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Lancashire Mathematics Newsletter
Lancashire Mathematics Newsletter
Lancashire Mathematics Newsletter
AUTUMN TERM 2008
Below is an example of a KenKen puzzle. The puzzles are similar to sudoku and were invented by a
Japanese mathematics teacher called Tetsuya Miyamoto
All the digits 1 to 6 must appear in every row and column. In each thick-link ‘block’, the target number
in the top left-hand corner is calculated from the digits in all the cells in the block, using the symbols
indicated (+/-/÷ /x). This was taken from the Times Online website (www.timesonline.co.uk).
This and future editions of the Lancashire Mathematics Newsletter will each
follow a subject theme. The newsletter will contain resources to support you in
that area of mathematics, including teaching ideas, staff meetings, staff INSET,
starter activities, ideas for incorporating ICT and useful resources.
Current news and issues from the world of mathematics teaching will still be
incorporated.
This term’s theme is:
Full Mathematics Team List
Senior Adviser Alison Hartley
SOLUTION NUMBER TRIANGLE
Primary Mathematics Consultants
Shirley Bush (Senior Consultant)
Sue Bailey
Tracy Dimmock
Lynsey Edwards
Sue Farrar
Tim Kirk
Anne Porter
Emma Radcliffe
Andrew Taylor
Peter Toogood
Angeli Slack
Secondary Mathematics Consultants
Louise Hastewell
Sue Taylor
Mary Ledwick
Maureen Magee
Team Contact Details
Phone:
01257 516102
Fax:
01257 516103
E-Mail:
LPDS.Numeracy@ed.lancscc.gov.uk
The biggest number that each of the sides can add up to is 23.
One possible solution is shown above. There are other solutions as the numbers in the middle of
each edge can be in the opposite order. The whole triangle could also be rotated around. Either
way, though, the total of the numbers along each side must still equal 23!
The above puzzle was taken from www.puzzlepixies.com
Write to us at:
LPDS Centre
Southport Road
CHORLEY
PR7 1NG
Website:
www.lancsngfl.ac.uk/curriculum/math/
Fraction, decimals and percentages converter
2
Progression through ‘I can’ statements
3
Intervention resources for FDPRP
4
Subject Leader meeting dates
4
Renewed Framework website update
5
Useful website for FDPRP
6&7
Every Child Counts
7
Williams Review of Mathematics Teaching
8
Girls and Mathematics project
9
Overcoming Barriers in Mathematics Level 2 - 3
10
Overcoming Barriers in Mathematics Level 3 - 4
11 - 13
Vocabulary bookmarks Year 1 - 6
14 - 15
Practical ideas for teaching ratio and proportion
16 - 17
Mental oral starters for FDPRP
18 – 19
Take an ITP……..Counting
20 - 21
Maths is Special
FDPRP resources for KS3 and KS4
Puzzle page
22
23 - 27
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This newsletter will be available to download in the
Autumn Term from
www.lancsngfl.ac.uk/curriculum/math/
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Lancashire Mathematics Newsletter
Fractions, decimals and percentages converter (FDP) Excel
Spreadsheet
This file enables you to explore the
relationships between improper
fractions, mixed numbers, decimals and
percentages. You can choose which
format you start with and then use
questioning to illicit the equivalents,
encouraging the pupils to explain their
methods and understanding.
It comes with a guidance document
which also includes key questions and
prompts.
This spreadsheet is available to download from the renewed framework website
www.standards.dfes.gov.uk/primaryframeworks/
Go to: Library - Mathematics - ICT resources - Spreadsheets.
Other Excel Spreadsheets available for fractions, decimals, percentages and proportion include “Calculate
percentages”, and “Fraction of Amounts”.
Fractions ITP
This ITP allows you to divide a green strip into a
number of equal parts and colour the individual
parts in yellow. You can label the strip to show
what proportion of the whole strip the yellow
parts are. This can be shown as a vulgar fraction,
a decimal (to three decimal places) or a
percentage. The ratio of yellow to green can also
be displayed. You can create more then one strip
and drag strips up and down the screen to
compare them.
The ITP can be used to explore equivalence
between fractions, decimals and percentages and the different representations of the same relative
quantities. The equal parts on the strips can also be used to demonstrate how to calculate fractions and
percentages of given amounts and to represent a horizontal bar chart. The ITP can be used to set up to
solve ratio and proportion problems.
This ITP is available to download from the renewed framework website.
www.standards.dfes.gov.uk/primaryframeworks/
Go to: Library - Mathematics - ICT resources - ITPs
Other ITPs that may be used to teach fractions, decimals, percentages and proportion include “Area”,
“Measuring Cylinder”, and “Ratio and Proportion”
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Lancashire Mathematics Newsletter
Mathedup
http://www.mathedup.co.uk/
Mathedup is another useful website with ready made and easy to use resources including Tarsia jigsaws like the one
below and interactive whiteboard resources. The site includes links to download free software so that all resources
can be accessed.
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Lancashire Mathematics Newsletter
The Progression Maps
What are they?
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Lancashire Mathematics Newsletter
This is an example of the progression of objectives, learning overview and AfL (assessment for learning)
from Reception to Year 6 linked to the Renewed Framework for fractions, decimals and percentages.
The whole document is available on the Lancsngfl maths website.
The progression maps comprise a set of objectives in a sequence of ten steps in each strand of mathematics. They
describe the progression in each strand. The objectives are drawn from the 1999 Framework for teaching mathematics
teaching objectives.
The progression maps:
•
Span the range from approximately below level 3 to GCSE grade C e.g. step 1 relating to a weak level 3, step 2
a secure level 3 and so on to step 10 which relates to a secure level 7 or C grade at GCSE;
•
Help teachers to identify appropriate curricular targets
•
Link with ‘Tracking for success’ and support assessment for learning through the use of probing questions;
•
Help teachers where pupils are having difficulties.
