View
13
Download
0
Category
Preview:
Citation preview
Primary 2 MathParents Workshop27 March 2018Presenters:Mrs Chong Wai ChingMrs Linda GohMs Alyani
Topics to be covered
Assessment Matters
Heuristics: Looking for a pattern
Heuristics: Guess and Check
Q and A
Model Drawing
Assessment Matters
Fractions
Heuristics: Supposition Method
Aim of Primary School Mathematics
Laying A Strong Foundation acquire mathematical concepts and skills for
everyday use and for continuous learning in Mathematics;
develop thinking, reasoning, communication, application and metacognitive skills through a mathematical approach to problem solving; and
build confidence and foster interest in Mathematics.
Problem Solving
Concepts, Skills, Processes,
Metacognition, Attitudes
Monitoring of one’s
own thinking
Self-regulation of
learning
Reasoning, communication
and connections
Applications and modelling
Thinking skills and heuristics Numerical
Algebraic
Geometric
Statistical
Probabilistic
Analytical
Algebraic manipulation
Spatial visualisation
Data analysis
Measurement
Use of mathematical tools
Estimation
Beliefs
Interest
Appreciation
Confidence
Perseverance
Lower Primary Assessments
Term Assessment Schedule
Term 1 Term 2 Term 3 Term 4
P1 Formative
Assessment
only
Formative &
Summative
Assessment
Formative &
Summative
Assessment
Formative &
Summative
Assessment
P2 Formative
Assessment
only
Formative &
Summative
Assessment
Formative &
Summative
Assessment
Formative &
Summative
Assessment
Formative Assessments
Help students to achieve the
learning goals
Teachers will adjust the
teaching and learning activities
Summative AssessmentsTo determine whether the students
understand the Mathematical concepts and are able to perform the Mathematical skills taught
End of the term assessments such as Continual Assessments or Semestral Assessments
Inform of Summative Assessments dates via Rivervale Connect
General Format of Mathematics
Assessments Paper
Section A
Multiple Choice Questions
Section B
Open-Ended Questions
Section C
Problem Sum Questions
Section A in P2 Summative Assessment Paper
Section A (15 X 2 = 30 marks)
Choose the correct answer and write its number in the brackets.
1. 533 + 412 = ______________
1) 845
2) 846
3) 945
4) 946 ( )
2. 55 less than ______ is 500.
1) 445
2) 455
3) 545
4) 555 ( )
Section B (20 X 2 = 40 marks)
Fill in the blanks with the correct answers.
16. 800 - 321 = 476
Section B in P2 Summative Assessment
Paper
7 9
8 10 10
3 2 1
4 7 9
Working is correct but
the answer is wrong.
As working is shown,
we consider this as
transfer error.
The child is awarded
the mark.
It is encouraged that students do
their working in the space given.
Example of method mark given
25) Chris has 750 more marbles than David. If David has 498 marbles, how many marbles do they have altogether?
Pupil wrote:750 + 498 = 1284
Ans: 1284 X (Wrong Ans)
M1 is awarded
Instructions For Section C
For P2 Paper
SECTION C (5 x 3 marks = 15 marks)
Do the following word problems. Show
ALL workings clearly.
students are taught to write equations in
their daily work.Jarren has 4 big fish.
He also has 3 small fish.
How many fish does he have altogether?
He has ________ fish altogether. Boxes and circular
shapes to help
students to write the
numbers and symbol
in the equation.
Answer must be written in
the final statement.
4 3 7=+
7
Sample Question in Section C in P2
Summative Assessments
36. There are 355 children in a school hall.
159 of them are girls.
How many boys are there?
355 – 159 = 196
There are 196 boys.
No lines or boxes are
provided.
In P2, students should
be able to show
equation and working.
Correct equation with
correct answer
2 marks is awarded
1 marks is awarded
Sample Question in Section C in P2
Summative AssessmentsRayson saves $3 each day.
