Lancashire Primary Mathematics Newsletter Summer Term 2010 The Lancashire Primary Mathematics Team Welcome to the summer edition of the Lancashire Primary Mathematics Team newsletter! The focus for this term is developing reasoning in mathematics. The 2009 DCSF report ‘Development of Maths Capabilities and Confidence in Primary School’ arose as the result of a project looking at the development of competence and confidence in different aspects of maths and the effect of this on young people’s results and future employment prospects. Three of their six key findings relate to the importance of reasoning, the main one stating that: ‘Mathematical reasoning, even more so than children’s knowledge of arithmetic, is important for children’s later achievement in mathematics.’ Alongside all of the regular updates and features, within this newsletter you will find a variety of resources aimed at supporting you to develop this important aspect of mathematics. These include: - starting points for reasoning and enquiry - learning prompts to support children’s responses - progression through the reasoning strand of the mathematics framework - a new ‘Home Corner’ section, outlining ways in which parents can help Don’t forget the newsletter section on our website which has links to further documents and a staff meeting for subject leaders to run in schools. As ever, if you have feedback on any of the articles in this newsletter, please contact us using the details on page two. In team news, we would like to bid farewell to Anne Porter who returns to school following her secondment. We would like to thank her for her contribution to the team and the schools that she has supported whilst working with us and wish her the very best for the future. We hope you have a fruitful summer term and a restful break when the holiday season appears.
Transcript
Lancashire Primary Mathematics Newsletter
SummerTerm 2010
The Lancashire Primary Mathematics Team
Welcome to the summer edition of the Lancashire Primary Mathematics Team newsletter!
The focus for this term is developing reasoning in mathematics.
The 2009 DCSF report ‘Development of Maths Capabilities and Confidence in Primary School’ arose as the result of a project looking at the development of competence and confidence in different aspects of maths and the effect of this on young people’s results and future employment prospects. Three of their six key findings relate to the importance of reasoning, the main one stating that:
‘Mathematical reasoning, even more so than children’s knowledge of arithmetic, is important for children’s later achievement in mathematics.’
Alongside all of the regular updates and features, within this newsletter you will find a variety of resources aimed at supporting you to develop this important aspect of mathematics. These include:
- starting points for reasoning and enquiry- learning prompts to support children’s responses- progression through the reasoning strand of the mathematics framework- a new ‘Home Corner’ section, outlining ways in which parents can help
Don’t forget the newsletter section on our website which has links to further documents and a staff meeting for subject leaders to run in schools.
As ever, if you have feedback on any of the articles in this newsletter, please contact us
using the details on page two.
In team news, we would like to bid farewell to Anne Porter who returns to school following her secondment. We would like to
thank her for her contribution to the team and the schools that she has supported whilst working with us and wish her the very best for the future.
We hope you have a fruitful summer term and a restful break when the holiday season appears.
2 The Lancashire Primary Mathematics Team
The Lancashire Mathematics TeamTeam Leader / Alison HartleySenior Adviser
Primary Mathematics Lynsey Edwards (Senior Consultant), Sue Bailey, Consultants Tracy Dimmock, Sue Farrar, Anne Porter, Emma Radcliffe, Angeli Slack, Kerry Swarbrick, Andrew Taylor, Peter Toogood
Team Contact Details Phone: 01257 516102 Fax: 01257 516103 E-Mail: [email protected] Write to: LPDS Centre, Southport Road Chorley, PR7 1NG Website: www.lancsngfl.ac.uk/curriculum/math
Steps to Success in Mathematics: Securing Progress for all Children 3
How Can the Mathematics Team Support Your Professional Development? 4
NRICH - Fantastic Resources to Enhance Children’s Understanding 5
EYFS Corner 6
Every Child Counts 7
National Strategies Publications 8
Numbers and Patterns: Laying the Foundations of Mathematics 9
The Home Corner 10
Reasoning Resources - NCETM 12
Prompts to Support Children’s Oral Reasoning 13
Reasoning and Enquiry Starting Points 14
Progression Through the Reasoning Theme in the Using and Applying Strand 18
Puzzle Page 20
Team Information and Contents
The Lancashire Mathematics TeamThe Lancashire Primary Mathematics Team 3
Mathematics Specialist Teacher Programme
Our 52 teachers have bravely embarked upon their journey towards becoming a Mathematics Specialist Teacher (MaST). In a world where admitting an inability to ‘do’ maths has become socially acceptable, they have somewhat of an uphill task in their role as champions of mathematics, but are ready to embrace the challenge!
