Mathematics

Mathematics is a creative and highly interconnected subject that has been developed over centuries, providing the solution to some of history’s most intriguing problems.  There are three main aims in the National Curriculum which underpin the teaching of the subject:-

• Fluency
• Reason mathematically
• Solve problems

Number and Place Value

Calculations

Algebra

 Reception Year 1 Year 2 EYFS (Reception)/National Curriculum Objectives (Years 1 and 2) Early Learning Goal Children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing. Cecil Gowing’s curriculum coverage ·         Explore a number a week in different ways. ·         Count forwards and backwards. ·         Understand the  + - and = signs. ·         Begin to solve missing number problems. ·         Use the equals sign (=). ·         Solve missing number problems including using inverse operation. ·         Recognise a symbol that represents a missing number. ·      Recognise the use of a symbol such as a square or triangle to stand for an unknown number. ·      Solve missing number problems using a range of methods (e.g. bar model). Fluency ·         Count forwards and backwards. ·         Begin to follow simple number and shape patterns. ·         Show curiosity about numbers and shapes. ·         Offer comments or asks questions. ·         Understand equals (=) as a balance. ·         Recognise and continue patterns involving numbers or shape. ·         Follow simple number and shape patterns. ·      Understand and use the equals sign correctly as a balance of an equation. ·      Be able to spot continue and generate patterns in numbers, shape and data. ·      Be able to recognise, verbalise and record patterns. ·      Use mathematical representations to help pupils notice patterns (e.g. arrays and numicon). Reasoning ·         Use mathematical language. ·         Begin to understand and answer questions to promote reasoning such as: convince me, describe/explain/justify/prove, show me… How do you know? What is the same/different? What do you notice? ·         Find missing numbers/patterns. ·         Use different resources to explain thinking. ·         Describe and explain patterns. ·         Begin to predict the next number in the sequence. ·         Spot mistakes in patterns and explain why. ·         Begin to use question prompts to promote reasoning such as: convince me, describe/explain/justify/prove, show me…., How do you know? What is the same/different? What do you notice? ·         Describe and explain patterns ·         Predict the next number in the sequence ·         Offer generalisations using specific examples ·         Spot mistakes in patterns and explain why ·         Use question prompts to promote reasoning such as: convince me, describe/explain/justify/prove, show me…., How do you know? What is the same/different? What do you notice? Problem Solving ·         Show an interest in number problems. ·         Begin to solve problems involving equivalence. ·         Solve problems involving pattern. ·      Solve problems involving equivalence. ·      Solve problems involving pattern. ·      Solve problems which involve finding all the possibilities, so that generalisations can be reached.

Proportionality (fractions, decimals, percent, ratio, proportion)

 Reception Year 1 Year 2 EYFS (Reception)/National Curriculum Objectives (Years 1 and 2) Early Learning Goal Children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing. ·      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. ·         Recognise, find, name and write fractions 1/3, 1/4, 2/4, 3/4 of a length, shape, set of objects or quantity. ·         Write simple fractions for example, 1/2  of 6 = 3 and recognise the equivalence of 2/4 and  1/2. Cecil Gowing’s curriculum coverage ·       To double, half and share objects. ·      Find 1/2 of a length, shape, set of objects or quantity. ·      Find 1/2 of a length, shape, set of objects or quantity. ·      Recognise that 4/4 make a whole. ·      Find and compare fractions of amounts. ·                    · Fluency ·         Use different resources to demonstrate doubling, halving and sharing. ·      Use concrete and pictorial representations of fractions. ·      Understand that fractions involve a relationship between a whole and parts of a whole. ·      Count in steps of 1/2 and 1/4 up to 10. ·      Use concrete and pictorial representations of fractions. ·      Recognise fractions as numbers. ·                  Understand that fractions involve a relationship between a whole and parts of a whole. Reasoning ·         Explain thinking using resource when doubling, sharing and halving. ·      When looking at concrete or pictorial representations begin to explain why two fractions do not always equal a whole (e.g. 1/2 + 1/4 does not equal 1 whole). ·      Use question prompts to promote reasoning such as: convince me, describe/explain/justify/prove, show me…., how do you know?, same/different, what do you notice? ·      Explain how fractions fit into the number system. ·      Explain why two fractions do not always equal a whole (e.g. 1/2 + 1/4 does not equal 1 whole). ·      What is the same and what is different between two fractions? (e.g. 1/2 and 1/4 or 1/2 and 1/3) ·      Use fractions vocabulary of numerator, denominator, part-whole, whole. ·      Use question prompts to promote reasoning such as: convince me, describe/explain/justify/prove, show me…., how do you know?, same/different, what do you notice? Problem Solving ·         Begin to solve problems using different resources. ·      Solve problems involving fractions of shapes, objects and quantities in practical situations. ·      Begin to use knowledge of fractions to support telling the time (half way round the clock for ½ past, all the way round for O’clock). ·      Solve problems involving fractions of shapes, objects and quantities. ·      Use knowledge of fractions to support telling the time. ·      Show in different ways (shading fractions of shape). ·      Program a robot using the language of fractions.

