Geraldton Numeracy Strategy

1
Geraldton Numeracy Strategy
With A Focus On Calculate
Presented by
Linda Spicer Martine Thurkle Celine Bellve Alex
Di Felice Katrina Di Felice
2
Session Objectives

• An outline of the Geraldton Numeracy Strategy
• Navigating the Geraldton Numeracy Strategy
  website
• What are the Basic Facts
• What are the First Steps Mental Strategies
• Linking the Key Understandings
• Where the concepts fit in the curriculum
• Conducting diagnostic tasks
• Using the Numeracy Monitoring Tool to support
  planning, teaching and assessment
• An introduction to the DoE Learning Sequences

3
The Geraldton Numeracy Strategy
4
What Numeracy Have You Encountered In The Past 24
Hours?

• Discuss what you did and why.
• What calculations did you carry out?
• What mathematics did you have to know to do the
  calculations?

5
What Research Shows Us

• What research shows us

Northcote McIntosh
Adults mostly use mental strategies or a
calculator for problems they cant do mentally.
6
Curriculum Framework Mathematics Learning Area
Outcomes
Number Cluster
N6 Understand Numbers
N8 Calculate
N7 Understand Operations
7
Calculate Outcome

• Students choose and use a repertoire of mental,
  paper and calculator computational strategies for
  each operation, meeting degrees of accuracy and
  judging the reasonableness of results

Mental computation
Written computation and traditional algorithms
8
Basic Facts

• Placemat Activity
• What is meant by basic facts?
• What are the basic facts?

9
The 5 Counting Principles

• Each object should only be touched or included
  once.
• Numbers must be said once in the right order.
• Objects can be counted in any order.
• It does not matter how you put them.
• The last number tells how many.

10
Basic Addition Facts
11
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Adding 1 and 2 to numbers 1-10. For example 1
more and 2 more.
12
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Adding 1 and 2 to numbers 1-10. For example 1
more and 2 more.
13
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Adding 10 to any number. For example 4 10
14, 7 10 17.
14
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Add 9 to any number by adding 10 and taking off
1. For example, 4 9 is 4 10 1.
15
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Add 8 to any number by adding 10 and taking off
2. For example, 4 8 is 4 10 2.
16
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Double numbers. For example 7 7 14, 9 9
18.
17
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Near doubles - doubles 1 and doubles 1. For
example whats 1 more or l less of 8 8 16.
18
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Combinations to 10. For example 7 3 10.
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Remaining basic facts to 20
20
Key Understandings - Calculate
Read through the Key Understandings on page 97 to
determine which are applicable to basic addition
facts.
Calculate Key Understanding 1 The same number
fact will be true no matter how you count the
objects or what the objects are.
Calculate Key Understanding 2 We can think of a
number as a sum or difference in different ways.
We can rearrange the parts of an addition without
changing the quantity.
Calculate Key Understanding 4 Place value and
basic number facts together allow us to calculate
with any whole or decimal number.
21
Developmental Learning
Ages 5 to 6 Students use imagery and mental
counting strategies to add and subtract numbers
such as 4 and 3, where the numbers are generated
by a story. They may not, however, be confident
that 4 plus 3 must always be 7. Ages 6 to
9 Students understand that the same basic
addition or subtraction fact will always be true,
in terms of counting collections, different
objects in collections and numbers alone. They
have constructed the addition facts to 10 10
(basic addition facts to 20) and remember many of
them. Ages 9 to 11 Students remember the basic
addition facts to 10 10 and have built up a
table of multiplication facts to 10 x 10 (basic
multiplication facts to 100) and remember many of
them. For example, they should know their 2s,
5s and 10s very strongly.
When students are working strongly with basic
addition facts, basic multiplication facts can be
introduced, as multiplication is connected to
repeated addition. Approximately ages 9 to 11.
22
Australian Curriculum
Year 1 Year 1
Content Strand Number and Algebra (Number and Place Value) Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts.
Elaborations Developing a range of mental strategies for addition and subtraction problems.
Year 1 Achievement Standard Students solve simple addition and subtraction problems.
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Australian Curriculum
Year 2 Year 2
Content Strand Number and Algebra (Number and Place Value) Solve simple addition and subtraction problems using a range of efficient mental and written strategies. Explore the connection between addition and subtraction.
Elaborations Becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10 Modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines. Becoming fluent with partitioning numbers to understand the connection between addition and subtraction. Using counting on to identify the missing element in an additive problem.
Year 2 Achievement Standard Students recognise the connection between addition and subtraction. Students represent problems involving addition and subtraction by number sentences.
24
Australian Curriculum
Year 3 Year 3
Content Strand Number and Algebra (Number and Place Value) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation.
Elaborations Recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers. Combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 19 57 20 1).
Year 3 Achievement Standard Students describe number patterns involving addition and subtraction and recognise the connection between multiplication and division. Students recall number facts for single digit numbers.
25
Basic Facts Games and Lesson Ideas
26
Calculate Diagnostic Tasks