The Spring term local meetings have focused on the progression in division and fractions. This has been further supported by working with Edge Hill University. Teachers are encouraged to network and share their experiences through the use of the Blackboard virtual learning environment set up by Edge Hill.
If you are lucky enough to have a MaST working in your school, please give them your support! If you don’t have a MaST in your school, and would like more information about becoming one, please contact Angela Jamieson on 01257 516102.
...Securing Progress for all Children
Steps to success in mathematics: Securing progress for all children is a DVD-based compendium of National Strategies primary-focused mathematics materials and resources. These resources have been developed to help you to plan and provide teaching and learning in mathematics that will ensure all children make progress through the National Curriculum levels over Key Stages 1 and 2. The DVD is structured around a level-to-level approach and brings together the following publications and documents:
• Securing levels in mathematics for levels 1 to 5• What I can do in mathematics for levels 1 to 5• Overcoming barriers in mathematics for level 1 to 2, level 2 to 3, level 3 to 4 and level 4 to 5• Assessing Pupils’ Progress mathematics guidelines for level 1 to 2, level 2 to 3, level 3 to 4 and level 4 to 5All of these publications are linked to the Primary Framework but to help you to access supporting materials the DVD also contains:
• Primary Framework yearly overviews for each year group, 1 to 6• Pitch and expectations for each year group, 1 to 6
One DVD will come into every school this term. All the materials on the DVD can be accessed in the same way on the following website:
In addition to providing National Strategy courses we also provide a wide range of marketed courses.
Why not take a look at the Learning Excellence site to see if we are running a course which would benefit the professional development of a member of your staff?
08/06/2010 MAT115a LPDS Centre Effective Use of the Starter Session in Mathematics Lessons
12/07/2010 MAT119a Woodlands Support for Mathematics – Moving Through Levels 2&3
29/09/2010 MAT115b LPDS Centre Effective Use of the Starter Session in Mathematics Lessons
15/10/2010 MAT117b LPDS Centre Guided Learning in Mathematics
21/10/2010 MAT116a LPDS Centre Problem Solving, Reasoning and Numeracy in the FS
05/11/2010 MAT114a Woodlands Improving Maths Subject Knowledge: Handling Data
11/11/2010 MAT122a Woodlands Support for Mathematics – Moving Through Level 5
19/11/2010 MAT106b Woodlands Mathematics for NQTs
26/11/2010 MAT118a Woodlands New to Mathematics Subject Leader Day One
02/12/2010 MAT121a Woodlands Support for Mathematics – Moving Through Level 4
Summer Term 2010
Autumn Term 2010
How Can the Mathematics Team Support Your Professional Development?
4 The Lancashire Primary Mathematics Team
For further information about all these courses access the Learning Excellence Website on www.learningexcellence.net or via our links on the Mathematics Team website www.lancsngfl.ac.uk/curriculum/math.
The Lancashire Mathematics Team
www.nrich.maths.org
A number of years ago, Cambridge University embarked upon developing this website dedicated to enriching children’s experience of mathematics.
There is a monthly theme and a number of problems, puzzles, games and articles are published on the site for use by teachers and pupils.
All of the puzzles, problems and games over the last few years have been aligned to objectives from the Renewed Framework in the Curriculum Mapping Documents.