Measurement

 Reception Year 1 Year 2 EYFS (Reception)/National Curriculum Objectives (Years 1 and 2) Early Learning Goal Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them. ·      Compare, describe and solve practical problems for: -       lengths and heights (e.g. long/short, longer/shorter, tall/short, double/half) -       mass/weight (e.g. heavy/light, heavier than, lighter than) -       capacity and volume (eg: full/empty, more than, less than, half, half full, quarter) -       time (e.g. quicker, slower, earlier, later) ·      Measure and begin to record the following: -       lengths and heights -       mass/weight -       capacity and volume -       time (hours, minutes, seconds) ·      Recognise and know the value of different denominations of coins and notes. ·      Sequence events in chronological order using correct language (for example, 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. ·      Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels. ·      Compare and order lengths, mass, volume/capacity and record the results using >, < and =. ·      Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value. ·      Find different combinations of coins that equal the same amounts of money. ·      Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change. ·      Compare and sequence intervals of time. ·      Tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times. ·      Know the number of minutes in an hour and the number of hours in a day. Cecil Gowing’s curriculum coverage ·           Compare the lengths of two of the same type of objects stating which is longest, which is the shortest. ·           Estimate and order familiar objects by length. ·           Understand what the terms ‘light’ and ‘heavy’ and ‘weighs the same as’ mean. ·           Use a balance to compare two objects by their weight. ·           Order more than two objects by their weight. ·           To understand full, empty and half full. ·           To name the days of the week in order. ·           To name the months of the year in order. ·           Order and discuss the order of events during a school day. ·           Estimate and measure how many times I can ………………………..in 10 seconds or a minute. ·         Make estimations about objects and measurements. ·         Chose and use suitable, uniform non-standard and standard units and measuring instruments. ·         Order the day of the weeks, months of the year and seasons of the year. ·         Order familiar events in time. ·         Begin to extend comparing to more than 2 objects. ·         Begin to estimate in different situations. ·         Use language such as wide, narrow, deep, shallow, width and depth. ·         Use the vocabulary related to time. ·         Order months of the year/days of the week. ·         Read the time to the hour, half hour or quarter hour on an analogue clock. ·         Know the sequence of time seconds, minutes, hours, days. ·         Understand the relationship between pounds and pence e.g. know that 100p is the same as £1. ·         Read scales in a practical situation where all numbers on the scale are given in divisions of ones, twos, fives and tens. ·         Read scales in a practical situation where not all numbers on the scale are given in divisions of ones, twos, fives and tens. Fluency ·         Compare weights of a range of items and identify which is heavier/lighter. ·         Discuss capacity e.g. full, empty, half empty, about the same. ·         To recognise and use coins in their play. ·         Be able to represent an amount in a range of different ways (20p – 10p and 10p or 5p, 5p and 10p). · Find the missing number in a money number problem (         - 3p = 7p). ·         Compare weights of a range of items and identify which is heavier/lighter. ·         Use the words more or less to complete sentences (full cup has less than ½ cup). ·         Discuss how to find which container holds the most water. ·         Follow a recipe and identify how to reduce or increase amount of food. ·      Recognise and explain why we need standard units of measurement. ·      Use exchange to find the same amount of money (5p x 2 = 10p x 1). ·      Use multiplication facts to read scales. ·      Read the time to the hour, half hour or quarter hour on an analogue clock. ·      Tell the time to 5 minutes. Reasoning ·           Use mathematical language. ·           Use different resources to explain thinking. ·         Answer questions including ‘how long ago?’, ‘how long will it be to?’, how long will it take to?’, how often?’ ·         Use true or false questions (e.g. all coins are round). ·         Find the odd one out (e.g. 20p, 2p, 5p, 30p). ·         Use always, sometimes and never (e.g. money in notes is always worth more than money in coins?). ·         Use words such as convince me, prove it (e.g. convince me that two 5p coins are the same as five 2p coins or a bigger object is always heavier than a smaller object). ·         Use language such as do you agree to solve problems involving priced items. ·         Compare measures including simple multiples such as half as high, twice as wide. ·         Reason which unit of measurement is most applicable in different situations. ·         Explain who telling the time to 5 minutes uses the 5 times table. ·         Use question prompts to promote reasoning such as: convince me, describe/explain/justify/prove, show me…., how do you know?, same/different, what do you notice? Problem Solving ·           Begin to solve simple problems using concrete apparatus. ·           Use different resources to solve a problem. ·           What if…? Questions ·           Show an interest in number problems. ·         Solve simple problems in a context using concrete apparatus. ·         Begin to solve more complex problems. ·      Solve simple problems in a context. ·      Use a variety of information to reach a conclusion. ·      Decide on which apparatus to use to solve a problem. ·     Find different combinations of coins that equal the same amount of money.

