primary 2 math parents workshop 27 march 2018 presenters ... · term assessment schedule term 1...

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


Example 3

710 ? 716 722 730 740

+2 +4 +6 +8 +10


-2 -4 -6 -8 -10

Example 4

?

?

Example 5


1 2 1 2 1 2 1

1 2 2 1 2 2 1 2

Example 6

?

?

Example 7


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



Example 9

Study the pattern below. How many

squares are there in Pattern 4?

Pattern 1 Pattern 2 Pattern 3

Let’s Try

This!


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.


How many apples and oranges are there altogether?

?

6 3

+6 3 = 9

Stage 2 Pictorial Representation

There are 6 apples.



?

6 3

Stage 3 Insert the boxes with Pictures

There are 6 apples.



?

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.


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:


18 smiley stickers.


What numbers do we put

in these boxes?


18 smiley stickers.


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?



There were ______ cars left.


Step 4: Part-Whole


254

123 ?

Step 6: Solve the question

254 – 123= 131 (left)

131


131

3) A fruit seller had 584 durians at first.

He sold 225 durians.

How many durians does he have now?



He has _____ durians now.


Step 4: Part-Whole


584

225 ?


584 – 225 = ____(now)359

359


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?



Amiya packed ____ sandwiches.


Step 4: ComparisonJ

A


50

12?Step 6: Solve the question 50 – 12 = _____(Amiya)38

38

shorter bar


38

5) Book A has 360 pages.

Book B has 36 pages more than Book A.

How many pages does Book B have?



Book B has ______ pages.


longer bar

Step 4: ComparisonA

B


360 36

?Step 6: Solve the question

360 + 36= _____ (B)396

396


396

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


Janice stayed for ____ days in Thailand.

Step 3: Decide who/what is involvedG

E

T

Step 4: Part-Whole


7

?


5 x 7 = _______ (days)35


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?



She bought ___ packets of noodles altogether.


G

ET

Step 4: Part-Whole


10

?


6 x 10 = ____

(packets)

60


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?



Each child gets _____ fruit tarts.


T G

E

Step 4: Part-Whole

Step 5: Chunk the problem ?

18

Step 6: Compute and solve

18 ÷ 2 = _______ (each

child)

9


9

9) A box contained 12 sweets.

2 children shared the sweets equally.

How many sweets did each child receive ?



Each child received _____ sweets.


T

G E

Step 4: Part-Whole

Step 5: Chunk the problem ?

12


12 ÷ 2 = _______ (each

child)

6


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?



He gives to ___ pupils.


TE

Step 4: Part-Whole


5

50

5


50 ÷ 5 = _____ (pupils)10


10

WB Pg 100

11) There are 15 crayons.

Mrs Li gives each child 5 crayons.

How many children get 5 crayons each?



____ children get 5 crayons.


TE

G

Step 4: Part-Whole


5

15

5


15 ÷ 5 = _______

(children)

3


3

Useful website for model drawing:

Thinking Blocks

primary 2 math parents workshop 27 march 2018 presenters ... · term assessment schedule term 1...

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