Blips Blops and BlapsBlips Blops and Blaps

Blips column Blops column Blaps column

Can you write 789 in terms of Blips, Blops and Blaps?

7 Blips + 8 Blops + 9 Blaps

So what's the difference between

7 hundreds + 8 tens + 9 units?

What does this tell us about What does this tell us about your understanding of Place your understanding of Place

Value?Value?

Hello Earthling I am aSnopsitswat.

I live on planet Shekle.Our number system is all

BASE 8Everything you now do is to

be done in base 8!!!!

So what is base 8?So what is base 8?

83 82 81 80

512 64 8 1

83 82 81 80

512 64 8 1

1. Write the number 84 in base 8?

124

2. Write the number 1394 in base 8?

2561

What is the number What is the number 4357base 8 in base 104357base 8 in base 10

4 x 512 = 2024, 3 x 64 = 192, 8 x 5 = 40, 7 x 1 = 7

2263

What is the number What is the number 7632 base 8 in base 107632 base 8 in base 10

7 x 512 = 3584, 6 x 64 = 384, 3 x 8 = 24, 1 x 2 = 2

3994

How did you feel working with base 8?

How do you think some of the students feel when we are doing base 10?

• What do students need to know before Place Value?

• Fractions Level 3 & decimals Level 4 New Curriculum

Material and imaging

Check out the 10 A2 sheets of paper

Get the students to work with their own

decimat.

Once students have had cut out the decimat get them to use the squares in their books and draw egs of

1. 0.32

2. 0.95

3. 1.30 etc

This keeps them imaging beyond the

decimat.

1.40 vs 1.41.40 vs 1.4

They could draw this in their books.

Number FansNumber Fans

Some important phrasesSome important phrases

Remember

ty on the end of a word means ‘tens’

eg 80(eighty) means 8 tens

30 (thirty) means 3 tens

• Express any fractions as follows:

65% = 65

100

Read this as 65 hundredths

How do you think our girls would answer this?

Pick the most appropriate answer

0.30 is

A. 3 tens B. 3 ones C. 3 tenths

D. 3 hundredths E. None of the above

• Use words zero wholes and three tenths and zero hundredths

( leave out 0 hundredths as meaningless.)

Add/SubAdd/Sub

Strategy framework for addition and subtractionStrategy framework for addition and subtractionStage and behavioural indicatorStage and behavioural indicator00 EmergentEmergentThe student has no reliable strategy to count an unstructured collection of The student has no reliable strategy to count an unstructured collection of

itemsitems11 One to One CountingOne to One CountingThe student has a reliable strategy to count an unstructured collection of The student has a reliable strategy to count an unstructured collection of

itemsitems22 Counting from One on MaterialsCounting from One on MaterialsThe student’s most advanced strategy is counting from one on materials to The student’s most advanced strategy is counting from one on materials to

solve addition problemssolve addition problems33 Counting from One by ImagingCounting from One by ImagingThe student’s most advanced strategy is counting from one without the use of The student’s most advanced strategy is counting from one without the use of

materials to solve addition problemsmaterials to solve addition problems44 Advanced CountingAdvanced CountingThe student’s most advanced strategy is counting on or counting back to solve The student’s most advanced strategy is counting on or counting back to solve

addition and subtraction tasksaddition and subtraction tasks55 Early Additive Part-Whole Early Additive Part-Whole The student shows any part-whole strategy to solve addition or subtraction The student shows any part-whole strategy to solve addition or subtraction

problems mentally by reasoning the answer from basic facts and/or place problems mentally by reasoning the answer from basic facts and/or place value knowledgevalue knowledge

66 Advanced Additive Part-Whole Advanced Additive Part-Whole The student is able to use at least 2 different mental strategies to solve The student is able to use at least 2 different mental strategies to solve

addition and subtraction problems with multi-digit numbersaddition and subtraction problems with multi-digit numbers77 Advanced Multiplicative Part-Whole Advanced Multiplicative Part-Whole The student is able to use at least two different advanced mental strategies to The student is able to use at least two different advanced mental strategies to

solve addition or fraction problems with decimals and fractions with related solve addition or fraction problems with decimals and fractions with related denominatorsdenominators