How do I use them?
First
Refer to your planning and identify the main teaching objective for the lesson or sequence of lessons for the pupil or
group of pupils. Locate the section of the maps for this objective. Find which step it is on or near to and look at the
Examples of what pupils should know and be able to do. This will help you to confirm that the work is at the right level.
Next
The maps will help you to decide whether the pupils have understood the mathematics by providing you with some
Probing questions to ask them.
Finally
If you have a pupil or group who clearly have not understood then the What to do if pupils find this a barrier will give
you some suggestions of how the understanding may be built up. Sometimes this will be to look at the previous
steps but more often there are teaching ideas and materials provided for that particular objective.
Below is a sample of the Progression Maps for Fractions, Decimals, Ratio and Percentages. A comprehensive set of
objectives can be accessed on
www.lancsngfl.ac.uk/curriculum/math then click secondary / intervention / progression maps
Progression through ‘I Can’ Statements The ‘I can’ statements in each block of the renewed framework for mathematics are useful for identifying the smaller steps to attaining the overall objective. The Lancashire Mathematics Team have created documents which identify the objectives for each year group and show the ‘I can’ statements for each in the order in which they appear in the blocks and units. This will support with planning and differentiation. Find these documents at: http://www.lancsngfl.ac.uk/curriculum/math/index.php?category_id=737 4
Lancashire Mathematics Newsletter
Intervention Resources for FDPRP
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Lancashire Mathematics Newsletter
Fractions, decimals and percentages Level 3-5 ‘ Learning from Misconceptions’ lesson
Cards to classify into equivalent sets
These are the different Springboard and Wave 3 units that can be used to support the teaching
and learning of fractions, decimals and percentages.
Springboard:
Year 3
Unit 4 Doubling and halving numbers
Year 4
Unit 5 Understanding multiplication and division
Unit 7 Fractions
Year 5
Unit 1 Doubling and halving
Unit 4 Fractions - finding fractions of shapes and numbers
- begin to recognise simple equivalent fractions
Unit 5 Decimals - decimal rounding and ordering
Year 6
Lesson 1 Order a set of decimal numbers and identify the most significant digit when sorting numbers
Lesson 3 Express a quotient as a fraction or as a decimal when dividing a whole number by 2, 4, 5 or 10
Represent halves, tenths, and fifths as fractions and decimals
Lesson 7 Order fractions by converting to a common denominator
Lesson 8 Express percentages as simple fractions and simple fractions as percentages
Lesson 9 Calculate simple percentages of whole number quantities
Lesson 10 Use a calculator to convert a fraction to its decimal equivalent and to find a fraction of a quantity
Lesson 19 Solve problems involving ratio and proportion
Lesson 29 Solve simple problems involving ratio and proportion
Lesson 30 Express part of a shape as a fraction
Wave 3:
3 YR x/÷ Makes unequal groups and is unable to compare the groups
4 YR x/÷ When sharing, can sometimes make equal groups, but has no strategies to deal with any left over
6 YR x/÷ When halving, makes two unequal groups or splits a single object unequally
5 Y2 x/÷ Does not use knowledge of doubles to find half of a number; for example, continues to find half by
sharing, using a ‘one for you’ approach and cannot apply knowledge of doubles.
6 Y2 x/÷ Is not systematic when sharing into equal groups, using a ‘one for you’ approach; does not use the
language of division to describe the process.
2 Y6 x/÷ Has difficulty, when appropriate, interpreting a remainder as a fraction, for example: 16 ÷ 3 = 5⅓
3 Y6 x/÷ Interprets division as sharing but not as grouping (repeated subtraction) so is unable to interpret a
calculation such as 12 ÷ ½
Subject Leader Meetings – Autumn Term 2008
Overall Aims:
Progression in Data Handling - Staff meeting for Subject Leaders
•
•
Lesson study and developing groups
Course
No
NUM805a
NUM805b
NUM805c
NUM805d
NUM805e
NUM805f
NUM805g
NUM805h
Date
Monday 17 November 2008
Monday 17 November 2008
Tuesday 18 November 2008
Tuesday 18 November 2008
Wednesday 19 November 2008
Wednesday 19 November 2008
Thursday 20 November 2008
Thursday 20 November 2008
Time
9.30
1.30
9.30
1.30
9.30
1.30
9.30
1.30
-
11.45 am
3.45 pm
11.45 am
3.45 pm
11.45 am
3.45 pm
11.45 am
3.45 pm
Book online at: www.lancsngfl.ac.uk/lses
Venue
Clayton Park Conference Centre, Clayton-le-Moors
Clayton Park Conference Centre, Clayton-le-Moors
Farington Lodge, Leyland
Farington Lodge, Leyland
Crofters Hotel, Cabus
Crofters Hotel, Cabus
Stanley House, Mellor Nr Blackburn
Stanley House, Mellor Nr Blackburn
Nrich.maths.org
Nrich is a website with a wealth of interactive activities that can be easily adapted and downloaded to use in lessons.
Nrich also has other useful documents such as curriculum maps for KS3 and KS4 linking resources to particular topic
areas.
Fractions Jigsaw
This resource provides an opportunity for pupils to find equivalent fractions and carry out some simple additions and
subtractions of fractions in a context that may challenge and motivate students.
Give the jigsaw to pairs of students to complete, being ready for discussion that may follow about fractions or puzzles
of this type.
For some students this will also invite questions like:
How has this puzzle been created, and how much freedom is there in this structure?
This resource can be downloaded from nrich.maths.org which can also be accessed via
www.lancsngfl.ac.uk/curriculum/math then click secondary maths / ictac / usefulwebsites
Study Plus Module; ‘MP3 Players’
www.standards.dfes.gov.uk/intervention then click modules/study plus
As with all the Study Plus modules MP3 Players covers more than just one area of mathematics but utilises pupils’
knowledge of percentages to solve different parts of this module.
