Mathematics Workshop

Middle Primary

For ParentsMath Matters & Problem Solving

9 April 2016

Middle Primary

Math Topics

Learning Math Through Problem Solving Approach

Primary 3Topics

Whole Numbers

Fractions

Measurement (Length, Mass, Volume)

Measurement (Area and Perimeter)

Time

Money

Geometry

Data Analysis (Bar Graphs)

Primary 4Topics

Whole Numbers

Decimals

Fractions

Measurement (Length, Mass, Volume)

Measurement (Time, Area and Perimeter)

Geometry

Data Analysis (Tables and Graphs)

Type of Mathematics Questions

Knowledge- Recall specific mathematical facts,

concepts, rules and formulae, and perform straightforward computations.

Comprehension- Interpret data and use mathematical

concepts, rules and formulae and solve routine or familiar mathematical problems

Type of Mathematics Questions

Application - Analyse data and/or apply mathematical

concepts, rules and formulae in a complex situation, and solve unfamiliar problems.

…are general methods or strategiesof achieving a solution to a given

complex word problem

What are Problem Solving Heuristics?

Heuristics for Problem Solving:

• Model Drawing• Make a supposition• Work Backwards

What is Model Drawing?

… basically a mathematics problem

solving strategy based on a pictorial

approach.

The representation is in the form

of bar diagram

The use of Model Diagram provides studentswith the means to:(1) handle information(2) deal with complexity and(3) communicate their thinking through the

use of visuals which they can manipulate

Stage 1: Understand the Problem� Read the entire problem� Decide who or what is involved

Steps to Model Drawing

Steps to Model Drawing

Stage 2: Devise a Plan� Decide the type of model you need to

draw (part-whole, comparative)� Read each sentence one at a time � Draw the model and add in the

information after each sentence � Make linkages

Stage 3: Carry out the plan� Do the working and solve the problem

Stage 4: Look back (Reflect)� Check your answer and make sure

the unit is included

Steps to Model Drawing

Part-Whole Model

• Finding the Whole, given Parts • Finding a Part, given the Whole and a

Part

Whole

Part Part

Part-Whole ModelDavid has 27 stamps.He buys 9 more stamps.How many stamps does he havenow? 27 9

?

There are 98 hats. 20 of them are pink and the rest are yellow. How many yellow hats are there?

Part-Whole Model

Part-whole Model: Whole Numbers

Calvin earns $2000 every month. He pays

$300 for food. He also spends $200 on his car, $500

on housing and saves the rest. How much does he save

every month?

Mr Goh earns $6000 every month. He pays

$1100 for food. He also spends $1500 on his car, $2100 on housing and saves the rest. How much does he save every month?

Try this!

Comparison Model

•Two or more quantities are compared.

•If one quantity is bigger than another by a certain amount, knowing the smaller quantity and the difference, we can find the bigger one.

•Or knowing the bigger quantity and the difference, we can find the smaller one.

Davian had 467 coins. Sharonhad 142 fewer coins than Davian.How many coins did Sharonhave?

Comparison Model

Comparison Model

Cindy’s mass is 31kg.

Ben is 4 times as heavy as Cindy.

How heavy is Ben?

Comparison Model: 3 items

Cindy, Betty and Alice have a total of 270 stickers. Cindy has thrice as many stickers as Betty. Alice has half as many stickers as Betty. How many stickers does Betty have?

Ben collected 240 cards.

Jerry collected 140 cards.

How many more cards did Ben collect than Jerry?

Make a suppositionSupposition is an act of supposing. That is to make an assumption.

Solution:

• Chicken � 2 feet, rabbit � 4 feet

• Suppose there are 15 chickens.

A farmer has 15 chickens and rabbits. These animals have 40 feet altogether. How many of each type of animals does the farmer have?

Make a supposition

2 x 15 = 30

Since a rabbit has 2

feet more than a

chicken, an excess

of 2 feet will make 1

rabbit; If there is an

excess of 4 feet,

there should be 2

rabbits.

Therefore, finding

the excess number

of feet can help us

to find the number

of rabbits.

40 – 30 = 10 (excess feet)

10 ÷ 2 = 5

There are 5 rabbits.

15 – 5 = 10

There are 10 chickens.

Make a supposition

Some motorcycles and cars are parked at a carpark. Thomas makes a count to find a total of 10 vehicles and 34 wheels. How many cars are there?

Make a suppositionGrace bought 20 blouses and skirts. There are 5 buttons on each blouse and 2 buttons on each skirt. She counted a total of 64 buttons. How many of each type of clothes did she buy?

Try this

Work BackwardsWorking backwards is a strategy that makes use of the end result of a problem to find what it begins with. Very often, answers can be found by tracking backthe steps and reversing the operations.

Work Backwards

I am thinking of a number. I double it. I add 8 to the result and my answer is 22. What is the number?

7 14 22X 2

÷ 2 - 8

+ 8

Reverse operations22 – 8 = 14

14 ÷ 2 = 7

The number is 7.

I am thinking of a number. I double it. I add 8 to the result and my answer is 22. What is the number?

Work Backwards

A is a number. Add 5 to A and multiple the result by 10. Subtract 8 from the product and divide the result by 2. The final result is 151. What is A?

Work Backwards

Try this

If you multiply a number by 8, then add 3, then subtract 9, you get 34. What is the number?

Study (Understand and

Analyse the scenario)

Think (Devise a plan and

choose a strategy)

Act (Work out the solutions)

Reflect (Check if the answer is

logical)

How you can help?(1) Monitor your child’s work• Ensure all steps are written, models are

drawn correctly.• Remind your child to check his/her work.

(2) Help your child learns the multiplicationtables.

(3) Have sufficient practice to acquireprocedural skills, speed and accuracy.

How you can help?

(4) Excite your child by making Math real andrelevant to him or her.

• Take your child shopping and talk aboutthe quantities of anything you buy.

• Let your child handle money and work out how much things cost.

(5) Try to make maths as much fun as possible

- games, puzzles and jigsaws are a greatway to start.

How you can help?(6) Work with your child’s teachers.

Enjoy learning together!

(7) Spend time reading books related toMathematics with your child.

https://www.schoolbag.sg/story/explore-mathematics-related-resources#.VwRT64f2PmI

Q & A