Transcript Thinking Skills in P6 PSLE Specimen Paper

Lower Primary Mathematics
Parents’ Workshop
21 April 2012
Endeavour Primary School
Mathematics Department 2012
Dear parents,
Please ensure that your powerpoint slides are
set in the “Notes” format so that you can read
the additional notes on each slide.
Thank you
Mathematics Department
Objectives
• Share how number sense is taught in the
classroom
• How parents can reinforce the children’s
learning at home
Workshop Outline
• Whole Numbers
• Importance of CPA Approach
• Use of Concrete Materials at home for
teaching number facts
• Multiplication Facts
• Heuristics & Thinking Skills
Whole Numbers
• P1 & P2 Syllabus
Primary 1
Primary 2
Number to 10
Numbers to 1000
Number Bonds
Multiplication Tables of 2 , 3,4, 5 & 10
Shapes & Patterns
Using Models
Ordinal Numbers
Length
Numbers to 20
Mass
Length
Money
Mass
Fraction
Picture Graphs
Time
Numbers to 40
Volume
Multiplication & Division
Graph
Division
Lines & Surfaces
Numbers to 100
Shapes & Patterns
Money
Whole Numbers
• Emphasis on the teaching & learning of
whole numbers in lower primary syllabus
• Learning of later units are built on the
understanding of concepts of whole numbers
Importance of Number Sense
• Number sense develops as students understand:
- the size of numbers
- develop multiple ways of thinking about and
representing numbers
- use numbers as referents
- and develop accurate perceptions about the
effects of operations on numbers
Importance of Number Sense
• An attribute of all successful users of Mathematics
• Developing confidence with numbers and logical skills
give a child a real head-start for school & adult life
• Number sense enables students to understand and
express quantities in their world.
Understanding Numbers in
their World
Examples:
-whole numbers describe the number of students in a class or
the number of days until a special event
-Decimal quantities relate to money or metric measures
-fractional amounts to describe ingredient measures
-percent amounts describing test scores or sale prices
How does number sense begin?
• In early years , children are able to literally
see small quantities, develop basic counting
skills, and add small amounts.
• An early sense of number is mostly intuitive,
developing through a variety of experiences.
Developing Number Sense at Home
• Home is a great place to start.
• Having early math conversations with children :
– “How many spoons?”
– “Which is more?”
– “How do you know?”
– “What’s one more?”
– “Two more?” “One less?”
– “How many steps to the door?”
– “How long do you think the drive will take?”
Talk, talk, talk!
• These experiences bring math into the
lives of children
• Students approach school with a
growing sense of number, and parents
and others can build on this
10
4
Number Bonds
6
4 + 6 = 10
100
40
60
40 + 60 = 100
Number Bonds
74 + 26 =____
100
90
10
Number Facts
Teaching of Number Facts in school
• Number Bonds Password Game
• Number Bonds
recitation in class
• Use of 2 sided
counters
Number Bonds
Family of Number
Sentence
whole
10
4
6
part
part
4 + 6 = 10
6 + 4 = 10
10 – 4 = 6
10 – 6 = 4
Misconception of more / less
• Students often have a
misconception of more than and
less than
More or Less
1. Siti has 10 marbles.
Tim has 3 more marbles than Siti.
How many marbles does Tim have?
10 + 3 = 13
Tim has _13 marbles.
More / Less
2. There are 10 cows on a farm.
There are 3 fewer goats than cows.
How many goats are there on the farm?
10 – 3 = 7
There are 7 goats on the farm.
More / Less
3. Dave has 12 toy cars.
He has 2 more toy cars than Peter.
How many toy cars does Peter have ?
Misconception
12 + 2 = 14
Answer
12 – 2 = 10
Teaching points
1.Dave has 12 toy cars.
2. He --- > Dave
3. Dave has more ---> Peter has
less
4. Dave has 2 more --- >Peter has 2
less
More / Less
4. May has 15 stamps.
She has 3 fewer stamps than Jim.
How many stamps does Jim have?
Misconception
15 – 3 = 12
Teaching points
1.May has 15 stamps.
2. She --> May
Answer
15 + 3 = 18
3. May has fewer -- > Jim has more
4. May has 3 fewer -- > Jim has 3
more
CPA Approach in Mathematics
Concrete components include manipulative (for example, linking cubes,
Cuisenaire,) measuring tools or other objects the students can handle during
the lesson.
Pictorial representations include drawings, diagrams, charts, or graphs that
are drawn by the students or are provided for the students to read and
interpret.
Abstract refers to symbolic representations such as numbers or letters that
the student writes or interprets to demonstrate understanding of a task.
Importance of CPA Approach
• Pictured relationships show visual representations
of the concrete manipulative and help students
visualize mathematical operations during problem
solving.
• Ultimately, students need to reach that final
abstract level by using symbols proficiently.
Importance of CPA Approach
This CPA approach benefits all students but has been
shown to be particularly effective with students who
have mathematics difficulties, mainly because it
moves gradually from actual objects through pictures
and then to symbols. (Jordan, Miller, &Mercer, 1998).