How many days does he need to save to have $18?
Fill in the brackets with the correct answers.
He needs to save for ____________ days to have $18.
( )
( )
Words are bold to
indicate it is important
for pupil to provide the
answers.
Learning Fractions The Fun Way
Do you agree?
Fractions is ABSTRACT
Example: 34
Overview of Progression of Fractions
• Part of a whole
• Part of a set of objects
• Number on a number line
• Operations of Fractions
• Ratio
0 1
← P2
← P4
← P5
← P5
↗ P6
Developing Conceptual Understanding of Fractions
Concrete
Pictorial
Abstract
Paper Folding
Understanding fractions as equal parts of a whole
Is this shape divided equally?
Are these shapes divided equally?
Common misconception:
students think these shapes are fractions
not divided equally
Are these shapes divided equally?
YES They are divided equally
Use of a pizza to teach fractions at
home.
While cutting the
pizza, parents
can say out, “I
cut into 2 equal
parts.”
Tell them about
half.
Also known one half
Each pizza is cut into 4 equal parts
Also known
as
one quarter
You may want to cut the pizza in these equal parts.
While having a bar of chocolate, can you think of a way to get your child to be interested in fractions?
Can you see the similarity between the bar of chocolate and the diagram given in the worksheet?
Understanding Basics of Fractions
•Equal parts
•Meaning of denominator
•Meaning of numerator
•Naming fractions
Basic Concept - Common Misconception
What fraction of the figure below is shaded?
a)b)
c) d)
Write a fraction.
Write a fraction.
Write a fraction.
Write a fraction.
Basic Concept - Common Misconception
What fraction of the figure below is shaded?
Write a fraction.
Write a fraction.
Write a fraction.
Write a fraction.
a)b)
c) d)
Cut into 8 equal parts.Get your child to compare the fractions
18
12or
Comparing Fractions
Comparing Fractions - Common misconception
Circle the smallest fraction
students take the fraction with the
smallest denominator
as the smallest fraction.
Comparing Fractions - Common misconception
Circle the greatest fraction
students take the fraction with the
greatest denominator
as the greatest fraction.
Denominators of given fractions should not exceed 12
P2 Heuristic Package
Objectives
To expose students to a variety of word
problems
To equip students with thinking skills and
strategies to help them solve word
problems
Heuristics to be covered in P2
Looking for a Pattern
Guess and Check
Supposition
Model Drawing
Looking For A Pattern
Involves looking for a
pattern/sequence/cycle
44 46 48 50 ?
Example 1
Example 2
300 400 350 450 400 500 ?
+100 - 50 +100 +100- 50 - 50
Looking For A Pattern
Example 3
710 ? 716 722 730 740
+2 +4 +6 +8 +10
Looking For A Pattern
-2 -4 -6 -8 -10
Example 4
?
?
Example 5
Looking For A Pattern
1 2 1 2 1 2 1
1 2 2 1 2 2 1 2
Example 6
?
?
Example 7
Looking For A Pattern
1 2 3 1 2 3 1
1 2 1 2 1
Example 8
How many circles are needed to build Figure 5?
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5
?
+2 +2 +2 +2
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5
Looking For A Pattern
Looking For A Pattern
Example 9
Study the pattern below. How many
squares are there in Pattern 4?
Pattern 1 Pattern 2 Pattern 3
Let’s Try
This!
Looking For A Pattern
Solution
Pattern 1 Pattern 2 Pattern 3
5
+ 4
+ 4
Number of squares in Pattern 4:
5 + 4 + 4 + 4 = 17
Guess and Check Math WB pg 86
Guess and Check Math WB pg 104
1) There are a total of 5 birds and dogs in an enclosure.
These animals have 14 feet altogether.
How many of each type of animals are there?
