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MATHEMATICS - UNIT PLAN 2008-2009 – B2- SECURING NUMBER FACTS, UNDERSTANDING SHAPE UNIT – LA CARRY OVERC2 – HANDLING DATA AND MEASURES – HA/MA – FDPRP FOCUS

Teacher: KD/JJ/SB Week beginning: Year group: Six 09/02/09 - W6 (5 days)

Class set: KD-HA, JJ-MA, SB-LA/SEN Booster/ConsolidationKD-HA, JJ-MA, PM-LA, SB-LA, SW-SENIntervention – LP – springboard/Wave 3Curricular Target:Layered Targets:

Objectives that have been taken form the Primary Framework for mathematics (Strand in italics):Mental/oral:

A) Knowing and using number facts - :Use knowledge of place value and multiplication facts to 10 x 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 x 7, 4.8 ÷ 6) (Can I rapidly recall my times tables facts?)

B) Using and applying mathematics - :Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use(Can I solve single and multi-step problems using mental strategies?)

Main activity:(Can I use the inverse operations and tests of divisibility to check results?)

1. Calculating – :Use a calculator to solve problems involving multi-step calculations(Can I use a calculator to solve problems involving more than one step?)

2. Handling Data - :Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate; draw conclusions and identify further questions to ask(Can I use data to solve problems?) :Describe and predict outcomes from data, using the language of chance or likelihood(Can I use data to work out problems about chance?):Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs; interpret pie charts(Can I represent data in different ways and understand its meaning?) :Describe and interpret results and solutions to problems, using the mode, range, median and mean(Can I solve problems, using mode, range, median and mean?)

3. Measuring - :Select and use standard metric units of measure and convert between units, using decimals to two places (e.g. change 2.75 litres to 2750 ml, or vice versa) (Can I convert measures between units including decimal numbers?):Read and interpret scales on a range of measuring instruments, recognising that the measurement made is approximate and recording results to a required degree of accuracy; compare readings on different scales, for example when using different instruments(Can I read and answer questions about scales and write down my answer as accurately as the question require?)(Can I compare readings from different scale?)

4. Counting and understanding number - :Express one quantity as a percentage of another (e.g. express £400 as a percentage of £1000); find equivalent percentages, decimals and fractions.(Can I work out a quantity as a percentage of another and find equivalent percentages, decimal numbers and fraction?)

Key objectives in bold

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ASSESSMENT FOCUS: MA2, FRACTIONS, DECIMALS, PERCENTAGES, RATIO AND PROPORTION As children measure, using different metric measures, look for evidence of their understanding of decimal numbers. Look for children who record measurements as mixed units, for example, 3 m 25 cm, and those who use decimal notation to record this as 3.25 m. Look for evidence that children understand the relationships between, for example, millimetres, centimetres and metres, and use their understanding of decimal numbers to express a measurement in different ways. For example, look for children who know that 1.25 m = 125 cm = 1250 mm, or that 250 ml = 0.25 l or one quarter of a litre. Look out for children who order decimal values as they compare measurements, recognising, for example, that 2.2 is greater than 2.15.

Continuous objectives that have been taken form the Primary Framework for mathematics (Strand in italics):

Using and applying mathematics – Explain reasoning and conclusions, using words, symbols or diagrams as appropriate

Year 6 Block C - Handling data and measures Speaking and listening objectives for the block Use a range of oral techniques to present persuasive argument

Vocabulary

problem, solution, calculate, calculation, method, explain, reasoning, reason, predict, pattern,

relationship, classify, represent, analyse, interpret

fair, unfair, risk, doubt, likely, unlikely, equally likely, likelihood, certain, uncertain, probable, possible,

impossible, chance, good chance, poor chance, no chance, equal chance, even chance, outcome,

biased, random

estimate, measure, standard metric units of measurement and their abbreviations

data, information, survey, questionnaire, graph, chart, table, scale, interval, division, horizontal axis,

vertical axis, axes, label, title, pictogram, bar chart, bar-line chart, line graph, pie chart

frequency, mode, maximum/minimum value, range, mean, average, median, statistics

Building on prior learning and intervention materials (Springboard/Wave 3)Check that children can already:

construct frequency tables, pictograms, bar charts and line graphs to represent the frequencies of

events and changes over time

collect, select and organise data to answer questions; draw conclusions and identify further

questions to ask

use ICT to collect, analyse, present and interpret information

find and interpret the mode of a set of data

describe the occurrence of familiar events using the language of chance or likelihood


Homework: Due in by date

Relevant to when homework is set – children to be given 5 school days to complete homework.

