Year 5 P-CAME
APP analysis
Lesson: Sports League
Summary: Pupils calculate the number of games played in a sports league involving more and more teams. As they focus upon sequencing their results for efficient calculation the pattern ‘you times the number of teams by the number of teams take away one because you don’t play yourself’ emerges i.e. n x n-1. Larger numbers are used until the idea of ‘any number’ of teams is grasped by the pupils. This opportunity to look at generalised number leads to the introduction of letters as number holders or carriers. As an extension pupils explore a range of algebraic expressions derived from real life scenarios i.e. “there are p players in a team what can p – 1 mean?”
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 43 / Problem Solving:
Select the maths they use i.e. use classroom discussions to break into a problem + put the problem into their own words + choose their own equipment appropriate to the task.
Try different approaches and find ways of overcoming difficulties i.e. check their work and make appropriate corrections + begin to look for patterns in results as they work and use them to find other possible outcomes.
Communicating:
Begin to organise their work and check results i.e. begin to develop their own ways of recording + develop an organised approach as they record their work.
Discuss their work and begin to explain their thinking i.e. use appropriate vocabulary + talk about their findings by referring to their written work.
Use and interpret maths symbols and diagrams.
Reasoning:
Understand a general statement by finding particular examples that match it i.e. make a generalisation with assistance.
Review their work and reasoning i.e. respond to ‘what if?’ questions + when they have solved a problem pose a similar problem for a partner. / Counting and Understanding numbers:
Understand place value in numbers up to 1000.
Recognise a wide range of sequences i.e. multiples of 2, 5 and 10.
Knowing and using number facts:
Derive associated division facts from known multiplication facts.
Begin to understand the role of the = equals sign.
Add and subtract two-digit numbers mentally.
Use mental recall of the 2, 3, 4, 5 and 10 times tables.
Use mental recall of addition and subtraction facts to 20.
Add and subtract three-digit numbers using written methods.
Multiply and divide tow-digit numbers by 2, 3, 4 or 5 as well as 10.
Using and applying maths: / Understanding shapes:
Measuring: / Processing and representing data:
Gather information i.e. make appropriate choices for recording data.
Interpreting data:
Extract and interpret information presented in simple tables and lists i.e. compare data + respond to questions of a more complex nature.
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 44 / Problem Solving:
Develop own strategies for solving problems i.e. pose and answer questions + check answers and ensue solutions make sense in the context of the problem + review their work and approaches.
Use their own strategies within maths and applying this to practical contexts.
Communicating:
Present information and results in a clear and organised way i.e. organise written work (record results in order) + work in an organised way fro the outset + use related vocabulary accurately.
Reasoning:
Search for a solution by trying out ideas of their own i.e. check their methods and justify answers + identify patterns as they work and form their own generalisations/rules in words. / Counting and Understanding numbers:
Recognise and describe number patterns.
Recognise and describe number relations.
Begin to understand simple ratio.
Knowing and using number facts:
Use inverse operation i.e. undo a two-step problem.
Understand the use of brackets in simple calculations.
Use a range of mental methods of computation with all operations.
Recall multiplication facts up to 10 x 10 and derive corresponding division facts.
Using and applying maths (Algebra):
Begin to use simple formulae expressed in words. / Understanding shapes:
Measuring: / Specifying the problem …:
Collect discrete data i.e. given a problem, suggest answers and data to collect + test a hypothesis.
Group data and record in a suitable manner.
Processing and representing data:
Represent data in a suitable manner (they may use tables, line graphs etc here).
Interpreting data:
Interpret different methods of data collation. See in light of bullet point above.
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 45 / Problem Solving:
Identify and obtain necessary information to carry through a task and solve problems i.e. recognise information that is important + consider efficient methods, relating problems to previous experiences.
Communicating:
Show understanding of situations by describing them mathematically using words, symbols and diagrams i.e. organise work from the outset, looking for ways to record systematically + decide how best to represent conclusions, using appropriate conclusions + begin to understand and use formulae and symbols to represent problems.