No. of dogs
(4 feet)
No. of birds
(2 feet)FIXED
D + B = 5
TARGET
Total feet = 14
Check
√ / x
2
2 x 4 = 8
3
3 x 2 = 6
2 + 3
= 5
8 + 6
= 14 √
Ans: 2 dogs and 3 birds
Guess and Check
A farmer has 15 chickens and rabbits.
These animals have 40 feet altogether.
How many of each type of animals does the farmer have?
No. of rabbits
(4 feet)
No. of chickens
(2 feet)FIXED
C + R = 15
TARGET
Total feet = 40
Check
√ / x
7
7 x 4 = 28
8
8 x 2 = 16
7 + 8
= 15
28 + 16
= 44 x
When doing guess and check/trial and error method,it’s encouraged to guess the number of each animal
by dividing the total by 2 first. In this case, 15 ÷ 2 = 7 R 1
So 1 type of animal will be 7 while the other is 8.
From the 1st guess, we need to look at the number of feet to see if we should decrease
the number of rabbits or chickens. Since rabbits have more feet, we should decrease
the number of rabbits.
6
6 x 4 = 24
9
9 x 2 = 18
6 + 9
= 15
24 + 18
= 42 x
5
5 x 4 = 20
10
10 x 2 = 20
5 + 10
= 15
20 + 20
= 40 √
Ans: 5 rabbits and 10 chickens
Let’s try!Guess and Check
Supposition Method
Also known as Assumption method
Involves making assumptions based on
information given in questions
At P2 level, students may draw diagrams
to help them solve supposition questions.
2) A dog has 2 more feet than a bird.
Since there are only 10 feet, we will add 2 more feet to each drawing
until we get 14 feet.
P2 Supposition Method
1) There are a total of 5 birds and dogs in an enclosure. These animals have
14 feet altogether. How many of each type of animals are there?
2) Suppose ALL the animals are birds.
Draw picture to help you.
1) Determine which animal has fewer legs.
bird
Suppose: 5 birds
dogs birds
There are __ dogs and __ birds.2 3
2) A rabbit has 2 more feet than a chicken.
Since there are only 30 feet, we will add 2 more feet to each drawing
until we get 40 feet.
P2 Supposition Method
2) A farmer has 15 chickens and rabbits. These animals have 40 feet altogether.
How many of each type of animals does the farmer have?
2) Suppose ALL the animals are chickens.
Draw picture to help you.
1) Determine which animal has fewer legs.
chicken
Suppose: 15 chickens
rabbits chickens
There are __ rabbits and __ chickens.5 10
Let’s try!
Heuristics:
Model Drawing
1) Part-Whole Model
2) Comparison Model
3) Model Drawing for Multiplication
and Division
Concrete Objects
Drawing of Rectangular Bars
Solve Word Problem
(Forsten’s 7 steps)
Introduction of Model Drawing
There are 6 apples.
There are 3 oranges.
How many apples and oranges
are there altogether?
Look at this
story sum.
Stage 1 Using Concrete Materials
There are 6 apples.
There are 3 oranges.
How many apples and oranges are there altogether?
?
6 3
+6 3 = 9
Stage 2 Pictorial Representation
There are 6 apples.
There are 3 oranges.
How many apples and oranges are there altogether?
?
6 3
Stage 3 Insert the boxes with Pictures
There are 6 apples.
There are 3 oranges.
How many apples and oranges are there altogether?
?
6 3
Stage 4 Replace the Picture with Boxes
+6 3 = 9
?
6 3
+6 3 = 9
Stage 5: Replace Boxes with Bars
This is a part-whole model
Part Part
Whole
What does the ‘?’ represent?
?
6 3Part Part
Whole
Total number of apples and oranges
Another example:
Mary has 10 star stickers and
18 smiley stickers.
How many stickers does she have altogether?
Study this story
sum.
Mary has 10 star stickers and
18 smiley stickers.
Star
Stickers
Smiley
Stickers
10
18
A
B
C
Which one of these model drawings is
the best to represent the story sums?