Geometry (properties of shape)

 Reception Year 1 Year 2 EYFS (Reception)/National Curriculum Objectives (Years 1 and 2) Early Learning Goal Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them ·         Recognise and name common 2D and 3D shapes, including: -       2D shapes - rectangles (including squares), circles and triangles, pentagon, hexagon -       3D shapes - cuboids (including cubes), pyramids, cones, cylinders and spheres. ·      Identify and describe the properties of 2D shapes, including the number of sides, corners and lines of symmetry. ·      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, for example, a circle on a cylinder and a triangle on a pyramid. ·     Compare and sort common 2D and 3D shapes and everyday objects. Cecil Gowing’s Curriculum Coverage ·       Recognise, extend and create a 2/3 step pattern. ·       Recognise rectangles (including squares), circles, and triangles. ·       Explore the characteristics of 2D shapes including corners and sides. ·       To sort and classify 2D and 3D shapes. ·       Recognise cubes, pyramids, spheres and cones. ·       Explore the characteristics of 3D shapes including face, edge and vertices. ·       Select a particular named shape. ·       Describe their position such as ‘behind’ or ‘next to’. ·       Use familiar objects and common shapes to create and recreate patterns and build models. ·         Visualise and describe common 2D shapes and 3D solids. ·         Use 2D shapes and 3D solids to make patterns, pictures and models. ·         Fold shapes in half, then make into symmetrical patterns. ·         Use vocabulary for 2D shapes such as corners and sides. ·         Use vocabulary for 3D shapes such as vertices (1 = vertex), edges and faces. ·         Visualise common 2D shapes and 3D solids. ·         To recognise the net of a 3D shape. ·         Order and arrange nominations of mathematical objects in patterns and sequences. ·         Know the difference between regular and irregular shapes. Fluency ·       Use a feely bag to identify, name and describe properties of shapes. ·       Sort a range of objects in to groups and say how they have sorted them. ·      Identify 2D shapes found on 3D shapes. ·         Use a feely bag to identify, name and describe properties of shape. ·         Sort a range of objects in to groups and say how they have sorted them. ·         Identify 2D shapes found on 3D shapes. ·         Identify 2D shapes on the surface of a 3D shape. ·         Compare and sort 2D and 3D shapes in everyday objects. ·         Order and arrange combinations of mathematical shapes in patterns and sequences. ·         Pupils identify what are shapes and what are not shapes. Reasoning ·       Using mathematical language. ·      Begin to describe simple patterns and relations. ·      Begin to talk about the properties of 2D and 3D shapes. ·          Describe simple patterns and relationships involving shapes and decide whether examples satisfy particular rules (e.g. is this shape a triangle? How do you know?) ·          Use questions such as ‘What is the same/different?’ ·          Find the odd one out and explain why (display 3 shapes). ·         What do you notice about 2D and 3D shapes?  What is the same? What is different? ·         Which shape is the odd one out and why? ·         Relate solid shapes to pictures of them. ·         Describe similarities and differences of shape properties.. ·         Use question prompts to promote reasoning such as: convince me, describe/explain/justify/prove, show me…., how do you know?, same/different, what do you notice? Problem Solving ·      Identify different shapes in the environment. ·      Identify shapes in a picture. ·         Solve problems involving shape (e.g. continuing a sequence). ·         Visualise 3D shapes from 2D shapes and visa versa. ·         Sort shapes in a logical way.