These documents are interactive to enable teachers to access the appropriate puzzle direct from the link beneath the objective (see below).
The puzzles are linked to appropriate Key Stages and each has a difficulty rating, from one star to three stars, with three stars being most challenging. The puzzles contain teacher notes (which illustrate how the puzzle can be differentiated up and down), a hint (a possible starting point for those who are struggling to get going) and answers that have been submitted by children, with exemplified explanations and processes.
The puzzles can be used in a number of ways, especially as stimuli for guided group work focusing on children’s problem solving, communicating and reasoning.
(Most of our puzzle page problems have been taken from the nrich website).
5The Lancashire Primary Mathematics Team
NRICH - Fantastic Resources to Enhance Children’s Understanding
NRICH www.nrich.maths.org problems linked to the Framework for teaching mathematics in Years 3, 4, 5 and 6 A list of recent updates can be found at the end of this document. The letters and numbers refer to blocks and units.
(N.B. This is work in progress– we would really appreciate your comments. Please email [email protected])
Year 3 Year 4 Year 5 Year 6 Year 6-7
Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations NRICH: A Square of Numbers A3 B2 B3 D1 D3 E2 E3
Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate NRICH: The Puzzling Sweet Shop A3 B1 B3 D1 D2 D3
Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use NRICH: Money Bags NRICH: Amy’s Dominoes D1 D2 D3 E1 E3
Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use NRICH: Two Primes Make One Square NRICH: What’s it Worth? D1 D2 D3 E1 E3
Solve problems by breaking down complex calculations into simpler steps; choose and use operations and calculation strategies appropriate to the numbers and context; try alternative approaches to overcome difficulties; present, interpret and compare solutions
Represent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and present it in context, where appropriate using £.p notation or units of measure
Represent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problem NRICH: Buying a Balloon E1 E2 E3
Represent a puzzle or problem by identifying and recording the information or calculations needed to solve it; find possible solutions and confirm them in the context of the problem NRICH: Sealed Solution NRICH: Prison Cells B2 B3 E1 E2 E3
Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy NRICH: Counting Cards B2 B3 E1 E2 E3
Represent information or unknown numbers in a problem, for example in a table, formula or equation; explain solutions in the context of the problem
Str
and
1 - U
sing
and
App
lyin
g
Follow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and interpret the information NRICH: Sweets in a Box C1 C2 C3 E1 E3
Suggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answers
Plan and pursue an enquiry; present evidence by collecting, organising and interpreting information; suggest extensions to the enquiry
Suggest, plan and develop lines of enquiry; collect, organise and represent information, interpret results and review methods; identify and answer related questions
Develop and evaluate lines of enquiry; identify, collect, organise and analyse relevant information; decide how best to represent conclusions and what further questions to ask
Overcoming BarriersThese materials provide guidance for teachers in undertaking an initial identification of the barriers in mathematics that slow pupils' progress and limit their attainment. They are based around the Renewed Framework and link to the Blocks and Units. There is support for planning and teaching to help pupils overcome the identified barriers, re-assess their learning, and recognise the progress they have made.
These resources can be ordered by contacting Teachernet on 0845 6022260.
National Strategy Publications
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These documents are supported by booklets entitled ‘What I can do in Mathematics’. These take the assessment checklists and present them in a form that can be used in the classroom with space for children to record their mathematical working and answers.
These can be downloaded from the One to One section of our website:
Securing LevelsThese materials identify key areas of learning that children need to secure to attain a particular level in mathematics. While you can integrate the ideas from these materials into your ongoing planning, you could also use them to plan targeted support for particular groups of children.
7The Lancashire Primary Mathematics Team
Numbers and Patterns...