B
The best model drawing to
represent the story sum is:
Mary has 10 star stickers and
18 smiley stickers.
How many stickers does she have altogether?
What numbers do we put
in these boxes?
Mary has 10 star stickers and
18 smiley stickers.
How many stickers does she have altogether?
10 18
10 18
?
10 + 18 = 28
Mary has 28 stickers
altogether.
John has 25 blue balls and 12 red balls.
He has 37 balls altogether
Choose the correct model
25 12
37
A
37 12
25
B
Let’s Try This!
Sarah has 22 green beads and 54 red beads.
How many beads does she have altogether?
Choose the correct model
22 54
?
A
54
?
B
22
Let’s Try This!
Forsten’s 7 steps (Problem Solving)
1) I _______________ the story sum.
2) I _______________ the statement.
3) I _______________ who and what is involved in the
story sum.
4) I _______________ a suitable strategy.
5) I _______________ the story sum.
6) I _______________ the question.
7) I _______________ my work.
read
write
decide
choose
chunk
solve
check
1) Mrs Li spent $65 on a dress and $28 on a blouse.
How much did she spent altogether?
WB Pg 59Step 1: Read the story sum
Step 2: Write the statement
She spent ____ altogether.
Step 3: Decide who/what is involved
Step 4: Part-Whole
Step 5: Chunk the problem
65 28
? 93Step 6: Solve the question
65 + 28 = 93 (total)
Step 7: Write and check answer
93
2) There were 254 cars parked at a shopping mall.
123 cars left the carpark.
How many cars were there left?
WB Pg 61Step 1: Read the story sum
Step 2: Write the statement
There were ______ cars left.
Step 3: Decide who/what is involved
Step 4: Part-Whole
Step 5: Chunk the problem
254
123 ?
Step 6: Solve the question
254 – 123= 131 (left)
131
Step 7: Write and check answer
131
3) A fruit seller had 584 durians at first.
He sold 225 durians.
How many durians does he have now?
WB Pg 66Step 1: Read the story sum
Step 2: Write the statement
He has _____ durians now.
Step 3: Decide who/what is involved
Step 4: Part-Whole
Step 5: Chunk the problem
584
225 ?
Step 6: Solve the question
584 – 225 = ____(now)359
359
Step 7: Write and check answer
359
There are 7 apples. If there are 2 more apples than oranges, how many oranges are there?
Comparison Model
There are 7 apples.
There are 2 more apples than
oranges.
Apples
Oranges
7 apples ?
The red rectangle represents the
number of apples and the orange
rectangle represents the numbers
of oranges.
Larger quantity
Smaller quantityDifference
This is the comparison
model
Sense of Sizes(Difference in quantities)
Put 20, 28 and 8 into the right brackets.
( )
( )
( )
( )
( )28The Answer is
Smaller quantity
Greater quantity
( )20
8
Sense of Sizes(Difference in quantities)
Greater quantity
28
Smaller quantity
20 8
Difference-
- =
=
( )
( )28
Smaller quantity
Greater quantity
( )20
8
Problem Sum (1)
Mrs Chan has 28 yellow balloons and 20 red balloons.
There are 8 more yellow balloons than red balloons.
Label the two bars and fill in the numbers for the following
model :
Yellow balloons
Red balloons8( )
____________
____________
( )28
( )20
4) Janice packed 50 sandwiches in a box.
Amiya packed 12 fewer sandwiches than Janice.
How many sandwiches did Amiya pack?
WB Pg 59Step 1: Read the story sum
Step 2: Write the statement
Amiya packed ____ sandwiches.
Step 3: Decide who/what is involved
Step 4: ComparisonJ
A
Step 5: Chunk the problem
50
12?Step 6: Solve the question 50 – 12 = _____(Amiya)38
38
shorter bar
Step 7: Write and check answer
38
5) Book A has 360 pages.