Theme/Strand:
Unit title:
Target group of pupils:
Timing of unit:
FDPRP, algebra, handling data
MP3 players
Year 10
Autumn term
Curricular targets:
•
Construct simple scatter graphs on paper and using ICT. (HD: part of step 7)
•
Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and
find the outcome of a given percentage increase or decrease. (FDPRP: step 7)
•
Express simple functions in symbols; represent mappings expressed algebraically. (SFG: step 6)
•
Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising
from real situations. (SFG: step 8)
Other curricular targets
•
Know that if the probability of an event occurring is p, then the probability of it not occurring is (1 – p).
(Probability: step 7)
Unit description
In this unit pupils investigate buying and using an MP3 player. They compare different MP3 players, using
proportional reasoning.
The pupils will need access to ICT and, if possible, the internet to research prices and data about MP3 players. If the
internet is not available, a range of shopping catalogues will provide the same information.
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Lancashire Mathematics Newsletter
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Lancashire Mathematics Newsletter
Starter or Plenary Activity
Students can work in groups to try and find all the solutions.
The teacher picks a group to start offering solutions - Ideally, answers should be justified. Each correct answer
results in a letter. Points can be awarded if you want to use the activity as a competition.
The group continues until an incorrect answer is given (a cross appears!!) or until they have exhausted their
collection of answers. Either way, the next group picks up the challenge to try and solve the problem. This is taken
from Higher Number Samples (GCSE) Subtracting Fractions.
Renewed Framework Website
From Autumn 2008, the Renewed Framework will have its own dedicated website, rather than being part of the
‘Standards’ site. This will allow for resources, such as the Overcoming Barriers – moving from level 3 to 4 and
moving from level 2 to 3, to be linked to the relevant blocks within the Renewed Framework.
The Primary National Strategy team are taking advantage of the change by revamping the organisation of the site
and some of the documents. This is in response to the Williams Review which suggests the Renewed Frameworks
be reconsidered in a ‘more suitable, user-friendly form’.
One of the key changes is to the organisation of the Block and Unit Overviews. Each Unit Overview will begin with
the Learning Overview, rather than the table of objectives and assessment for learning prompts.
Also, in order to further develop assessment for learning, the Learning Overviews will have assessment opportunities
linked to the Assessment Focuses from the APP materials. These are similar to the ‘Look, Listen and Note’
suggestions in the Early Years Foundation Stage Non-statutory guidance.
Below is an example from Year 3 Block A Unit 1
Children locate and position multiples of 10 or 100 on a number line and recognise the relative position of other
numbers. They use their knowledge of place value to establish that 374 is closer to 400 than 300 and closer to 370
than 380. They add or subtract mentally one-digit numbers to or from two-digit numbers, bridging through a
multiple of 10 where appropriate. For example, they calculate 72 - 8 by subtracting 2 to give 70 and then subtracting
the remaining 6, using a number line to record the steps if necessary. Children use counting on when adding 5 to 36
or counting back when subtracting 5 from 39.
Assessment focus: Ma1 Reasoning
Look for children who identify patterns in results, for example:
6 + 5 = 11
16 + 5 = 21
26 + 5 = 31
Maths 4 real 1: Set A - Ratio and Proportion
Video Information
Length:
15 minutes
Key Stage 4
Secondary
Mathematics
Number
Pupil Resources (5)
Download video
Log in to download
•
•
•
•
•
•
•
•
Synopsis
In the cafeteria, Ben and Katie introduce some simple ideas about ratio. Chef Neil Nugent uses ratios in his recipes.
Ben and Katie are called in to test three different versions of Neil’s new dip and decide which has the best proportion
of garlic. A recipe to serve four is given, and Ben describes how to adjust the recipe to cater for different numbers of
people.
Neil’s latest korma sauce will have to be scaled up for factory production, so he has to know exactly how much of each
ingredient he has used to make his batch of three jars. Katie shows us the main ingredients for this quantity of sauce
and asks how we could calculate the amounts needed to produce 4,000 jars. Katie will need to visit the factory to find
out how Neil’s recipe is adapted for a production run.
In Tick or Trash, Ben and Katie tackle a sharing problem, based on projects supported by Comic Relief. Katie
explains her mistake and emphasises the importance of checking that an answer is sensible.
http://www.teachers.tv/video/1740
Look for children who use the patterns they identify to generate further calculations. As children explain their
results, look for the reasoning they use to decide if a particular example will appear later in their list of
calculations. Using the pattern above for example, look for children who predict and explain which addition will
give the first total greater than 50 or greater than 100.
Year 6 Test Analysis Spreadsheets
The Lancashire Mathematics Team spreadsheets for SATs analysis have been updated for 2007/2008.
These are now compatible with the new RAISEonline QLA analysis to enable easy transition between both for
more in depth analysis.
The guidance document contains the following information:
1) Entering the data into the Analysis Spreadsheets
2) Entering the data into RAISEonline
3) Exporting data from RAISEonline into the Analysis Spreadsheets
4) Exporting data from the Analysis Spreadsheets into RAISEonline
5) Analysing the data
6) Printing the spreadsheets
7) Using graphs to support analysis
8) Creating individual strand graphs
The analysis spreadsheets can be found at:
http://www.lancsngfl.ac.uk/curriculum/math/index.php?category_id=240
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Lancashire Mathematics Newsletter
Useful Websites for Teaching Fractions, Decimals, Percentages, Ratio and Proportion
http://clg.coventry.gov.uk/ccm/csln/private/curriculum/mathematics-file-storage-items/gordons/gordons.en
This link will take you to simple teaching programmes from Coventry LEA that are
useful for teaching a range of objectives. You will find the fractions programmes
in the number section. The programmes include:
FDP balance: use the equivalence between fractions, decimals and percentages
to make the scales balance.