...Laying the Foundations of Mathematics
This document was provided for all schools during the Spring term. The file is divided into six sections:
Introduction• - an overview of the structure of the materials and how they relate to the Development Matters statements and the Year 1 Primary Framework objectives.Observation, assessment and planning• - guidance on how these support children’s development and learning in mathematics, along with an example of an observation schedule.Steps in learning• - charts outlining the phases within the Number words and numerals and Counting sets themes; includes potential difficulties and guidance on the use of models and images to help overcome these.Enabling environments• - 12 cards with examples of how children’s learning in mathematics can be supported through the environment.Role of the adult• - how adults can support and extend children’s mathematical learning. It offers examples of how to interact with children’s freely-chosen play and some starting points for activities.Supporting material• - additional key messages, audits and extracts from related publications.
Progression through the phases for each of the themes can be seen below.
Phase Number words and numerals Counting sets
1Children’s awareness, understanding and use of the language of number
Development of children’s early awareness of quantity
2Development of children’s knowledge and use of the number sequence from one to five, and recognition of the numerals 1 to 5.
Development of children’s ability to count up to five objects and to recognise, without counting, sets of one, two or three objects.
3Development of children’s knowledge of the number sequence from one to nine and recognition of the numerals 1 to 9.
Extending children’s counting skills to enable them to count up to ten objects, actions or sounds accurately.
4
Extending the range of numbers that children can confidently use, to include zero and numbers to 20.
Extending children’s counting skills to enable them to count up to ten objects accurately, in any arrangement. The early stages of addition and subtraction are developed as children begin to partition and combine sets and to remove objects from sets.
5
Extending the range of numbers that children can confidently use, to include numbers to 30. Children also start to explore the sequences of numbers when they count from zero in twos, fives and tens.
Extending children’s counting skills to enable them to estimate, count and compare sets of up to 20 objects. Addition and subtraction are further developed as children partition and combine sets and count on and back.
6
Extending the range of numbers that children can confidently use, to include numbers to 100. Children also become more secure in counting forwards and backwards in twos, fives and tens.
Using children’s counting skills to support addition and subtraction through counting on and back and through counting from the smaller to the larger number to find a difference. Children also use their ability to count in twos, fives and tens to count large groups of objects efficiently.
For information on how to order this publication please see page 8.
These recent publications support and help to develop this view of mathematics with young children...
Numbers and patterns - laying the foundations of mathematics
This excellent new resource provides support for Early Years practitioners and Year 1 teachers. This resource can be downloaded from: http://nationalstrategies.standards.dcsf.gov.uk/node/273401
Published in 2009Ref: 01011-2009DOM-EN
Mark Making Matters – young children making meaning in all areas of learning and development
This booklet aims to support practitioners in understanding the significance of their role in fostering and celebrating children’s mark making, through the provision of a thoughtfully planned environment that is rich in opportunities.
Case studies are used throughout to provide ‘real-life’ examples of how practitioners work with children to support their all-round development but with specific emphasis on mark making. This resource can be downloaded from: http://nationalstrategies.standards.dcsf.gov.uk/node/132558.
Published in 2008Ref: 00767-2008BKT-EN
Children thinking mathematically: PSRN essential knowledge for Early Years practitioners
This booklet takes Mark Making Matters further and extends and develops the concepts explored there with particular reference to the three strands of PSRN.This booklet aims to help practitioners ‘see’ the mathematics in children’s play and concludes with consideration of transition between EYFS and Year 1.
Published 2009Ref: 00861-2009BKT-EN
EYFS Corner
8 The Lancashire Primary Mathematics Team
‘For children to become (young) mathematicians requires creative thinking, an element of risk-taking, imagination and invention –
dispositions that are impossible to develop within the confines of a work-sheet or teacher-led written mathematics.’
Carruthers, E. and Worthington, M. (2003)
9The Lancashire Primary Mathematics Team
Every Child Counts
The National Annual data for Numbers Count has been very positive with children making on average 13.5 months progress within just three months. Lancashire was ranked 4th out of the 27 Local Authorities during 2008/09.
The successes of the Every Child Counts programme have been recognised by Parliament, where a number of MPs congratulated the hard work of the pupils and teachers involved.