Reasoning:
Draw simple conclusions of their own and give an explanation of their reasoning i.e. explain and justify their methods and solution + identify more complex patterns, making generalisations in words and begin to express generalisations using symbolic notation + use examples and counter-examples to justify conclusions. / Counting and Understanding numbers:
Recognise and use number patterns and relationships i.e. make generalisations about sequences saying whether much larger numbers will be in the sequence or not.
Understand simple ratio.
Knowing and using number facts:
Use known facts, place value and knowledge of operations to calculate i.e. multiply a two-digit number by a single digit.
Apply inverse operations.
Use brackets appropriately.
Using and applying maths (Algebra):
Construct, express in symbolic form, and use simple formulae involving one or two operations i.e. understand that ‘1 less than n’ can be written as n-1 + use symbols to represent an unknown number or a variable. / Understanding shapes:
Measuring: / Specifying the problem …:
Ask questions, plan how to answer them and collect the data required.
Processing and representing data:
No suitable examples given in the guidance.
Interpreting data:
As above – guidance is linked to graphical interpretation, the understanding of distribution (mean, mode etc) and the language of probability.
Lesson: Digit Detective
Summary: Pupils explore their intuitive methods for solving simple addition and subtraction problems. As they do this they explore the idea of place value through inverse operations. The aim of the lesson is to help pupils develop a sense of number size related to the reasonableness of answers. Pupils handle problems with multiple or no solutions before progressing onto problems (including multiplication) with a number of steps and alternative solutions.
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 43 / Problem Solving:
Select the maths they use i.e. use classroom discussions to break into a problem + put the problem into their own words.
Try different approaches and find ways of overcoming difficulties i.e. check their work and make appropriate corrections (the example they give is very appropriate for this lesson e.g. decide that two numbers less than 100 cannot give a total more than 200) + begin to look for patterns in results as they work and use them to find other possible outcomes.
Communicating:
Begin to organise their work and check results i.e. begin to develop their own ways of recording.
Discuss their work and begin to explain their thinking i.e. use appropriate vocabulary + talk about their findings by referring to their written work.
Use and interpret maths symbols and diagrams.
Reasoning:
Understand a general statement by finding particular examples that match it i.e. make a generalisation with assistance.
Review their work and reasoning i.e. respond to ‘what if?’ questions + when they have solved a problem pose a similar problem for a partner. / Counting and Understanding numbers:
Understand place value in numbers up to 1000.
Use place value to make approximations.
Recognise a wide range of sequences i.e. multiples of 2, 5 and 10.
Knowing and using number facts:
Derive associated division facts from known multiplication facts i.e. uses inverses to find missing numbers in problems.
Begin to understand the role of the = equals sign.
Add and subtract two-digit numbers mentally.
Use mental recall of the 2, 3, 4, 5 and 10 times tables.
Use mental recall of addition and subtraction facts to 20.
Add and subtract three-digit numbers using written methods.
Multiply and divide two-digit numbers by 2, 3, 4 or 5 as well as 10.
Using and applying maths: / Understanding shapes:
Measuring: / Processing and representing data:
Gather information to answer a question i.e. make appropriate choices for recording data.
Interpreting data:
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 44 / Problem Solving:
Develop own strategies for solving problems i.e. pose and answer questions + check answers and ensue solutions make sense in the context of the problem + review their work and approaches.
Use their own strategies within maths and applying this to practical contexts.
Communicating:
Present information and results in a clear and organised way i.e. organise written work + use related vocabulary accurately.
Reasoning:
Search for a solution by trying out ideas of their own i.e. check their methods and justify answers + identify patterns as they work and form their own generalisations/rules in words. / Counting and Understanding numbers:
Recognise and describe number patterns.
Recognise and describe number relations.
Use place value to describe number relationships.
Begin to understand simple ratio.
Knowing and using number facts:
Use inverse operation i.e. undo a two-step problem + use a calculator and inverse operations to find missing numbers.
Use a range of mental methods of computation with all operations.
Recall multiplication facts up to 10 x 10 and derive corresponding division facts.
Solve a problem with or without a calculator.
Check the reasonableness of results with reference to the context or size of numbers.