How the stages operateHow the stages operateEach stage says what students should be able Each stage says what students should be able

to doto do

In the books there are:In the books there are:Activities to consolidate knowledge/strategies Activities to consolidate knowledge/strategies

at the stageat the stageThenThenActivities to move students to the next stageActivities to move students to the next stage

Note: Some students who have just reached Note: Some students who have just reached a stage have more in common with those a stage have more in common with those who are ready to make the transition that who are ready to make the transition that those who are proficient at the stage…those who are proficient at the stage…

In the teaching of strategy, one of In the teaching of strategy, one of the critical concepts to develop is the critical concepts to develop is whenwhen it is appropriate to use a it is appropriate to use a certain strategycertain strategy

Focus of SNPFocus of SNP

PPROGRESSIONSROGRESSIONS

PPEDAGOGYEDAGOGY

PPARTICIPATIONARTICIPATION

ProgressionProgression

Step 1: Step 1: Identify and build the computational strategies Identify and build the computational strategies

of students using a framework.of students using a framework.

Step 2: Step 2: Exploit what the students are using Exploit what the students are using

computationally and formalise it to develop computationally and formalise it to develop algebraalgebra. .

PedagogyPedagogy

Building on the experience of teachers in the Building on the experience of teachers in the department and developing a broad department and developing a broad understanding of how to teach mathematics.understanding of how to teach mathematics.

Use a concrete representationUse a concrete representation

Encourage imaging and visualisationEncourage imaging and visualisation

Push to the inherent property and generalisationPush to the inherent property and generalisation

ParticipationParticipation

Who asks the questions?Who asks the questions? Who answers the questions?Who answers the questions? Who explains the reasoning behind a Who explains the reasoning behind a

method?method? Who explains the key ideas?Who explains the key ideas? Who does the most talking?Who does the most talking? Who checks the work?Who checks the work? Who decides if the answers are Who decides if the answers are

correct?correct?

The teaching modelThe teaching model

Start by:Start by: Using materials, diagrams to Using materials, diagrams to

illustrate and solve the problemillustrate and solve the problemProgress to:Progress to: Developing mental images to help Developing mental images to help

solve the problemsolve the problemExtend to:Extend to: Working abstractly with the number Working abstractly with the number

propertyproperty

Lesson planningLesson planning Work in groups of twos or threes (relating to the Work in groups of twos or threes (relating to the

ability of the class you teach) to plan a lesson on ability of the class you teach) to plan a lesson on whole number add/sub.whole number add/sub.

9H/9ARM top work on stage 79H/9ARM top work on stage 79PT top & mid 9ARM stage 69PT top & mid 9ARM stage 69ARM/9PT low stage 59ARM/9PT low stage 5 Plan lesson 1 for Add/sub (Use SNP Plan lesson 1 for Add/sub (Use SNP

books/FIO/internet)books/FIO/internet) StarterStarter Materials -> Imaging -> AbstractionMaterials -> Imaging -> Abstraction How many lessons would you expect the progression to How many lessons would you expect the progression to

take?take? Present Overview to the group?????Present Overview to the group?????

Written RecordingWritten Recording

Students are expected to record their mental Students are expected to record their mental calculations in a appropriate mannercalculations in a appropriate manner

Models of appropriate recording need to be Models of appropriate recording need to be carefully taughtcarefully taught

Students will interact with written material a great Students will interact with written material a great deal while working on practice activitiesdeal while working on practice activities

Approaching problemsApproaching problemsFirst port of call:First port of call:Is there a quick mental strategy that I can use?Is there a quick mental strategy that I can use?

Second Stop:Second Stop:Informal jottings – “memory joggers” that will help me thinkInformal jottings – “memory joggers” that will help me thinkthrough the problemthrough the problemEmpty number lineEmpty number line

Third stop:Third stop:A written algorithmA written algorithm

Question:Question:What do I need to write down so others can see what I have What do I need to write down so others can see what I have

done?done?