Fractions: investigate different aspects of fractions - half/not half, fraction
charts, number lines etc.
Higher and lower: as the TV game 'Play your cards right' - using numbers,
fractions, decimals and measures.
Pizza Fractions: work out the price for a slice of pizza - fraction of amounts.
Percentage / Fraction Chains: use related facts to find percentages of amount and quantities.
Proportion grids: use the various sized grids to represent different fractions, decimals, percentages and ratios.
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/percentages/index.htm
This site contains a short series of interactive demonstrations focusing on finding
percentages of money.
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Lancashire Mathematics Newsletter
Fractions, Decimals, Percentages, Ratio and Proportion
Resources for KS3 and KS4
Here are some ideas and Strategy Resources that may help classroom practitioners when teaching Fractions, Decimals,
Percentages, Ratio and Proportion. Most of the resources listed can be accessed directly through the Lancashire
Secondary Mathematics website which can be found at
www.lancsngfl.ac.uk/curriculum/math
If you have or know of any useful resources that you would like to share with other colleagues in Lancashire please
email the Secondary Mathematics team at LPDS.Numeracy@ed.lancscc.gov.uk and we will pass these on via the next
newsletter and the website.
Year 9 Booster Lesson 3
www.lancsngfl.ac.uk/curriculum/math
Secondary Mathematics / Intervention / Y9 Intervention / Booster Kit
Using the target board on OHT M3.1, ask pupils to calculate a percentage increase/decrease of one of the amounts.
Invite them to explain how they arrived at their answers. Discuss their methods.
Encourage pupils to use jottings, when appropriate, to record steps in their working.
Q How did you work that out?
Q How did you partition 35%?
As preparation for the main teaching, ask:
Q If you increase an amount by 15%, what percentage of the original will you then have?
http://nrich.maths.org/content/id/5540/preview/
This section of the nrich website has resources to enrich the experiences of children who are just
being introduced to fractions. Each problem is accompanied by hints and examples of pupils'
solutions in addition to notes.
http://www.amblesideprimary.com/ambleweb/mentalmaths/fracto.html
This website allows the children to see how a fraction changes as the numerator and
denominator are increased or decreased with a link to the decimal equivalent.
http://nlvm.usu.edu/en/nav/frames_asid_102_g_1_t_1.html
This site allows you to select different shapes to be the whole and change the number of pieces within it. By clicking on
different portions, it creates the fraction representation.
Kangaroo Maths
This is a free resource that can be linked to directly through the Lancashire website. There is a wealth of resources on
this website from interactive Schemes of Work and to levelled homework sheets. Bring on the Maths is part of
Kangaroo Maths.
www.lancsngfl.ac.uk/curriculum/math
Secondary Mathematics / ICT (ictac):website links
http://www.kangaroomaths.com/samples/index.htm
Bring on the Maths
Bring on the Maths is an incredibly flexible resource that can be used to assess learning and inform future planning
and teaching. It can be used as a starter or plenary activity, during the main section of a lesson, or as a series of
homework tasks to track students’ progress during the year. The key to its success is that it provides great learning
opportunities through interactive discussion. Below are some ideas for using the resource effectively in your
classroom.
Teachers TV : Maths 4 Real
Maths 4 Real is an excellent resource that is aimed at KS4 but can be easily adapted to use with KS3 classes. With
each clip there are past GCSE questions which can be used interactively with the films. There are also question
sheets which help focus pupils’ attention to the main points in the programme. Although each clip is only 15 minutes
in length the resource will require longer than this if used interactively within the lesson.
http:// www.teachers.tv/video/1740
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Lancashire Mathematics Newsletter
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Lancashire Mathematics Newsletter
Maths is Special
http://www.gamequarium.com/fractions.html
This site has a variety of fraction games which
look at fractions of shapes and numbers.
The Special schools were keen to hold the ‘Maths is Special’ events again this year and these were
organised through the enthusiasm and hard work of members of the Special School Network
cluster. Thanks need to go to all the members of the team who organised such super activities as
without this hard work the events wouldn’t be able to take place. A special thanks to Lee Toulson
of Astley Park School and Carol Davies of Pear Tree School for their hard work in organising and
hosting the events.
Five schools took part in the “Maths is Special Key Stage 3 Challenge” where the children had to
work as a team to meet the challenges set them. There were rounds on problem solving with
number, time and listening skills, data handling, measures and logic money problems. Many
thanks to Carole Brooks, Michelle Westhead, Lee Toulson, Ian Richardson and Rachel Kay for
organising such varied and interesting activities. All participants were awarded certificates with
Rossendale Tor View coming second and Great Arley winning the event, both teams receiving
medals. Congratulations also to Astley Park, Pendle Community High School and West Lancashire
Community High.
The “Maths is Special Event” took place at Pear Tree School and a special thank you to the schools
who provided the stimulating games. Activities included practical activities on data handling, size
and measure supported by ‘The Three Bears’ interactive book, directional work using ‘Bee-Bot’
programmable floor robots and sequencing and ordering using tactile shape tiles. There was also a
selection of different number games. Students from Pear Tree School led the children through a
Dave Godfrey song to end the event. All participating schools - Moor Hey, The Loyne, Holly
Grove, Kingsbury, White Ash, Pear Tree, Mayfield, Great Arley, The Elms and Royal Cross Primary
- received a framed certificate and all the children attending received individual certificates.
http://illuminations.nctm.org/Activities.aspx?grade=all&standard=all
The illuminations website has a variety of resources for teaching fractions.
Equivalent fractions, fraction game, fraction model I, fraction model II, fraction
model III.
