Sunday, 29 September 2013

Final lesson - Breaking down numbers into smaller form
Math problems!  It is better to term them “math magic” or “math tricks.” Breaking down numbers into small, easily understood steps will transform those “problems” into fun solutions. Using objects, looking for patterns, acting out problems, making charts and visualizing are just a few of the many keys.
  • Use “real world examples.” Sometimes math seems too obscure when it’s only an equation. Math becomes fun your students see how math applies to the real world. The key is to change how math is viewed. Think, explore and experience!
  • Look for patterns. Train your eye to look for repetition. There are some great books, such as “The Grapes of Math” by Greg Tang, that teaches this concept. Children learn how to add by seeing numbers in sets, and creatively solve problems with patterns and symmetries.
  • Make charts. It’s so much easier to discuss the percentage of a sales increase by looking at a bar chart than at numbers on a page. You can measure everyone in your family and make a bar chart of the heights. Calculate the “average” height.
  • Find some magic. Discover fun “math tricks”.  For example:
breaking down numbers into smaller form

Breaking the whole number 354 into smaller form in the hundreds, tens and ones place makes it easier to be divided by 3.

300 ÷ 3 = 100   /  30 ÷ 3 = 10 /  24 ÷ 3 = 8
  • Draw a picture to help you understand the problem in a new way. Word problems are best when a child can visualize what is happening.
  • Visualize. Visualize all the steps involved in solving a problem and try to find the answer. Take math “tricks” to the next step and do “mental math.” It’s simpler and more fun than you thought possible.
  • Use objects. Lay out candy, buttons, beans, blocks, paperclips or pennies to see the parts of a problem. Dividing a pie can be educational—and delicious!
  • Learn to take “one step at a time.” Break down equations into easy-to-do parts. After all, one runs (and wins!) a marathon one step at a time. A long math equation doesn’t need to be solved in one large leap.
After your child has created a plan of attack, approaching the any test should seem less intimidating. As students become more comfortable with the form and process, they can create their own problems.

How do we introduce this concept to preschoolers?  We could start with smaller numbers.  However, it is important that they have developed a sense of ‘ten’ and ‘place value’.  Here are some tips to develop this skill in young children.

Number Sense Series: A Sense of 'ten' and Place Value

Once a basic number sense has developed for numbers up to ten, a strong 'sense of ten' needs to be developed as a foundation for both place value and mental calculations. (This is not to say that young children do not have an awareness of much larger numbers. Indeed, there is no reason why children should not explore larger numbers while working in depth on 'tenness').


Ten-Frames are two-by-five rectangular frames into which counters are placed to illustrate numbers less than or equal to ten, and are therefore very useful devices for developing number sense within the context of ten.

The use of ten-frames was developed by researchers such as Van de Walle (1988) and Bobis (1988). Various arrangements of counters on the ten frames can be used to prompt different mental images of numbers and different mental strategies for manipulating these numbers, all in association with the numbers' relationship to ten.

Plenty of activities with ten-frames will enable children to automatically think of numbers less than ten in terms of their relationship to ten, and to build a sound knowledge of the basic addition/subtraction facts for ten which are an integral part of mental calculation. For example, a six year old child, when shown the following ten-frame, immediately said, "There's eight because two are missing."

This child had a strong sense of ten and its subgroups and was assisted by the frame of reference provided by the ten-frame. Once this type of thinking is established, the ten-frame is no longer needed. Although dealing with whole numbers initially, the 'part-part-whole' thinking about numbers supports the understanding of fractions, in particular tenths.

Place Value

'Ten' is of course the building block of our Base 10 numeration system. Young children can usually 'read' two-digit numbers long before they understand the effect the placement of each digit has on its numerical value. For example, a 5 year-old might be able to correctly read 62 as sixty-two and 26 as twenty-six, and even know which number is larger, without understanding why the numbers are of differing values.

Ten-frames can provide a first step into understanding two-digit numbers simply by the introduction of a second frame. Placing the second frame to the right of the first frame, and later introducing numeral cards, will further assist the development of place-value understanding.

 I hope these tips were helpful.



Friday- Form squares with different shapes

Its Friday!  Drawing shapes!  My favourite!  We explored with different shapes that could form congruent squares.  Suddenly, I realized that I was facing difficulties in coping the shapes to form complete squares.  Somehow, it did not fit.  You will understand better by looking at these images.


some parts do not fit although it looked complete from afar

Even an extra millimetre would make a difference.....  I need to sharpen my visual and spatial skills.  Here is a great game for that and can be simplified for young children.  You could use any kind of sticks for it.

Matchsticks game
Matchsticks game is a great geometric game and it will definitely sharpen your mind, especially your visual and spatial skill.


The game has 24 matchsticks.

Form squares by removing a specified number of matches!

For instance you could be asked to remove 3 matches to form 7 squares.


Carefully think about it before you remove a match. Once you remove it, you cannot put it back.

Therefore, one false move at the beginning could make things really challenging.

