; on a straight line and ½ a turn, multiples of 90?
- Use the properties of rectangles to deduce related facts and find missing lengths and angles
- Identify, describe and represent the position of a shape following a reflection or translation

*Statistics*

- Solve comparison, sum and difference problems using information presented in a line graph
- Complete, read and interpret information in tables, including timetables

__Stage 6__

*Place Value *

- PV up to 10 000 000. Round any whole number to a required degree of accuracy
- Negative numbers; calculate across zero. Solve problems involving the above

*Adding, Subtracting, Multiplication and Division*

- Multiply/divide 4 by 2-digits (written methods); remainders as whole numbers, fractions, or by rounding
- Identify common factors, common multiples and prime numbers
- Use their knowledge of the order of operations to carry out calculations involving the four operations
- Add/sub multi-step problems in contexts, deciding which operations and methods to use and why

*Fractions*

- Use factors to simplify fractions; multiples to express fractions in the same denomination
- Add/subtract fractions with different denominators and mixed numbers, using equivalent fractions
- Multiply simple proper fractions and simplify the answer. Divide proper fractions by whole numbers
- PV of digits to 3 decimal places; multiply/divide numbers by 10, 100, 1000 with answers up to 3 decimal places
- Multiply 1 digit numbers with 2 decimal places by whole numbers. Written divide where answer has 2 decimal places
- Use equivalences between simple fractions, decimals and percentages

*Ratio and Proportion*

- Problems involving the calculation of % such as 15% of 360 and the use of percentages for comparison
- Problems involving shapes with known scale factor; unequal sharing/grouping using fractions/multiplication

Algebra

- Express missing number problems algebraically. Use simple formulae expressed in words
- Generate and describe linear number sequences
- Find pairs of numbers that satisfy no sentences involving 2 unknowns. Enumerate all comb of 2 variables

*Measures *

- Calculate and convert units of measure (up to 3 decimal places). Convert between m and km
- Convert between standard units of measure, using decimal notation to up to 3 decimal places
- Recognise that shapes with the same areas can have different perimeters and vice versa
- Calculate area of parallelograms and triangles. Use formulae for area and volume of shapes
- Calculate, estimate, compare volume of cubes and cuboids using standard units, including cm? and m?

*Geometry*

- Draw 2D shapes to given dimensions/angles. Describe/build 3D shapes, including making nets
- Classify shapes by their properties; find angles in triangles, quadrilaterals, and regular polygons
- Name parts of circles (e.g. radius, diameter, circumference); know diameter is twice the radius
- Recognise angles at a point, on a straight line, or vertically opposite, and find missing angles

*Position and Direction *

- Describe positions on the full coordinate grid (all four quadrants)
- Draw and translate simple shapes on the coordinate plane, and reflect them in the axes

*Statistics*

- Interpret and construct pie charts and line graphs and use these to solve problems
- Calculate and interpret the mean as an average

__Homework__

All mathematics homework is on a programme called Maths Whizz. Maths-Whizz is a interactive and fun maths tutor, which adapts learning to each child’s specific needs, delivering lessons in line with their unique pace of learning. It guides each student through the maths curriculum by providing lessons at the appropriate level of difficulty based upon prior performance.

Children are expected to complete thirty minutes on Maths Whizz per week, with year six children being expected to complete sixty minutes per week. Every Friday certificates are given out to those children in each year group who have either made the most progress or have had the largest usage during the week.