Teaching and Learning focus

Introductory teaching to assess and review learning

Direct teaching of new knowledge, skills and concepts, with opportunities to practise and apply learning

Interactive whole class teaching

Consolidation and further practice

Interim review of achievement and progress

Intervention support with groups

Enquiry, extension enrichment work, problem solving, reasoning

Summary assessment of progress over the unit with children

Evaluation (inc brief comments which will inform your future planning i.e. observations/success of lessons/resources/children/concepts that need revisiting):


Mathematics planning – SPR1-WK6-Wb-090209Mental/Oral Main Activity Plenary/Key Questions Assessment for

LearningQuestions and success criteria

Slide - 1 Learning intentions

A) Multi-step problems using mental strategies?Maths plus from Heinemann - Mental maths practice

Can I solve single and multi-step problems using mental strategies?

Slide - 2HA/MA/LA20 questionsQ1-10 (5 secs each)Q11-15 (10 secs each)Q16-20 (15 secs each)

HA/MA-FDPRP involving measures and data handlingLA – Symmetry – reflection and rotation -recognise where a shape will be after reflection

HA/MA – slide 3&4Can I work out a quantity as a percentage of another and find equivalent percentages, decimal numbers and fractions?Look at SATs questions level 4 and 5Gauge understanding - ask children to explain their reasoning and conclusions. Relate fractions to decimals and percentages. Discuss how to use our knowledge of multiplication and division in order to find a given percentage. Use comparison methods. Explain that they are expected to understand how to find the percentage and/or fractions of amounts involving measures, quantities and values. They are also expected to represent, explain and calculate fractions and percentages in given data sets – data handling. LA4) -slide 6&7Can I recognise where a shape will be after reflection?Discuss rotation and reflection – what do the children understand? Children to indicate understanding by using their bodies – work in pairs for reflection. Draw a shape on interactive board. Using vertical and horizontal, ask children to come to the board and further demo understanding. Demo use of tracing paper. Reflection example from Target maths to be stuck into books. http://www.primaryresources.co.uk/online/reflection.swf

AfL

LA – slide 8Draw the reflection of this shape.

Hand out Homework – make sure each child is given a sheet of tracing paper.

AfLHA/MA – slide 5What is twenty out of forty as a percentage? Make up some more questions like this for me to answer. You must tell me whether I am right or wrong.What percentage of £8 is £2?What percentage of £4 is £16?Tell me two amounts where one is 25% of the other. Now give me two amounts where one is 5% of the other. What about 40?%Put a ring around the fraction which is equivalent to forty per cent.

HA Find simple percentages of small whole-number quantitiesPCM13Children to fill in grid – BUT they must use written methods as described during input to calculate answers. Grid to be stuck into books.

Extension.Children to mentor/assist less able children in the class

MA As HA

ExceptEnsure children are secure with method as shown on SCM13

LA use SCM13

MA/HA – PCM13

Extension.Children to mentor/assist less able children in the class

LAReflectionVLA – guided - to work through step by stepMathspace year 6SCM42

MA – LP group to work in pairs to solve problems – they must however both produce the work.Mathspace year 6SCM42Ext. PCM42

HA – SB – Start with PCM42Ext. ECM42


http://www.primaryresources.co.uk/online/reflection.swf

Learning intentions



Slide 10HA/MA/LA20 questionsQ1-10 (5 secs each)Q11-15 (10 secs each)Q16-20 (15 secs each)

HA/MA- FDPRP involving measures and data handlingLA – Symmetry – reflection and rotation -recognise where a shape will be after reflection

HA/MA – slide 11Can I work out a quantity as a percentage of another and find equivalent percentages, decimal numbers and fractions?Show a picture of Mr. Boyle and a graph showing his weight loss program – he weighs 89KgDemo how to find 100%, 10% 1% of a given weight. They will need to convert to grams!Verbally – how could the children find 2%, 15%, 62% and 17.5% of the given weight?Explain that the children have been challenged by Mr. Boyle to calculate percentage weight losses. Start with finding 10%, 20%, 30% etc... They should create a table showing the percentage, the value of the percentage and the new weight and its percentage.