Keep track in your head of how many you already removed since the game will not tell you.

A good strategy!

Practice with real matches before removing them from the game.

Pretend the game says remove 9 matches to form 4 squares.

Since you have 15 matches left, you could get 15 real matches and try to make 4 squares with them.

Once you have made the 4 squares, you can go back to the game and remove the ones you need to end up with your shape

You will notice that it is easy to get started, but not as easy to finish.

The more you play, the more you will know which matches to remove and where to remove them.

So have fun and remember. Practice makes perfect!

Lesson on fractions (25 September 2013)

Point 1: When we are partitioning a whole into fractional parts, they must be the same size but need not be of the same shape like the image on the top left.
Point 2: When the number of equal sized parts determines the fractional amount, we need to make them into equivalent fractions in order to divide them equally.  Thus, they were written into simplest terms. 
Young children must understand fractions meaningfully.  Using appropriate representations and different categories of models broaden and deepens their understanding.  This is essential for their future learning as fractions are used as measurement across various professions.

Fractions for young children - Simple methods for 4 to 6 year olds.


There are many ways how to teach fractions, and the success or failure of the child to understand fractions will depend on the teaching method used.  The methods outlined below have been proven to be easy for young children to grasp, and easy for every preschool teacher to implement.

It's been said that if a child understands fractions, then they can understand any mathematics concept.  It is then very important for every preschool teacher to know how to teach fractions in the most approachable way possible.
Explain every fraction in terms of pizza or pie to make the concept familiar.
When deciding on a method of how to teach fractions, we need to use fractional analogies that children will immediately recognize.  The pizza is the perfect instrument to teach the concept of the fraction.

Use fractions that every child understands.  For example, take the fraction: ½.  Take the time to explain that this fraction represents a pizza that has been cut into two pieces, but you only have one of the pieces left. 


1/3 or one third
Next, tell them that the numerator of the fraction is the top number and the denominator of the fraction is the bottom number.  Always keep in mind that using the best methods of how to teach fractions involves moving very slowly, giving multiple examples involving fractions until every child is comfortable.  Use familiar examples involving fractions such as 1/4, 1/3, and 3/4 to reinforce the concept of what a fraction is.

1/4 or a quarter

Draw lots of pictures of fractions.
Children are visual learners and the best technique of how to teach fractions involves drawing pictures of fractions.  For example, take the fraction: 1/4.  This fraction can be best described by drawing a pizza cut into four pieces, but you only have three of the pieces such as in this picture of the fraction.  Get children to figure out the fraction of the missing piece.

2/8 or 1/4
Ensure that you teach fraction simplification slowly and thoroughly.
Most students have a very hard time understanding the concept of equivalent fractions, otherwise known as fraction simplification.  The best way how to teach fraction simplification is to show pictures of many such fractions that we know to be equivalent.  For example, we know that:

1/4 or a quarter



is equivalent to 

For those new to learning fractions, this concept can be hard to understand.  As always, when it comes to how to teach fractions, pictures are almost always the superior teaching tool. 

To show how these fractions are equivalent, we draw each case separately.  The teacher can then show children that the fraction 2/4 is “two out of four pieces” and that 1/2 are "one out of two pieces".  It is a very powerful method of teaching fractions to show visually how these two fractions represent the exact same amount of pizza. 
In conclusion, learning how to teach fractions in the best way possible is very much worth the teachers’ time because when we form a good foundation in the essentials of fractions, it will make the future topics much easier to understand.  Childdren will then have a good foundation in fractions to understand how to add, subtract, multiply, and divide fractions without problems.  And by using the methods outlined above, the teacher will know how to teach fractions to young children in the most approachable way possible.

Wednesday, 25 September 2013

Yesterday's lesson was interesting and made simple with a slight flavour of primary school math.  Reading this might provide some answers to what's going through our minds now.

A Brief History of Singapore Math by a source from the US

A relatively small and densely populated island, Singapore’s only natural resource is their people. The country has chosen to focus on building strong Singaporean citizens beginning with their earliest education.
The mathematics curriculum was developed with this goal in mind. The first primary mathematics curriculum was developed in 1981 by the Curriculum Development Institute of Singapore. In Singapore, it is simply referred to as “maths”.
The term “Singapore Math” refers to the Marshall Cavendish Primary Mathematics series of materials used in the U.S. and several other countries.
The 1981 curriculum focused on basic content.  This curriculum was revised in 1992 to make it a problem solving curriculum. The Primary Mathematics (2nd Edition) was based on the 1992 curriculum.
The Primary Mathematics (3rd Edition) series was based on a reduced syllabus in 1994.  In 1999, Singapore’s Ministry of Education decided to reduce the content in the curriculum up to 30% for most subjects.
In 1998, the first books were imported from Singapore for use in this country (Primary Mathematics 3rd Edition). These books were written in British English and contained Singaporean money and only metric measurement. The U.S. Edition was created in 2001 and included American measurement and money.
The most recent series published in the United States is the Primary Mathematics Standards Edition. This series was designed to meet all state standards in California; a state that has written standards based on the National Council of Teachers of Mathematics (NCTM) Focal Points.