The fraction model tools explore several representations for fractions using
adjustable numerators and denominators. You can see decimal and percent
equivalents, as well as a model that represents the fraction.
http://www.atm.org.uk/boris/fractions/
This site links objectives related to the three areas to appropriate
probing questions to support diagnosis of specific misconceptions or
gaps. These, in turn, are linked to teaching images to address the
difficulties that children are encountering.
Every Child Counts Edge Hill University in partnership with Lancashire County Council has been appointed to develop the Every Child Counts programme. The aim is to provide intensive support in mathematics to enable the lowest attaining children in Year 2 to make greater progress towards expected levels of attainment in mathematics and to achieve level 2 or where possible level 2B or better by the end of Key Stage 1. For further information on this go to www.edgehill.ac.uk/everychildcounts/. In June 2008 nine Lancashire Schools took part in a pilot study of the new training programme for Every Child Counts (ECC). The teachers took part in 5 days training at Edge Hill University and then worked 1‐1 with 2 children in their school settings. The teachers were very enthusiastic about the training and the impact it had on their teaching not only when working independently with the children but also back in the classroom. As this was a pilot project the teachers only worked with the children for a short time, but they all felt it had had a massive impact on the children not only with their improvement with number but also on their self esteem and confidence. The teachers were all keen to continue the programme and some support is going to be given by a primary maths consultant next year to build on this experience. A special thanks to all the schools, St John’s RC, Skelmersdale, St John’s RC, Burscough, Bishop Martin, Hillside, Holland Moor, Aughton Christ Church, Woodland, Brookfield Park and Tarleton CP for taking part in the programme and for their hard work, enthusiasm and commitment to the project. In September ECC is being launched in 21 Local Authorities. Lancashire is one of these authorities and ten schools will take part in the programme. A Teacher Leader, Emma Radcliffe, from Peel Park Primary, Accrington has been appointed by Lancashire who, alongside a National Trainer, will support the Intensive Support Teachers working in each school. 8
Lancashire Mathematics Newsletter
Williams Review of Mathematics Teaching
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Lancashire Mathematics Newsletter
Year 3 – Read and write proper fractions (e.g.
,
), interpreting the denominator as the parts of a
whole and the numerator as the number of parts; identify and estimate fractions of shapes; use
diagrams to compare fractions and establish equivalents
Use the input button to enter ten flowers. Randomly colour
in five of them by clicking in the middle of the flower.
How many flowers are there? How many of them are
coloured red?
⎛5⎞
What fraction of the flowers is coloured red? ⎜⎝10⎟⎠
The Williams Review of Mathematics Teaching in Early Years Settings
and Primary Schools has now been published.
The key recommendations which impact directly on teachers
currently working in schools are outlined below:
Recommendation 3: There should be at least one Mathematics
Specialist in each primary school, in post within 10 years, with deep
mathematical subject and pedagogical knowledge, making
appropriate arrangements for small and rural schools.
Implementation should commence in 2009 and be targeted initially to
maximise impact on standards and to narrow attainment gaps.
Recommendation 4: The DCSF should commission a set of materials on mathematical mark
making and children’s mathematical development which can be used to support early years
practitioners’ CPD.
Recommendation 5: The forthcoming review of the EYFS in 2010 considers the inclusion of
time and capacity within the early learning goals.
Recommendation 7: Before any intervention programme is implemented, it is important that
the child is committed to it and that the parents or carers are involved and understand the
nature of the programme. These issues, and the question of the integration of intervention
teaching and classroom teaching, should be considered in the development phase of Every
Child Counts. (Recommendation 8 goes into further details regarding the ‘Every Child
Counts’ intervention programme.)
Recommendation 9: The primary National Curriculum in Mathematics should continue as
currently prescribed, subject to any changes which may result from Sir Jim Rose’s forthcoming
review of the primary curriculum; the latter should examine the concept of ‘use and
application’ more generally across subjects to assess whether the mathematical or other
aspects of the curriculum need amendment.
Recommendation 10: A renewed focus by practitioners on ‘oral and mental mathematics’.
Providers of ITT and CPD should ensure that this practice receives careful attention, both
during ITT and in CPD programmes.
The report can be ordered or downloaded from the link below:
http://publications.teachernet.gov.uk/default.aspx?
PageFunction=productdetails&PageMode=publications&ProductId=DCSF-00433-2008
Can you say this another way?
⎛1⎞
⎜ ⎟
⎝2⎠
If necessary demonstrate that you have actually coloured in half of the flowers by sharing them into two groups.
Repeat with other numbers in order to demonstrate factions as parts of a whole.
Year 4 – Use a fraction to describe a part of a whole
Use the input button to create 8 objects such as counters.
Click on the circle button and choose one circle. Place six of
the counters in the circle.
Ask the children to say what fraction of these counters is
⎛6⎞
circled?
⎜ ⎟
⎝8⎠
You can demonstrate that this is equivalent to ¾ by
arranging the counters in two lines of 4
Repeat with other numbers and other fractions.
Year 5 - Understand percentage as the number of parts in every 100 and express tenths and
hundredths as percentages
Having input 30 objects, arrange them into rows and
columns by clicking on the
button.
Change the colour of the 3 objects on the end of each
row.
⎛1⎞
⎜ ⎟
What fraction of each row is highlighted? ⎝ 10 ⎠
What fraction of the 30 objects is highlighted?
⎛ 3 1⎞
⎜ = ⎟
⎝ 30 10⎠
What is this as a percentage? (10%) Repeat with other
amounts and fractions.
Year 6 – Express one quantity as a percentage of another
Select 8 objects and put them in a circle. Say that this number is
25% of the total amount. The rest are hidden. How many more do
there need to be for this to be true?
Ask the children to give two other amounts where one is 25% of
the other; where one is 5% of the other; what about 40?%
Find all of the ITPs through the Lancashire site – www.lancsngfl.ac.uk/curriculum/math under Interactive
Teaching Programmes in the ‘Using ICT in Mathematics’ section on the Primary Site.