Accreditation
Numbers Count Teachers need to provide evidence about how they have met a total of 23 standards and requirements in order to be awarded accreditation. On the 21st January, nine Numbers Count Teachers were awarded their accreditation by Jonathan Hewitt and Paul Duckworth.
Numbers Count Teachers who have been awarded accreditation include:
Cath Harrison (Cherry Fold Community Primary School, Burnley)Nicky Smith (Lord Street Primary School, Colne)Sally Bryden (St Matthew’s CE Primary School, Preston)Tracey Beaven (Walverden Primary School, Nelson)Liz Tobin (St John’s Catholic Primary School, Skelmersdale)Katie Leyland (Blessed Sacrament Catholic Primary School, Preston)Joanne Richards (Hyndburn Park Primary School)Rachel Warner (Seven Stars Primary School, Leyland)Therese Lakeland (St Joseph’s Catholic Primary School, Preston)
Congratulations to all!
Numbers Count Teachers who joined the programme in September are currently working towards their accreditation.
The Home Corner
This new section is aimed at highlighting how parents can help their children in everyday activities involving reasoning...
Shopping - MoneyTalk about which coins could be given to get the correct change or what would be the smallest number of coins that still give the right change? Try to guess the value of a coin from its description.
What’s in the shopping bag?Describe the shape of an item in the shopping bag for another person to identify. Talk about what it can’t be and why before finally identifying what the item is.
NumbersTalk about numbers on a car registration plate and rearrange them to make: the largest number; smallest number; number nearest to 500 etc.
When laying the table at meal times, talk about how many mats will be needed and
how many knives, forks and plates will be used if everyone is having a main course and dessert.
Order and Sequencing Talk about:The order in recipes and why certain items need to be included at certain points; The order in which you put clothes on to get dressed – which items have to be put on before others and why?
MeasurementEstimate how many drinks could be made from a bottle of cordial.
Wrapping presents and parcels, talk about the amount of paper and the length of ribbon needed
Estimate how many apples in a kilogram or potatoes in a bag.
Puzzles and Games
Play and solve puzzles and games in newspapers and magazines. Sudoku is particularly good for developing children’s reasoning skills.
Can you place six X's on a Noughts and Crosses board without making three-in-a-row in any direction?
Solution
Z 283 QZX
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Nine dots are arranged in a three by three square. Connect each of the nine dots using only four straight lines and without lifting your pen from the paper.
Solution
Arrange the numbers 1 to 9 on a 3 by 3 board so that the numbers in each row, column and diagonal add up to 15.
Solution
Other helpful hints and suggestions
www.direct.gov.uk/homeworksupport
‘Working Together’
is a useful booklet
to help parents feel
involved in their
child’s learning.
It contains
useful advice
and activities,
including links
to other fun
learning
websites.
‘So What Happens
at School’ is a
quick guide to
the National
Curriculum,
Key Stages
and
Attainment
Levels, and
gives useful
advice for parents on
building relationships up with a
child’s class teacher.
‘Top 10 Tips for
Homework Survival’
does exactly what it
says on the tin. Ten
easy to follow tips
to give children the
best opportunity to
succeed with their
homework, and
allow parents
to get involved
too.
Even more useful information can
be found at www.direct.gov.uk/en/
Parents/Schoolslearninganddevelopment/
HelpingYourChildToLearn/DG_4016596.
4 3 89 5 12 7 6
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The Lancashire Primary Mathematics Team
The National Centre for Excellence in the Teaching of Mathematics (NCETM) website contains useful resources to support teachers with aspects of reasoning...
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Reasoning Resources - NCETM
The self-evaluation tool that we have mentioned in previous issues exemplifies what is meant by reasoning in EYFS, Key Stage 1 and Key Stage 2.
The EYFS section focuses on children developing their own meanings and representing them, making choices and justifying decisions, developing mathematical reasoning and communicating with others.