• Blocks in a Box
• Hide the Jellybeans
• Emus 1
• Emus 2
• Tomatoes and Bean Bags / Dogs and Bean Bags
• Number Tiles 1
• Number Tiles 2

27
Morning Tea
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Basic Multiplication Facts
How do you teach the multiplication facts to your
students?
p.190
29

• 1 x
• x 1
• 10 x
• x 10
• 5 x
• x 5
• 2 x doubles
• x 2 doubles
• 4 x double/ doubles
• x 4 double/ double
• 3 x double add one group
• x 3 double add one group
• 6x double 3s
• x 6 double 3s
• 9x take one group from 10x
• x9 take one group from 10x
• Squares

64
49
29
30
Basic Multiplication Facts.
1 x a number
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
10 x a number
5 x a number Or half of the 10 x Eg 5 x 7 ½
of 10 x 7
2x can be doubled to tell you 4 x and 4 x
doubled to tell you 8x
3x can be doubled to make 6x
Square numbers
Only one factto memorise
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Basic Multiplication Facts

• Multiplication Facts to 100 (10 x 10)
• x 1 one times, times one
• x 10 ten times, times ten (Link to skip
  counting)
• x 5 five times, times five (Link to skip
  counting) Also half of the 10s
• Doubles x 2 teach turnarounds, e.g. 2 x 4 is 4
  x 2
• Squares e.g. 7 x 7, 9 x 9
• Doubles/doubles 2s apply to 4s, 4s apply to
  8s, 3s apply to 6s
• Double add one 2 x 3 or 2 groups of 3, 3 x 3 is
  just one more group of 3

32
Key Understandings - Calculate
Read through the Key Understandings on page 97 to
determine which are applicable to basic
multiplication facts.
Calculate Key Understanding 1 The same number
fact will be true no matter how you count the
objects or what the objects are.
Calculate Key Understanding 3 We can think of a
number as a multiplication or division in
different ways. We can rearrange the factors of a
multiplication without changing the quantity.
Calculate Key Understanding 4 Place value and
basic number facts together allow us to calculate
with any whole or decimal number.
Calculate Key Understanding 5 There are
strategies we can practise to help us do
calculations in our head.
33
Developmental Learning
Ages 6 to 9 Students understand that the same
basic addition or subtraction fact will always be
true, in terms of counting collections, different
objects in collections and numbers alone. They
have constructed the addition facts to 10 10
(basic addition facts to 20) and remember many of
them. Ages 9 to 11 Students remember the basic
addition facts to 10 10 and have built up a
table of multiplication facts to 10 x 10 (basic
multiplication facts to 100) and remember many of
them. For example, they should know their 2s,
5s and 10s very strongly. Ages 11 Students
remember almost all of the basic facts and can
work out those they do not remember.
When students are working strongly with basic
addition facts, basic multiplication facts can be
introduced, as multiplication is connected to
repeated addition. Approximately ages 9 to 11.
34
Australian Curriculum
Year 2 Year 2
Content Strand Number and Algebra (Number and Place Value) Recognise and represent multiplication as repeated addition, groups and arrays. Recognise and represent division as grouping into equal sets and solve simple problems using these representations.
Elaborations Representing array problems with available materials and explaining reasoning. Visualising a group of objects as a unit and using this to calculate the number of objects in several identical groups. Dividing the class or a collection of objects into equal-sized groups. Identifying the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three.
Year 2 Achievement Standard Students recognise and communicate number sequences involving twos threes and fives. Students describe patterns with numbers.
35
Australian Curriculum
Year 3 Year 3
Content Strand Number and Algebra (Number and Place Value) Recall multiplication facts of two, three, five and ten and related division facts. Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital Technologies.
Elaborations Establishing multiplication facts using number sequences. Writing simple word problems in numerical form and vice versa. Using a calculator to check the solution and reasonableness of the answer.
Year 3 Achievement Standard Students recall number facts for single digit numbers. Students recognise the connection between multiplication and division.
36
Australian Curriculum
Year 4 Year 4
Content Strand Number and Algebra (Number and Place Value) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9. Recall multiplication facts up to 10 10 and related division facts. Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder.
Elaborations Recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences. Using known multiplication facts to calculate related division facts. Using known facts and strategies, such as commutativity, doubling and halving for multiplication, and connecting division to multiplication when there is no remainder.
Year 4 Achievement Standard By the end of Year 4 students recall multiplication facts up to 10 x 10 and the related division facts. They solve problems by using relevant number sentences involving the four operations.
37
Mental Computation Continuum
By Dr Paul Swan
38
Basic Facts Games and Lesson Ideas
39
Calculate Diagnostic Tasks

• Bags of Lollies
• Finding Equal Groups
• How Did You Do It

40
Mental Strategies

• IMPORTANT POINTS TO REMEMBER

• Students (like adults) may use informal jottings
  on paper to help keep track of their thinking and
  this should be encouraged.

• Mental methods backed up by informal, written
  jottings should receive more attention than
  standard written methods.

• The choice is not between fully mental approaches
  and standard written approaches. The goal is
  flexibility and efficiency rather than
  standardisation.