Book B has 36 pages more than Book A.
How many pages does Book B have?
WB Pg 62Step 1: Read the story sum
Step 2: Write the statement
Book B has ______ pages.
Step 3: Decide who/what is involved
longer bar
Step 4: ComparisonA
B
Step 5: Chunk the problem
360 36
?Step 6: Solve the question
360 + 36= _____ (B)396
396
Step 7: Write and check answer
396
Common mistakes in model drawing:
Common mistakes in model drawing:
Common mistakes in model drawing:
Suggested activities to do with
your child at home
Useful websites for model drawing:
Thinking Blocks
Thinking Blocks (Addition and Subtraction)
Model Drawing for
Multiplication and Division
Multiplication
G x E = T
Number of groups x number of items in eachgroup = Total number of items
WB Pg 101
6) Janice stayed in Thailand for 5 weeks.
There are 7 days in a week.
How many days did Janice stay in Thailand?
Step 1: Read the story sum
Step 2: Write the statement
Janice stayed for ____ days in Thailand.
Step 3: Decide who/what is involvedG
E
T
Step 4: Part-Whole
Step 5: Chunk the problem
7
?
Step 6: Solve the question
5 x 7 = _______ (days)35
Step 7: Write and check answer
35
WB Pg 102
7) Mrs Koh buys 6 boxes of instant noodles.
In each box, there are 10 packets of noodles.
How many packets of noodles does Mrs Koh buy altogether?
Step 1: Read the story sum
Step 2: Write the statement
She bought ___ packets of noodles altogether.
Step 3: Decide who/what is involved
G
ET
Step 4: Part-Whole
Step 5: Chunk the problem
10
?
Step 6: Solve the question
6 x 10 = ____
(packets)
60
Step 7: Write and check answer
60
DivisionT G = E
Total number of groups
= number of items in each group
÷
÷
8) Siti’s mother bakes 18 fruit tarts.
She divides the fruit tarts equally between Siti and her friend.
How many fruit tarts does each child get?
WB Pg 101Step 1: Read the story sum
Step 2: Write the statement
Each child gets _____ fruit tarts.
Step 3: Decide who/what is involved
T G
E
Step 4: Part-Whole
Step 5: Chunk the problem ?
18
Step 6: Compute and solve
18 ÷ 2 = _______ (each
child)
9
Step 7: Write and check answer
9
9) A box contained 12 sweets.
2 children shared the sweets equally.
How many sweets did each child receive ?
Step 1: Read the story sum
Step 2: Write the statement
Each child received _____ sweets.
Step 3: Decide who/what is involved
T
G E
Step 4: Part-Whole
Step 5: Chunk the problem ?
12
Step 6: Compute and solve
12 ÷ 2 = _______ (each
child)
6
Step 7: Write and check answer
6
DivisionT E = G
Total number of items in each group
= number of groups
÷
÷
WB Pg 102
10) Mr Lee has 50 straws.
He gives each pupil 5 straws.
How many pupils does he give his straws to?
Step 1: Read the story sum
Step 2: Write the statement
He gives to ___ pupils.
Step 3: Decide who/what is involved
TE
Step 4: Part-Whole
Step 5: Chunk the problem
5
50
5
Step 6: Compute and solve
50 ÷ 5 = _____ (pupils)10
Step 7: Write and check answer
10
WB Pg 100
11) There are 15 crayons.
Mrs Li gives each child 5 crayons.
How many children get 5 crayons each?
Step 1: Read the story sum
Step 2: Write the statement
____ children get 5 crayons.
Step 3: Decide who/what is involved
TE
G
Step 4: Part-Whole
Step 5: Chunk the problem
5
15
5
Step 6: Compute and solve
15 ÷ 5 = _______
(children)
3
Step 7: Write and check answer
3
Useful website for model drawing:
Thinking Blocks
Useful website for model drawing:
Thinking Blocks
Recommended