Number Bonds ( CPA)
whole
5
3
2
part
part
Use of concrete materials for teaching
Whole Numbers
Normal household items such as :
•Beans
•Lego blocks
•ice-cream sticks
•straws
•buttons, etc.
•Poker cards
Importance of Knowing Multiplication
Facts
• an essential part of the children's
primary education
• building blocks for other math
topics taught in school
Importance of Knowing Multiplication
Facts
• applied in higher learning such as division,
long multiplication, fractions & algebra.
• students who have not memorized the times
tables will find these levels of math much
more difficult than they need to be
• students who have not mastered their tables
will very often fall behind in math and begin
to loose confidence.
What is more important,
memorization or understanding?
• It's not one or the other, it's both!
• A child must understand
and memorize the facts.
Importance of Knowing Multiplication
Facts
At P3, pupils will be able to
carry out Multiplication
procedure and Division
Procedure.
At P4, pupils will need to
use their multiplication
facts into learning of
Factors and Multiples,
Fractions.
H
T
O
9
3
6
x
6
_
3
8
8
_
x
5
Multiplication Facts
• Skip – counting
• Password Game
• Multiplication Song
Charts
• Multiplication Card
Games
Helping your Child Memorize the
Times Tables
1. Make sure there is understanding.
2. Explain why it is important.
3. Demonstrate what fast recall is.
4. Involve your child in the goal setting process.
5. Use a chart to monitor progress.
Helping your Child Memorize the
Times Tables
6. Provide encouragement along the way.
7. Acknowledge their success.
8. Spend quality time together practicing.
9. And most importantly: Have fun!
Thinking Skills in P6 PSLE Specimen Paper
- MCQ
Lily spent 4 days making paper dolls for her
friends. Each day, she managed to make 2
paper dolls more than the day before. She
made a total of 24 paper dolls. How many
paper dolls did she make on the last day?
Thinking Skills in P6 PSLE Specimen Paper
Hassan had 5 tins of marbles. At first, each of
the tins contained the same number of
marbles. He took 18 marbles from each tin.
After that, the total number of marbles left in the
5 tins was equal to the total number of marbles
in 2of the tins at first.
What was the number of marbles in each tin at
first?
HEURISTICS
Making a Drawing / Models
Looking for a Pattern
Act It Out
Make a List / table
Working Backwards
Guess and Check
Using Before-After Concept
Making Supposition
Restate the problem
Simplify the problem
Solve part of the problem
P1
X
X
X
Thinking Skills
Analysing Parts and Wholes
Comparing
Identifying patterns and relationships
Deduction
Induction
Spatial Visualisation
Total no of skills
P1
X
X
4
P2
X
X
X
P3
X
X
P4
X
X
P5
X
X
P6
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X*
P2
X
X
X
P3
X
X
X
P4
X
X
X
X
P5
X
X
X
X
X
6
7
9
10
P6
X
X
X
X
X
X
11
Why does my child require
Thinking Skills ?
• Part of Assessment includes ‘Thinking Skills’
• Requirements based on Mathematics
Framework
Math Framework
Beliefs
Interest
Appreciation
Confidence
Perseverance
Numerical calculation
Algebraic manipulation
Spatial visualisation
Data analysis
Measurement
Estimation
Use of Mathematical tools
Monitoring of one’s own thinking
Self-regulation of learning
Mathematical
Problem
Solving
Concepts
Numerical , Algebraic
Geometrical, Statistical
Thinking Skills
Heuristics
Modeling
Applications
reasoning,
communication and
connections
Challenges due to Paper format
• Paper 1 to be completed within 50 minutes
(30 questions – less than 2 minutes/qn)
• Paper 2 – focuses on thinking skills as well as
heuristics
• Culture shock in P5 for pupils
Our move in preparing your child
• Mathematics Department - a progressive
approach
• Adoption of a Spiral Approach – Skills and
Number Facts moving back continuously
• Focusing on Heuristics from lower primary
levels – Act It Out, Draw a Diagram & Look
for a Pattern
Act It Out
There are 4 girls and 4 boys in a group.
The teacher wants 2 children to be the group
leaders, a girl and a boy. How many different
pairs can he choose from?
B1
G1
B2
G2
B3
G3
B4
G4
16 pairs
Act It Out
The picture below is made up of 13
toothpicks. Rearrange 4 toothpicks so that
the picture shows one square above 3
squares.
SOLUTION
Look for a Pattern
Study the pattern below.
Draw the next pattern in the
sequence.
?
Look for a Pattern
What is the missing number?
17
3
8
6
5
?
4
9
1
7
8
Draw a Diagram
2 kg of grapes cost $5.
How many kilograms of grapes can I buy
with $20?
$5
$5
$5
$ 20 = 4 groups of $5
$ 20
2 kg 2 kg 2 kg 2 kg
?
4 × 2 kg = 8 kg
Draw a Diagram
Some children are in a queue for ice
cream. Sally is the fourth child from the
front and fifth from the end of the queue.
How many children are there in the
queue?
Front
End
Thank You