Using and applying maths (Algebra): / Understanding shapes:
Measuring: / Specifying the problem …:
Collect discrete data i.e. given a problem, suggest answers and data to collect + test a hypothesis.
Group data and record in a suitable manner.
Processing and representing data:
Represent data in a suitable manner.
Interpreting data:
Interpret different methods of data collation. See in light of bullet point above.
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 45 / Problem Solving:
Identify and obtain necessary information to carry through a task and solve problems i.e. recognise information that is important + consider efficient methods, relating problems to previous experiences.
Check results, considering whether they are reasonable i.e. check as they work, spotting and correcting errors and reviewing methods.
Communicating:
Show understanding of situations by describing them mathematically using words, symbols and diagrams i.e. organise work from the outset, looking for ways to record systematically.
Reasoning:
Draw simple conclusions of their own and give an explanation of their reasoning i.e. explain and justify their methods and solution + + use examples and counter-examples to justify conclusions. / Counting and Understanding numbers:
Use understanding of place value to multiply and divide whole numbers by 10, 100 and explain the effect.
Recognise and use number patterns and relationships i.e. make generalisations about sequences saying whether much larger numbers will be in the sequence or not.
Understand simple ratio.
Knowing and using number facts:
Use known facts, place value and knowledge of operations to calculate i.e. multiply a two-digit number by a single digit.
Apply inverse operations.
Estimate using approximations.
Understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing and three digit number by any two-digit number.
Uses approximation to check answers to problems are of the correct magnitude.
Check solutions by applying inverse operations or estimating using approximations.
Using and applying maths (Algebra): / Understanding shapes:
Measuring: / Specifying the problem …:
Ask questions, plan how to answer them and collect the data required.
Processing and representing data:
Interpreting data:
Lesson: Largest Rectangle
Summary: Pupils investigate the meaning of the term ‘largest’ in relation to 5 different sized rectangles. Their ideas are quantified and the meaning of area and perimeter are discussed together. Various methods of expressing the formula and for finding both area and perimeter are explored before the opportunity to look at the conservation of size is investigated i.e. area 24 = 12 x 2, ½ x 48 etc.
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 43 / Problem Solving:
Select the maths they use i.e. use classroom discussions to break into a problem + put the problem into their own words + choose their own equipment appropriate to the task.
Try different approaches and find ways of overcoming difficulties i.e. check their work and make appropriate corrections + begin to look for patterns in results as they work and use them to find other possible outcomes.
Communicating:
Begin to organise their work and check results i.e. begin to develop their own ways of recording + develop an organised approach as they record their work.
Discuss their work and begin to explain their thinking i.e. use appropriate vocabulary + talk about their findings by referring to their written work.
Use and interpret maths symbols and diagrams.
Reasoning:
Understand a general statement by finding particular examples that match it i.e. make a generalisation with assistance.
Review their work and reasoning i.e. respond to ‘what if?’ questions + when they have solved a problem pose a similar problem for a partner. / Counting and Understanding numbers:
Recognise a wide range of sequences i.e. multiples of 2, 5 and 10.
Use simple fractions. I.e. understand and use unit fractions such as ½, ¼, 1/3 etc.
Knowing and using number facts:
Derive associated division facts from known multiplication facts.
Begin to understand the role of the = equals sign.
Add and subtract two-digit numbers mentally.
Use mental recall of the 2, 3, 4, 5 and 10 times tables.
Use mental recall of addition and subtraction facts to 20.
Add and subtract three-digit numbers using written methods.
Use mental recall of the 2, 3, 4, 5 and 10 times tables i.e. multiply a two-digit number by 2, 3, 4 or 5.
Add and subtract three-digit numbers using written methods.
Multiply and divide two-digit numbers by 2, 3, 4 or 5 as well as 10.
Using and applying maths: / Understanding shapes:
Classify 2-D shapes in various ways using mathematical properties.
Measuring:
Use non-standard units and standard metric units of length in a range of contexts. / Processing and representing data:
Gather information i.e. make appropriate choices for recording data.
Interpreting data:
Extract and interpret information presented in simple tables and lists i.e. compare data + respond to questions of a more complex nature.