In Key Stage 1 and 2, the focus progresses to conjecture, finding a counter example, generalising and using mathematical reasoning.
Examples include:
EYFS - Developing mathematical reasoning
Let children handle and shake a number of closed containers and then guess how many things are inside. This encourages them to think about the size of the objects and the capacity of the containers. The one with the biggest capacity will not necessarily hold the most, especially if it contains large beads rather than small ones.
KS1 - Using mathematical reasoning
If you want to make cakes for 15 people and the recipe card is for 10 then children need to think about what to do with the recipe. Give the children a real recipe then make the food and share it out amongst 15 class mates. Similar problems can then be given and the children can discuss what to do.
KS2 - Using mathematical reasoning
Each shape stands for a number. The numbers shown are the totals of the line of four numbers in the row or column. Find the remaining totals.
The Lancashire Mathematics Team have put together all the information from the NCETM site into three documents. Find
them in the newsletter section of the Lancashire Mathematics Team website at www.lancsngfl.ac.uk/curriculum/math/
index.php?category_id=182.
The Lancashire Primary Mathematics Team
Prompts to support children’s oral reasoning
These speech bubbles or sentence starters could be modelled by the adults within the classroom prior to the children using them when explaining their thinking or
reasoning. They are also available on our website www.lancsngfl.ac.uk/curriculum/math/index.php?category_id=182.
I wonder if…
This didn’t work so I…
I would like to add…..
I decided to… so that / because…
I disagree… because…
Do you think….?
I also think that…..
I already know that… so I…..
The method I used to solve this was…
It looks like…
This worked so…
I noticed that…
I tried this… because…
This is true because….
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I’m not sure I agree…
I think that…
I wondered why…
I think what you might mean is…
This didn’t work so…
I found out that…
Reasoning and Enquiry Starting Points
These statements can be used as starting points for children to investigate. They may also consider whether they are always, sometimes or never true.
When children embark upon these investigations, we should be encouraging them to include reasoning in their responses.
This information can prove particularly useful to inform teacher assessment, especially for Ma1 Using and Applying Mathematics.
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s
I can make all the numbers between 5 and 20 by adding consecutive numbers.
If you choose a number and square it, the answer you get is always one more than the product of one less and one more than the number you first chose (e.g. 5x5=25; 4x6=24).
If you add three consecutive even numbers the answer is always a multiple of 6 (e.g. 2+4+6= 12).
If I choose a 2x2 square on a 100 square and add the diagonal pairs they always make the same total (e.g. 2+13=3+12).
If I draw a pentomino on a 100 square the two extreme numbers sum to double the centre number
(e.g. 35+57 = 46x2).
If I multiply two numbers they always get bigger.
If you increase the perimeter of a shape its area increases.
I can draw a square with an area of 2 squares.
If I choose any 2x2 square on a multiplication grid the product of the diagonals are always the same as each other (e.g. 3x8=6x4).
All numbers have an even number of factors, (e.g. the number 6 has 4 factors: 1,2,3,6).
I can pay for anything from 1p to 5p if I have two 2p coins and one 1p coin.
I can make four different numbers with two different digits.
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When I subtract 10 from a number the units digit stays the same.
There are three numbers less than 10 that divide exactly by 3.
Any even number can be written as the sum of two odd numbers.
All squares are rectangles.
The difference between any two odd numbers is an even number.
A number is divisible by 3 if the sum of the digits is divisible by 3.
With twelve squares you can make three different rectangles.
The perimeter of a rectangle is double the sum of one short side and one long side.
The number of lines of reflective symmetry in a regular polygon is equal to the number of sides.
If you add three consecutive numbers, the answer is three times the middle number.
The imperial measure of 1 foot would need a size 12 shoe.
A triangle can have two right angles.
You can work out the eight times table by doubling the 4s.
All four sided shapes are called squares.
When I multiply two multiples of ten the answer always has the same number of zeroes as the
original numbers combined (e.g. 20x30=600).