Alternatively find them in the library section of the renewed framework.
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Lancashire Mathematics Newsletter
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Lancashire Mathematics Newsletter
Take an ITP ……. Counting
This is a regular feature of the newsletter. Each issue we will look at an ITP and suggest activities which link to
objectives from Reception to Year 6.
Ensure you are using version 0.6 of this ITP. (Check by clicking on the
button after opening the
program)
If necessary download the latest version from the library section of the renewed framework.
Year R – Share objects into equal groups and count how many in each group.
Click on the input button
and select the
number 10 and the ladybird icon. Press the play
button and ten ladybirds will randomly appear on the
screen.
Click on the circles button
and choose two
circles for sorting.
Ask the children how many ladybirds there are.
Can they tell you how many there will be in each
circle if you share the ladybirds equally between the
two circles? Demonstrate the process of sharing the
ten objects between the two circles to show that half
of ten is five.
Girls and Mathematics Project
The second girls and maths project has proved to
be as successful as the first round. Twenty three
schools took part this year and provisional results show that the
percentage of girls achieving level 4 has increased in most schools, with
some by as much as 25%. More importantly, all schools reported a
significant improvement in attitudes and confidence.
The top 3 most successful strategies to improve girls’ confidence:
♦ Use of paired discussion and thinking time
Girls liked to have time to discuss their answers and have their
ideas confirmed before ‘taking the risk’ in answering the question.
Year 1 – Use the vocabulary of halves and quarters in context.
Click on the input button and select eight fish.
Using the circle button, choose one circle and ask
a child to put half of the fish into it. How many will
there be?
If the children do not know the answer,
demonstrate that we can find half of a number by
sharing the objects between two.
Repeat with other numbers up to finding half of
twenty.
♦ Enable girls to work together in single gender groups
A girls only maths club - ‘Girls Allowed’ – gave girls a platform to ask
questions and clarify strategies in a small group without anyone
‘laughing at us’.
♦ Use of process success criteria
This gave girls a scaffold to support their learning and
the opportunity to have success, even when they hadn’t got the
answer correct.
Year 2 – Find one half, one quarter and three quarters of sets of objects.
Click on the input button and enter twelve stars
randomly on the screen. Using the circles button
select two large circles and share the stars between
the two groups to demonstrate a half of twelve.
Show the children how to halve each half using four
more small circles (sharing the six stars into two
smaller groups).
Demonstrate that we have now found one quarter of
twelve.
Use this image to model how we find two quarters
and three quarters of twelve.
Repeat with other numbers such as twenty and
twenty four.
These strategies can be utilised in any age group and transferred
across the Key Stages.
There will be an opportunity to become involved in the project in the
Autumn Term. For further details please contact Tracy Dimmock on
01257 516102 or look out on the portal early in the Autumn Term.
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Lancashire Mathematics Newsletter
These materials are designed to help Year 3 and Year 4 teachers ensure their
children make secure progress from Level 2 to Level 3. The materials focus on
key areas of mathematics that Year 3 and Year 4 children working at level 2
often find challenging. The choice of objectives was informed by a scrutiny of
optional QCA test scripts of children whose attainment fell below, but was close
to, the level 2 to 3 boundary.
Disclaimer
Copyright
Select a strand and then an objective to be addressed.
•
Click on the objective and you are able to drill
down to more precise aspects of the objective
which are set out as “Can I” questions.
This is a game for 4 or more players.
Each player needs a 10x10 piece of squared paper.
They cut up their squares in to sections of 10,15,20,25 or 30 squares and then everyone shuffles the
pieces together.
The children take turns to throw a dice marked 10%, 15%, 20%, 25%, 30% and 30% and they collect the
appropriate strip.
The winner is the first player to collect exactly 100%.
Introduction
Overcoming barriers in mathematics –
helping children move from level 2 to level 3
Select a highlighted strand from the list to view the objectives
Using and applying mathematics
Counting and understanding number
Knowing and using number facts
Odd one out
Calculating
Understanding shape
Measuring
Show children a selection of 4 fractions where 3 of them are equivalent.
Children have to identify the odd one out. You can download sets of Fraction Matching Cards from
Sparklebox to create your selection.
Handling data
© Crown copyright 2008
00099-2008 CDO-EN
Overcoming barriers in mathematics – helping children move from level 2 to level 3
•
Lancashire Mathematics Newsletter
Percentage jigsaw
Overcoming Barriers in Mathematics Moving Children from Level 2 to Level 3
The materials are organised under the seven strands
for mathematics set out in the Framework; although
you will notice Using and Applying is not live – it is
integrated into the other six strands.
19
Home
Understanding shape
Click on an arrow to select an objective
Relate 2-D shapes and 3-D solids to drawings
of them; describe, visualise, classify, draw
and make the shapes
Draw polygons and classify them by
identifying their properties, including their
line symmetry
Visualise 3-D objects from 2-D drawings; make
nets of common solids
Draw and complete shapes with reflective symmetry;
draw the reflection of a shape in a mirror line along
one side
Clicking on these takes you to a page that always has
the same format.
Read and record the vocabulary of position, direction
and movement, using the four compass directions to
describe movement about a grid
Use a set-square to draw right angles and to identify
right angles in 2-D shapes; compare angles with a
right angle; recognise that a straight line is
equivalent to two right angles
Recognise horizontal and vertical lines; use the
eight compass points to describe direction;
describe and identify the position of a square
on a grid of squares
Know that angles are measured in degrees and
that one whole turn is 360°; compare and order
angles less than 180°
© Crown copyright 2008
00099-2008 CDO-EN
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Shape
Draw polygons and classify them by identifying their
properties
They focus on the following cycle:
Monitoring children’s prior learning
Can I make, name and describe 2-D and 3-D shapes?
Can I sort shapes choosing my own criteria?