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 44 / Problem Solving:
Develop own strategies for solving problems i.e. pose and answer questions + check answers and ensue solutions make sense in the context of the problem + review their work and approaches.
Use their own strategies within maths and applying this to practical contexts.
Communicating:
Present information and results in a clear and organised way i.e. organise written work (record results in order) + work in an organised way fro the outset + use related vocabulary accurately.
Reasoning:
Search for a solution by trying out ideas of their own i.e. check their methods and justify answers + identify patterns as they work and form their own generalisations/rules in words. / Counting and Understanding numbers:
Recognise and describe number patterns.
Recognise and describe number relations.
Use place value to multiply and divide whole numbers by 10 or 100.
Begin to understand simple ratio.
Knowing and using number facts:
Use inverse operation i.e. undo a two-step problem.
Understand the use of brackets in simple calculations.
Quickly derive division facts that correspond to multiplication facts up to 10 x 10.
Use efficient written methods of addition and subtraction and of short multiplication and division.
Use a range of mental methods of computation with all operations.
Recall multiplication facts up to 10 x 10 and derive corresponding division facts.
Solve problems with or without a calculator.
Using and applying maths (Algebra):
Begin to use simple formulae expressed in words. / Understanding shapes:
Use the properties of 2-D shapes i.e. recognise a line of symmetry + use maths terms such as horizontal, vertical etc + understand properties of shapes (why a square is a special rectangle) + visualise shapes and recognise them in different orientations.
Draw common 2-D shapes in different orientations on grids.
Measuring:
Choose and use appropriate units and instruments.
Interpret, with appropriate accuracy, numbers on a range of measuring instruments.
Find perimeters of simple shapes and find areas by counting squares. / Specifying the problem …:
Collect discrete data i.e. given a problem, suggest answers and data to collect + test a hypothesis.
Group data and record in a suitable manner.
Processing and representing data:
Represent data in a suitable manner (they may use tables, line graphs etc here).
Interpreting data:
Interpret different methods of data collation. See in light of bullet point above.
Assessment focus
Level
/ Ma 1 / Ma 2 / Ma 3 / Ma 45 / Problem Solving:
Identify and obtain necessary information to carry through a task and solve problems i.e. recognise information that is important + consider efficient methods, relating problems to previous experiences.
Communicating:
Show understanding of situations by describing them mathematically using words, symbols and diagrams i.e. organise their work from the outset, looking for ways to record systematically + decide how best to represent conclusions, using appropriate conclusions + begin to understand and use formulae and symbols to represent problems.
Reasoning:
Draw simple conclusions of their own and give an explanation of their reasoning i.e. explain and justify their methods and solution + identify more complex patterns, making generalisations in words and begin to express generalisations using symbolic notation + use examples and counter-examples to justify conclusions. / Counting and Understanding numbers:
Recognise and use number patterns and relationships i.e. make generalisations about sequences saying whether much larger numbers will be in the sequence or not.
Understand simple ratio.
Knowing and using number facts:
Use known facts, place value and knowledge of operations to calculate i.e. multiply a two-digit number by a single digit.
Apply inverse operations.
Use brackets appropriately.
Check solutions by applying inverse operations or estimating using approximations.
Using and applying maths (Algebra):
Construct, express in symbolic form, and use simple formulae involving one or two operations i.e. understand that ‘1 less than n’ can be written as n-1 + use symbols to represent an unknown number or a variable. / Understanding shapes:
Use a wider range of properties of 2-D shapes i.e. understand parallel and begin to understand ‘perpendicular’.
Measuring:
Use language associated with angles.
Read and interpret scales on a range of measuring instruments, explaining what each labelled division represents.
Make sensible estimates of a range of measures in relation to everyday situations.
Understand and use the formula for the area of a rectangle and distinguish area from perimeter i.e. find the length of a rectangle given its perimeter and width. / Specifying the problem …:
Ask questions, plan how to answer them and collect the data required.
Processing and representing data:
No suitable examples given in the guidance.
Interpreting data:
As above – guidance is linked to graphical interpretation, the understanding of distribution (mean, mode etc) and the language of probability.
Lesson: Share an Apple