% Weight New weight %100 89kg 89 10010 890g 8900-890=8010g 90

LA – slide 134)Can I recognise where a shape will be after reflection?Draw a shape onto the Interactive board – ask children to come to the board and demonstrate how to reflect the shape. Increase difficulty by using diagonal mirror line as used in yesterdays plenary.

Again model the use of tracing paper.http://www.primaryresources.co.uk/online/reflection.swf

AfL

HA/MA - slide 12Discuss main activity – children to share with each other any problems encountered. What did they find easy – they need to be able to explain and demonstrate.

Can they express these percentages as fractions ratios and proportion

Set questions related to the main task

LA – slide 14

Ask children from independent group to come to the board and demonstrate understanding – class to assist where necessary.

Set a question that asks the children to firstly translate a shape, then reflect and finally rotate it.

HA Derive percentages of amounts using comparison technique

As directed during main activity

MAAs HA except work in pairs

LAReflectionVLA – guided - to work through step by stepMathspace year 6SCM42

MA – LP group to work in pairs to solve problems – they must however both produce the work.Mathspace year 6SCM42Ext. PCM42

HA – SB – Start with PCM42Ext. ECM42



Learning intentions



Slide 16HA/MA20 questionsQ1-10 (5 secs each)Q11-15 (10 secs each)Q16-20 (15 secs each)

LAA)Can I rapidly recall multiplication and division facts up to and including 10 x 10100 club – maths challenge

See 100 club challenge strategy.

HA/MA- FDPRP involving measures and data handlingLA – Symmetry – rotation - solve mathematical problems, recognize and explain patterns and relationships involving translations, reflection and rotation.

HA/MA - slide 17Discuss the testbase questions they are to answer – the questions will be on each table – they are mixed level 3, 4, 5 and 6. How many questions can they answer. VHA child to be host for each table to act as mentor (5 tables of 6-7)

LA – slide 194) Can I recognise where a shape will be after rotation?

-recognise where a shape will be after a rotation through 900 about one of its vertices

AfLHA/MA – slide 18

Look at a level 6 question

Discuss

LA – slide 20The shape below is rotated 90° clockwise about point A. Draw the shape in its new position on the grid.

HAChildren to work their way through testbase questions

Levels 4, 5 & 6

Children to give explanations for their answers

MAAs HA

LAUsing tessellating shapes - children practice on squared paper rotating the shape 90, 180 & 2700

RotationTargetmaths6 pg.104LA Section A & BMA/HA Section B & C

Thur

sday

12

/02/

09

AssessmentSATs paper A2007

Frid

ay

13/0

2/09

AssessmentSATs paper B2007

Extension/Practical activities: Resources: FDPRP resource sheets / PCM13, SCM13 / SCM42, PCM42, ECMIntervention Springboard6: Wave 3: Coordinates- symmetryhttp://www.primaryresources.co.uk/online/reflection.swf



Percentages and Fractions - word problems - Using and applying

Level 4

Hassan scores 40 out of 80 in a test.

Kate scores 40% in the same test.

Who has the higher score?

Circle Hassan or Kate.

Hassan / Kate

Explain how you know.

Level 4

John had £5

He gave 25% of it to charity.

How much did he give?


Level 5

Emily makes 250 grams of a snack mixture.

15% of the weight is raisins, 25% is banana chips and the rest is peanuts.

How many grams of peanuts does she use?

Showyour .workingYou m ay get

a m ark.

g

2 marksLevel 5

Here is a pattern on a grid.

What percentage of the grid is shaded?

%


Level 5

Write in the missing numbers.3

30% of 60 is

30% of is 60


Mathematics planning – SPR1-WK7-Wb-230209Mental/Oral Main Activity Plenary/Key Questions Assessment for

LearningQuestions and success criteria

1

Slide - 1 Learning intentions



Slide - 2HA/MA/LA10 questionsQ1-5 (5 secs each)Q6-8 (10 secs each)Q9-10 (15 secs each)

All - Handling data2)Can I represent data in different ways and understand its meaning?Can I solve problems, using mode, range, median and mean?Slide – 3&4Look at the slide. Surveys are used for what? To collect data. What should we do with it? Organise it. Why? Look at the data collected - how should this be organised? Tally chart/frequency table.How should it be represented – discrete or continuous? Look at bar chart or bar-line graph.What questions could we ask?