Give the children a conversion chart for some simple fractions, percentages and decimals
Such as:
Shape
Review – focused questions
to help assess current
understanding and identify
any specific misconceptions.
Can I make, name and describe 2-D and 3-D
shapes?
Can you identify and name the
shapes in this set that have:
• no right angles;
• all sides equal?
Pick one shape and describe it to
a friend. Can your friend identify
your shape?
Teaching
guidance
Teach – direct
teaching, practical
activities, models
and images,
mathematical
vocabulary
© Crown copyright 2008
00099-2008 CDO-EN
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Example review questions
Find and name the shapes in this
set that are not quadrilaterals.
Consolidation
and practice
Here are some drawings of 3-D
solids. Which drawings show
cylinders? Name the other
shapes you can see in the
drawings. Which shapes are
prisms?
Find a solid shape that has four
triangular faces and one square
face. What is it called?
Opportunities
to use and apply
Class snap
Confirming
learning
20%
1/5
0.2
25%
1/4
0.25
50%
1/2
0.5
90%
9/10 0.9
75%
3/4
50%
3/4
0.5
© Crown copyright 2008
00099-2008 CDO-EN
Overcoming barriers in mathematics – helping children move from level 2 to level 3
Practise – opportunity to
consolidate
understanding with links
to available resources
such as Springboard or
ITPs
Apply – alternative
contexts within
which learning can
be used and applied
Review – probing
questions to
establish learning
is secure
Copies of the CD and accompanying guidance booklet can be ordered from
DCSF publications, Tel 0845 60 222 60 Ref: 00149-2008PCK-EN
0.75
SNAP
Divide the class into three groups, Fractions, Percentages and Decimals. Number each member of
the team. Number 1 team members write down, in secret, any number on the board that belongs to
their team (so a decimal team member will choose a decimal). The teacher asks the children to
show the numbers written by saying ‘Show me’. If two of the numbers are the same, i.e. 50% and 0.5,
whichever team shouts ‘SNAP’ first wins the point.
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Lancashire Mathematics Newsletter
11
Mental Oral Starters for Fractions, Decimals, Percentages, Ratio and Proportion
Overcoming Barriers to Learning L3 – L4
Equivalent fraction matching game
Fractions on a number line
2008
Examples from L3 - L4 Barriers on Learning Y6 Booster support on FDPRP
Give out cards to the children with a variety of fractions on them. Children move around the room and form a
group with equivalent fractions. Children give explanations as to why the fractions are equivalent.
This activity could be extended to include equivalent decimals and percentages.
Lancashire Mathematics Newsletter
Objective - Counting and understanding number - Use decimal notation for tenths, hundredths and
thousandths, partition and order decimals with up to three places, and position them on a number line
Monitoring prior learning - Can I read, write and order decimal numbers?
Display a washing line from 0 to 1. Give out fractions and ask children to place in correct place on number line
with reasons why.
Sample review questions:
Alternatively, display either fractions or decimals and ask children to place the equivalent percentage on the
number line.
•
Tell me a number that lies between 5.2 and 5.3
•
Tell me a decimal fraction that lies between 4.17 and 4.18
Fractions loop card game
•
What does the 4 mean in each of these numbers? 3.4
•
Write the decimal fraction equivalent to three tenths and two thousandths
•
Put the following in order from largest to smallest:
Children have to identify the answer from the
question to complete the loop. You can find a free set
of fractions and decimal loop cards for year 5 fractions
and decimals at Sparklebox:
http://www.sparklebox2.co.uk/171-175/s2b171.html
a) 5.25, 15.3, 5.78, 5.87, 5.2
•
Show Me Fraction strips
4.5 0.34 3.654
b) 1.5, 1.375, 1.4, 1.3, 1.35, 1.425
Place these decimals on a number line from 6.9 to 7.1: 6.93 6.91 6.99 7.01 7.06
Teaching guidance See attached sheet
Each child will need a number strip 0-1 and an elastic band or a hair grip.
Ask the children to slide the elastic band/hair grip along to where they think 2/3 would be. Repeat with other
fractions such as 1/4, 3/4, 1/8, 7/10 etc.
Ask questions such as ‘Here’s a fraction - double it’.
Consolidation and practice
Decimal number line ITP
Spreadsheet – a) Place value charts and partitioning tool / b) Increasing number grid generator
0
Show me 2/3
1
Alternatively ask children to show fractions which are more, or less than the stated fraction:
Show me a fraction which is a bit larger than: a half; three quarters; two thirds…
Show me a fraction which is just less than: a quarter; an eighth; three tenths…
Show Me Decimal strips
Ask children to slide the elastic band/hair grip along to where they think 0.6 would be. Similarly, ask children to
show the position of other decimals such as: 0.1, 0.9, and 0.4
Show a card with a percentage and ask the children to show the equivalent decimal.
‘Show me a % greater than …’
Fractions Bingo
Springboard 6 Lesson 1 Place value and resources / Springboard 7 Unit 5 section 3 Decimals / Springboard 7
Unit 13 section 4 Ordering fractions and decimals
Opportunities to use and apply
•
Calculation e.g. 17.82 -
= 17.22
•
Using a calculator, e.g. changing 7 to 0.07 in one step (operation)
•
Converting metric units e.g. write 3855 grams in kilograms; write 750 millilitres in litres
•
Word problems involving mixed units of measure e.g. ‘A packet contains 1.5 kilograms of guinea pig food.
Remi feeds her guinea pig 30 grams of food each day. How many days does the packet of food last?’
•
Number sequences, e.g. continue these patterns:
1.8 1.6 1.4 1.2 … /
1.92 1.94 1.96 1.98 … /
Children have a bingo board each or one between two.
Confirming learning What do you look for first when you order a set of decimal numbers? Which part of each
number do you look at to help you?