Reasoning and Enquiry Starting Point
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All numbers that end in 4 are multiples of 4.
If a quadrilateral has two acute angles and all four sides are the same length it must be a rhombus.
The larger the denominator of a fraction the smaller the fraction.
The number one is a prime number.
Consecutive triangular numbers sum to make square numbers.
If I continue the sequence 1, 8, 15, 22, 29… the number 777 will appear.
Make a list of similarities and differences between a square and an oblong. If both shapes are rectangles, create a clear definition of a rectangle.
Sarah buys 16 packets stickers at 26p each. This costs £4.16. Use this information to work out:
The cost of 17 packets• The cost of 15 packets• The cost of 16 packets at 25p • eachThe cost of 16 packets at 28p • eachThe cost of 32 packets• The cost of 16 packets at 52p • each
What other questions would this information help you to answer?
ts (continued)
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Progression Through the Reasoning Theme in th
Make a butterfly pattern. Count the spots on each side of your butterfly.
Find two shapes with only five straight sides. Draw a circle around them.
Below is a table showing the progression within the reasoning theme in the Primary Framework’s Using and applying mathematics strand. Linked examples from the Pitch and Expectations document, Learning Overview – Assessment for Learning prompts and 1999 Framework Supplement of Examples have been identified.
Year Reasoning objective
Pitch and Expectations, Learning Overview – AfL Prompts and 1999 Framework – Supplement of Examples
EYFS Talk about, recognise and recreate simple patterns
Use the beads. Copy this pattern.
Year 1 Units
B1 B2 B3 E3
Describe simple patterns and relationships involving numbers or shapes; decide whether examples satisfy given conditions
Here are five rectangles of the same size. How many different bigger rectangles can you make using two or more of the rectangles?
Make a string of beads for me. First a red one, then a blue one. Carry on threading one red, one blue. What colour is the sixth bead on your string? What colour will the tenth bead be? The twentieth bead? How do you know?
Year 2 Units
B1 B2 B3
Describe patterns and relationships involving numbers or shapes; make predictions and test these with examples
We have worked out that 3 + 5 = 8 and 13 + 5 = 18. Without calculating, tell me what 23 + 5 will be. What about 63 + 5?
Write the missing digits to make this correct.
Year 3 Units
B1 E1 B2 B3 E3
Use patterns and relationships involving numbers or shapes, and use these to solve problems
Year 4 Units
B1 B2 B3
Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples
How have these shapes been sorted? Is there more than one way that they could have been sorted?
Use the sponges. Continue this pattern that I have started.
9 – 3 = 6. What is 90 – 30, and 900 – 600? How do you know?
Count all the triangles in this diagram.
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he Using and Applying Strand
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Year Reasoning objective
Pitch and Expectations, Learning Overview – AfL Prompts and 1999 Framework – Supplement of Examples
Year 5 Units
B1 B2 B3
Explore patterns, properties and relationships, and propose a general statement involving numbers or shapes; identify examples for which the statement is true or false
Year 6 Units
B1 B2 B3
Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test hypotheses; construct and use simple expressions and formulae in words then symbols (e.g. the cost of c pens at 15 pence each is 15c test pence)
Year 6 into
Year 7
Generate sequences and describe the general term; use letters and symbols to represent unknown numbers or variables; represent simple relationships as graphs
One of these numbers is not in the correct place. Which is it and why?
Two square tiles are placed side by side. How many tiles are needed to surround them completely?
What if three square tiles were laid side by side? Four tiles? Five tiles? How many tiles would be needed if 100 tiles were laid side by side? Explain your answer.
This shape has been drawn on isometric paper. Explain how you could work out the internal angles of the shape.
Puzzle Page
Summer Term Puzzle - Jugs
Using two jugs, one which holds 3 litres and one which holds 5 litres, how can you measure out exactly 4 litres?
Solution to last term’s puzzle…Sets of Four Numbers