LA – assess understanding of mode, median, range and mean and reinforce where necessary.

AfLGroups working on Mathspace6 – PCM75 to present their work to the rest of the class.

They will have to explain the reasoning behind their answers. Also demo using the flipchart. Children, especially low ability, to ask questions.

A big focus on method and talking maths!

HA

LA– Target maths6 interpreting data – pg. 113- Section B Ext. C

MA - Target maths6 interpreting data – pg. 113- Section B &CExt. Mathspace6 – PCM75

HA - Mathspace6 – PCM75Solve a problem by representing, extracting and interpreting data in tables, charts and diagrams.This group should also pose questions for the rest of the class

MA LA – Target maths6 interpreting data – pg. 112 - Section A Ext. B

MA – Target maths6 interpreting data – pg. 113- Section B Ext. C


LAVLA – Abacus 6 grouped dataGrouped frequenciesChildren to work in pairs

LA – Mathspace6 - SCM75 – solve a problem by representing, extracting and interpreting data in tables, charts and diagrams.

MA – Target maths6 interpreting data – pg. 112 - Section A Ext. B



2Slide 5 Learning intentions




All - Handling data1&2) Can I use a calculator to solve problems involving more than one step?Can I use data to solve problems?Can I use data to work out problems about chance?Can I represent data in different ways and understand its meaning?Can I solve problems, using mode, range, median and mean?Slide7Using a SATs question and a volunteer from the ‘audience’ demo how you should approach answering the levelled questions.Children to work in pairs/groups to discuss and answer questions –How does it work?Groups of like ability challenge each other to answer questions. They should first look at the question – discuss as a group then answer the question, explaining what needs to be done and reasoning behind their answer. The other members of the group should challenge the explanations if they are unsure. Calculators should be used to check answers – but remember to estimate first.

AfL slide 8

Ask children to work with a partner - they should write a statement showing what they believe they are good at (data handling), what they believe they have leaned today and what they need to work on.

Share responses – a super chance for bolstering children’s confidence.

HA KS2 Maths and revision practice - Exercise 1

HA – L4-5VHA – L4-6Possible mentoring situation for the VHA

MAAs HA

LA – L3-4MA – L4-5HA – L4-6

LAAs HA

VLA – Level3LA – Level 3MA – Level4HA – Level 4-5






HA – Pie chartsMA/LA - Bar charts and grouped data1&2) Can I use data to solve problems?Can I represent data in different ways and understand its meaning?

Slide 11MA/LA - Look at slide and the data of peoples ages at a wedding – what can we do with this data? Emphasis on organisation and grouping. Why should we group this data? With so many different numbers over a wide range it is helpful to put the ages into groups. What groups should we use? How should it be organised? Tally chart. Demo or ask children to come to the board. NOTE: When drawing graph the bars should be touching! Grouped data – touching.

Slide 12

HA – Demo how to interpret a pie chart – using example 2 from Targetmaths6. 300 members of the audience at a performance of Toy Story. Except leave out essential percentages. What questions could we pose?Relate angle to percentage. E.g 1% = 3.60, 10% = 360 etc...

AfLMA groups from all three classes to take plenary. Using flipchart etc... to demonstrate understanding.

These groups should also ask the class to pose questions.

HALA - TargetMaths6 – pg.116 section AExt B

MA – Letts Keystage 2 pupil’s book – children o work together in readiness for presenting to the whole class during the plenary.

HA - TargetMaths6 – pg.116 section B&C

MALA - TargetMaths6 – pg.114 section AExt B

MA – Letts Keystage 2 pupil’s book – children o work together in readiness for presenting to the whole class during the plenary.

HA - TargetMaths6 – pg.114 section B&C

LAAs MA except teacher to support MA group.





Slide 14HA/MA10 questionsQ1-5 (5 secs each)Q6-8 (10 secs each)Q9-10 (15 secs each)LA

A)Can I rapidly recall multiplication and division facts up to and including 10 x 10100 club – maths challenge

See 100 club challenge strategy.

