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Blips 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?. - PowerPoint PPT Presentation
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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?