Geometry (position and direction)

Reception

Year 1

Year 2

EYFS (Reception)/National Curriculum Objectives (Years 1 and 2)

Early Learning Goal

Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them

·         Describe position, direction and movement, including whole, half, quarter and three-quarter turns.

·         Order and arrange combinations of mathematical objects in patterns and sequences .

·         Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti- clockwise).

Cecil Gowing’s Curriculum Coverage

·         Talk about things which can turn.

·         Use vocabulary such as under, over, above, below, inside, outside, around, opposite, apart, between, centre, next to, through, along and beside.

·         Use programmable toys to develop direction language.

·         Visualise and use everyday language to describe the position of objects and direction and distance when moving them (e.g. when placing or moving objects on a game board).

·         Recognise movements in a straight line and in rotations, combine them in simple ways (e.g. give instructions to get to the Head teacher’s office or for rotating a programmable toy.

·         Talk about things which can turn.

·         Use vocabulary such as under, over, above, below, inside, outside, around, opposite, apart, between, centre, next to, through, along and beside.

·         Recognise right angles in squares and rectangles.

·         Recognise and use whole turns.

·         Give instructions for moving along a route along straight lines and right angled corners.

Fluency

·      Describe position of objects.

·         Identify shapes with in a grid and recognise the position of each item (e.g. top, middle or bottom? Above or below?).

·     Check that a right angle is a right angle using equipment.

Reasoning

·           Explore and explain positional language within a play context e.g. the doll is behind the castle.

·         Provide images of shape in a grid context:

·         Sarah chooses a shape from the grid. You can ask her 4 questions to work out which shape she is thinking of. She can only answer ‘Yes’ or ‘No’. Which 4 questions would you ask? Can you explain why? Could you ask a different set of questions?

·         Decide whether the statements are true or false and explain your answers.

·         Use the concept of angles to describe ‘turn’ by applying rotations.

·         Use question prompts to promote reasoning such as: convince me, describe/explain/justify/prove, show me…., how do you know?, same/different, what do you notice?

Problem Solving

·           Use bee bots to solve problems e.g. what is the fewest steps to get the bee bot from the cave to the pond?

·           Explain thinking.

·         Solve problems such as – Bill built a tower using 4 different coloured cubes.  The red cube was below the green cube.  The blue cube was above the yellow cube.  Which was above the green cube?  Which cube is on top?

·         Use these clues to colour the 4 squares.

Blue is above green.

Red is below yellow.

Yellow is to the left of blue.

•    Use a floor robot to solve problems including position and direction.

Statistics