All – Data in groups and line graphs1&2) Can I use a calculator to solve problems involving more than one step?Can I use data to solve problems?Can I use data to work out problems about chance?Can I represent data in different ways and understand its meaning?Can I solve problems, using mode, range, median and mean?

Slide 15

Recap areas covered in the previous three days – discuss areas for development – dependent upon ongoing formative assement.

Set home work - SATs based questions – Levels 2-6

AfL Slide 16

These pie charts show the results of a school's netball and football matches. The netball team played 30 games. The football team played 24 games.

David says: ‘The two teams won the same number of games.’ Is he correct? Explain how you know.

HAKS2 Maths and revision practice - Exercise 2 Use prepared questions – work in groups/ pairs to discuss and answer questions.

This is a challenge – how many can they answer in the given time frame?

MAAs HA except focus on accuracy rather than speed.

LAAs MA

Teacher to work with reluctant mathematicians

TA – support nurture group – VLA

LP – intervention group.

Remainder to be independent.

5

Slide 17 Learning intentions




Booster Maths – consolidation – using and applyingInterpret frequency tables, bar charts, grouped data and line graphs. Draw conclusions and report them.Compare sets of dataMode, range, mean and median to solve problems and interpret results.

AfL Slide 18

Would you use the mode, median or mean to describe these test scores? Explain your answer.Look at this data set. Work out the mode, range, median and mean.One more item of data is added to the data set [e.g. a temperature of 24 °C when the rest of the temperatures were all between 8 °C and 14 °C]. Which average do you think will be most affected by this extra result? Which gives the most sensible average now?

HA -KD MA-JJ LA - PM LA – SBFocus group6 children, all with confidence issues.Level 4 potentialJemma, Shelley, Sophie, Megan T, Tino, Lucie M

VLA - SW

5 childrenAmelia, Lauren T, Andie, Chloe,

Courtney (30 mins Mrs Powell)


Extension/Practical activities: Resources: Intervention Springboard6: Wave 3: http://www.standards.dfes.gov.uk/primaryframework/downloads/PDF/Wave3_resources.pdf


http://www.standards.dfes.gov.uk/primaryframework/downloads/PDF/Wave3_resources.pdf

Level 3 - 1999

(a) Complete the tally.1 mark

(b) How many vehicles were seen altogether?

1 mark

(c) Complete this graph using the tally.

1 markLevel 4 - 1999

Five children collect money to plant trees.

Here is a bar chart of the amounts they have raised so far.

Their target is £40 altogether.

How much more money do they need to reach the target?


lorries

cars

bicycles

vans

motorbikes

8

4

Tally of traffic passing school

cars

m otorb ikes

bicycles

vans

lorries

0 2 4 6 8 10 12 14

0 1 2 3 4 5 6 7 8 9

Louise

Hassan

David

S arah

Donna

am ount in pounds (£)

Level 5 - 1998

Here is a bar chart showing rainfall.

Kim draws a dotted line on the bar chart.

She says,

‘The dotted line on the chart shows the mean rainfall for the four months.’

Use the chart to explain why Kim cannot be correct.

...........................................................................

...........................................................................

...........................................................................1 mark

What is the mean rainfall for the four months?

mm

1 mark

Level 6 - 1999

Two telephone companies, Supertalk and Quickline, have different charges for long distance calls.

This graph shows the charges for different lengths of calls.

Estimate from the graph how many seconds longer a £2 call lasts with Supertalk compared to Quickline.

1 mark

Estimate from the graph the length of a call when Quickline becomes cheaper to use than Supertalk.

Give your answer to the nearest 10 seconds.


16

14

12

10

8

6

4

2

0

16

14

12

10

Rainfall from M ay to August

m illim etresof ra in

M ay June July Augustm onth

350

300

250

200

150

100

50

0

100 200 300 400 500 600 700 800

Supertalk

Q uickline

cost of callin pence

length of ca ll in seconds

Level 6 - 1999

The pie chart below shows the different kinds of homes in Lamton village.

Altogether there are 550 homes in Lamton.

Use an angle measurer (protractor) to help you calculate how many flats there are.


Terracedhouses

S em i–detachedhouses

D etachedho uses

FlatsO thers

Hom es inLam ton

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