• Students should be able to clearly explain their
  written informal jottings before any formal
  algorithms are introduced.

• Students need to practice a wide range of
  strategies for calculating mentally. Therefore,
  teach a new strategy daily, weekly or
  fortnightly, dont teach one strategy per term or
  year as it is not fair for students who may
  prefer to use other strategies.

• Mental arithmetic is flexible and only
  occasionally automatic and so it cannot be made
  routine.

41
Calculate Strategies

• We teach children to
• Be flexible with numbers.
• Choose when they can do things in their head.
• Jot things down if they need to.
• Use the most efficient way to do the
  calculations.
• Know when a calculator is best.

42
Focus For Mental Computation

• With mental computation the focus is two fold

• Students explaining their own mental strategies
• Students listening to and evaluating, in their
  own minds, the methods other students are using.
• Your questioning needs to facilitate this.

43
Link To Working Mathematically

• In order to assess a student in Working
  Mathematically we often need to get inside their
  head.
• How Did You Do It sessions are a good source of
  Working Mathematically information. (especially
  in Apply and Verify)

44
Addition and Subtraction Mental Strategies Based
on Partitioning

• Counting on by 1 s
• Addition - The order doesnt matter
• Counting back
• Skip Counting on or back (2 or 5)
• Subtraction change to an addition, e.g. 13 8
  is 8 ? 13
• Generalise basic facts. e.g. 8 7 15, so 18
  7 25, 28 7 35
• Break numbers up into hundreds, tens and ones

45
Addition and Subtraction Mental Strategies Based
on Partitioning

• Front Load
• Bridge to 10 (or 20, 30 etc) then add/take the
  rest
• Compatible Numbers
• Imagine a number line
• Near Doubles
• Take one from one number and give to the other
  (compensate)

46
Multiplication and Division Mental Strategies
That Require Partitioning and Factoring

• x 2 - Double
• x 4 Double double
• x 8 - Double double double
• Generalise basic facts, e.g. 6 x 7 42 so 60 x 7
  420
• Multiplying - The order doesnt matter
• Place Value partition and multiply or divide the
  parts

47
Multiplication and Division Mental Strategies
That Require Partitioning and Factoring

• Multiply by nearest decade or hundred then adjust
• Division - change to multiplication
• x 5 Multiply by 10 then half the result
• Double and halve
• x 25 Look for lots of 4 to make 100
• Factors - make a basic fact that you know
• Even number x 5 make groups of 2

48
Key Understandings - Calculate
Read through the Key Understandings on page 97 to
determine which are applicable to mental
strategies.
Calculate Key Understanding 5 There are
strategies we can practise to help us do
calculations in our head.
49
Developmental Learning

• Ages 5 to 6
• Students mentally add and subtract small numbers
  generated from stories. They work with small,
  easily visualised numbers that they can count in
  their minds eye.
• Ages 6 to 9
• Students have begun to use some mental strategies
  to work out addition and subtraction facts that
  they do not know from those that they do know,
  and to make simple extensions.
• Ages 9 to 11
• Students use mental strategies to work out basic
  multiplication facts that they do not yet
  remember. They have begun to build a repertoire
  of strategies, such as compensation, which helps
  them add and subtract easy two-digit numbers
  mentally.
• Ages 11 to 13
• Students have considerably extended their
  repertoire of strategies for reducing memory
  load. They can mentally add and subtract
  two-digit numbers and mentally multiply and
  divide by single-digit numbers and multiples of
  ten for easy numbers such as 4 x 32.
  Furthermore, they will try mental computation
  first for one-off calculations.
• Ages 13
• Students are skilled in mental computation with
  whole numbers and money, and calculate mentally
  with easily visualised fractions.

50
Calculate Diagnostic Tasks

• How Did You Do It

51
Lunch
52
Geraldton Numeracy Strategy Website
53
Numeracy Monitoring Tool - Calculate
54
The DoE Learning Sequences
55
Geraldton Numeracy Strategy Website
56
Have we covered the objectives?

• An outline of the Geraldton Numeracy Strategy
• Navigating the Geraldton Numeracy Strategy
  website
• What are the Basic Facts
• What are the First Steps Mental Strategies
• Linking the Key Understandings
• Where the concepts fit in the curriculum
• Conducting diagnostic tasks
• Using the Numeracy Monitoring Tool to support
  planning, teaching and assessment
• An introduction to the DoE Learning Sequences

57
Where to from here?

• Commitments From You
• Calculate Diagnostic Tasks
• Calculate Monitoring Tool
• Basic Facts
• Mental Strategies
• Term Planner / Scope and Sequence
• DoE Learning Sequences
• Australian Curriculum

58
Thank you

• Thank you for your participation today.
• ?
• Linda.Spicer_at_det.wa.edu.au Bluff Point PS
• Martine.Thurkle_at_det.wa.edu.au Allendale PS
• Celine.Bellve_at_det.wa.edu.au Beachlands PS
• Alex.DiFelice_at_det.wa.edu.au Rangeway PS
• Katrina.DiFelice_at_det.wa.edu.au Rangeway PS