The caller says the fraction and children use counters to cover the corresponding fraction on their boards.
For an alternative version, the caller calls/shows decimals or percentages and the players match the
corresponding fraction.
Fraction bingo base boards are available free to download from Sparkle Box :
http://free2.sparklebox2.co.uk/downloads/s2b86.pdf
•
Which number lies exactly halfway between 1.2 and 1.5?
•
Write two different decimals that contain 3 units and 7 hundredths
•
On a number line, which of these numbers is closest to 1? 0.2, 0.92, 1.2, 1.9 Explain how you know
using words/ diagrams
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Lancashire Mathematics Newsletter
Overcoming L3 - 4 Barriers to Learning Y6 Booster support
Objective - Calculating
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Lancashire Mathematics Newsletter
Statue
Find fractions and percentages of whole-number quantities
Monitoring prior learning - Can I calculate simple percentages of whole numbers or quantities?
Sample review questions
This statue stands on a hill in Arona, Italy. It is
possible to climb up the inside of the statue and look
out through the head.
•
Find 10% of £40
•
What is 25% of 50?
•
Use a calculator to find 20% of £362
•
Find 75% of 200 ml. How did you do this?
•
There is 50% off all prices in a sale. An MP3 player costs £45 in the sale. How much was it before the
/
What is 99% of 200?
Starting with any information in the picture, estimate,
in metres:
sale?
the length of the statue’s arms
the length of its ears
the circumference of its head
Teaching guidance See attached sheet
What assumptions did you make?
Consolidation and practice
Spreadsheet: Fraction and percentage equivalence / Calculate percentages
Springboard 6 Lesson 9 Calculate simple percentages of whole number quantities
Section 2 Fractions and percentages
/ Springboard 7 Unit 13
Opportunities to use and apply
•
Money, e.g. ‘The agent’s fee for selling a house is 5%. Calculate the fee on a house sold for £80,000
•
Look for examples of and ask questions about percentages in everyday life, e.g. use local newspaper
advertisements to work out how much money you are saving after a percentage discount.
•
Data handling, e.g. children collect data from 36 people, use a data handling software package to present
this as a pie chart, and respond to questions about the percentage represented by each section of the pie
chart
Confirming learning
Robots
Give the children a robot drawn on squared paper.
•
Kate says, ‘To find 10% of an amount, you divide it by 10. So to find 20% of an amount, you divide it by
20. Is Kate correct? How do you know?
•
What calculations would you do to find 15% of £150?
On squared paper, draw a similar robot with dimensions
half those of the original (i.e. so that their lengths are in
the ratio 1 : 2).
•
When finding percentages of quantities, what percentage do you usually start from? How does this
percentage help you work out other percentages?
Next draw a third similar robot which is three times the
size of the smaller one. (Ratio 1 : 3)
•
Tell me two amounts where one is 25% of the other.
What are the ratios of the heights of the original and the
largest robot?
Express this ratio in the form 1 : x.
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Lancashire Mathematics Newsletter
Practical ideas for teaching ratio and proportion
Photographs
13
Developing the L3/4 CDROM
Objective
Use the same photograph enlarged in different scales to ask questions such as:
Find the ratio of the corresponding lengths in photos B and C, expressing them as a ratio C : B, reducing it
to its lowest terms.
Monitoring prior learning
Now find the ratio of lengths A : C
Sample review questions
What do you need to do to check that the four photographs are mathematically similar?
Teaching guidance
Consolidation and practice
Opportunities to use and apply
Confirming learning
Scale models
Use toys such as scale models of cars, trucks, aeroplanes etc. These are often in the ratio 1:64 or 1:72.
Ensure the children are aware that this means 1 unit of measurement on the model is the equivalent to 64
or 72 units of measurement on the full scale item e.g.1cm on the model is 64 cm on the full scale vehicle.
Ask questions such as:
What is the length of the full sized car?
What is the diameter of the full sized wheel?
Calculate the capacity of the trailer of the full sized truck?
Lancashire Mathematics Newsletter
Lancashire Mathematics Newsletter
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Lancashire Mathematics Newsletter
14
Year 1
Vocabulary bookmark
Fractions
part
equal parts
share
equal groups
one whole
one half
one quarter
Year 4
Vocabulary bookmark
Fractions and decimals
part, equal parts
fraction
one whole
half, quarter
eighth
third, sixth
fifth, tenth
twentieth
hundredths
numerator
denominator
ratio
proportion
in every, for every
decimal
decimal fraction
decimal point
decimal place
Year 2
Vocabulary bookmark
Fractions
part
equal parts
share
equal groups
fraction
one whole
one half
two halves
one quarter
two quarters
three quarters
four quarters
Year 5
Vocabulary bookmark
Fractions, decimals, percentages, ratio
and proportion
part
equal parts
fraction
proper/improper fraction
mixed number
numerator
denominator
equivalent
reduced to
cancel
one whole
half, quarter, eighth
third, sixth, ninth, twelfth
fifth, tenth, twentieth, hundredth
proportion, ratio
in every, for every
to every, as many as
decimal
decimal fraction
decimal point
decimal place
percentage,
per cent, %
Year 3
Vocabulary bookmark
Fractions
part,
equal parts
fraction
one whole
one half
two halves
one quarter
two quarters
three quarters
four quarters
one third
two thirds
one fifth
one sixth
one eighth
one tenth
two thirds
three fifths
Year 6
Vocabulary bookmark
Fractions, decimals, percentages, ratio
and proportion
part, equal parts
fraction,
proper/improper fraction
mixed number
numerator
denominator
equivalent, reduced to
cancel
one whole
half, quarter, eighth
third, sixth, ninth, twelfth
fifth, tenth, twentieth
hundredth, thousandth
proportion, ratio, in every, for every
to every
as many as
decimal, decimal fraction
decimal point
decimal place
percentage, per cent, %