Number bonds is a concept used in Singapore Math. It is a visual image that can be used to show the relationship between addition and subtraction. Number bonds consists of a minimum of three circles connected by lines. The “whole” is written in the first circle and its “parts” are written in the adjoining circles. The "parts" when added together will then equal the "whole"

The following number bond can be used to represent four number sentences.
3 + 2 = 5, 2 + 3 = 5, 5 − 3 = 2, 5 − 2 = 3
number bond
Numbers To 10: Making number bonds with cubes
The video shows how number bonds can be used to "split" numbers.             

What makes 10? Basic number facts to 10 using the tens frame

Tuesday, 24 September 2013

Any preschool classroom without tangram puzzles is a bore.  The amount of learning that children can gain from it is endless.  Recently, my colleague and I went on a strike when a leader asked, “Why do I see pattern blocks at your learning centre all year around?  Children will get bored you know…” I was telling myself, “Hmm.. actually, a simple and boring tool as such can create wonders….”.
Call us outdated or inflexible; these are objects that are precious to my K2 children.  So, when I attempted to remove it, I received a lot of disapproval and unhappy grunting.  Of course, I asked them, “It’s not fun to keep old stuff…” and one boy replied, “But pattern blocks can be used everywhere!  Can use for playing blocks, can make puzzles, can make things, can use for drawing, can use for art!  Whyyyyy?”
So, in the end, they won of course.  His reply sums up preschool learning; the path for life-long learning.   “Geometry”, a ‘fancy’ name for learning about properties and dynamics of space, shape, size and proportions; that can be applied to practical applications in life.    That’s what we did in class today; forming congruent shapes through “PLAY”. 
Similarly, playing with objects as such, trains children’s mind, hands and senses to understand these properties which lays the foundation for primary school learning.  This can happen with “PLAY! PLAY! PLAY!”; purposeful and meaningful play.  The emphasis therefore, is on creating familiarity with the basic concepts.

"Rather than to schoolify preschool, we must focus on what would be relevant to teach at that stage.  Education is a life long journey, not a short sprint."
                              - Minister for Education, Heng Swee Kiat, MOE Workplan Seminar 201
Here are some tips for teaching young children about the properties of shapes.
 Building Knowledge of Shapes
Begin by helping children build a basic knowledge of shapes. Point out all the circles around you, such as plates or cans.  Naming the shapes in their environment is important. 
Analyzing Shapes
Next, involve children in analyzing objects and pictures in their environment by identifying their basic shapes. For example, they might:
·         Find circles in picture books
·         Go on a "shape hunt" and find all the rectangles in the classroom
·         Look for shapes such as triangles or squares that you have hidden all around a room  When you are teaching about shapes that are not as numerous in most environments, such as triangles or rhombuses (diamonds), you can make copies out of cardboard or construction paper.  Make sure you make different shapes and sizes. Children learn limited ideas about shapes unless we show them a variety of examples.
 Supporting Visual Memory
The next step is to build children's visual memory of pictures and shapes. For example,  show a child a very simple picture, such as a line drawing, for only two or three seconds. Then cover it and ask the child to describe it. Move to more complicated pictures as the child's ability increases.
Continue to play this "flash" game with variations. For example, show a child one of three drawings that are very simple for two seconds. Then mix all three up and let the child find the one that you showed. Later, when you have worked with several shapes, and combinations of shapes, this can be fun and challenging: the child might have to remember if she saw a triangle inside a circle or a circle inside a triangle.
 Combining Shapes
As soon as you have worked with several shapes, combine these shapes in your activities. For example, after you have studied horizontal and vertical lines, examine pictures with children, such as city scenes, and invite them to find all the horizontal and vertical lines they can. Talk about the vertical and horizontal lines in your classroom, and how they combine to make different shapes and objects.
 Reproducing Shapes and Combinations of Shapes
After building children's knowledge of shapes and combinations of shapes, encourage them to reproduce them. For example, show a child a square you made with pattern blocks or pipe cleaners. Then, challenge the child to copy the shape.
 Creating with Shapes
Children should use the shapes you are working with to make their own designs and pictures. Soon after reproducing shapes, encourage children to invent their own ways of using the shape to make designs with pipe cleaners, buildings with blocks, and pictures with crayons.
Supply children with a combination of different materials, such as small blocks, pipe cleaners, and paint. Remind children of the shapes you have explored. Then, give them the opportunity to use the materials to create the shapes in their own ways.
Different materials encourage children to think about the shape in different ways. To make a square, you have to choose the correct number of blocks (four equal lengths). Using pipe cleaners, you have to bend them "just right" to make the square corners.
A football tossed into the air

Cool isnt’t it! Just look at what's behind children's  thinking.  Done by a K2 girl.




Saturday, 21 September 2013

Understanding and meeting the needs of your children

“Children do not gain understanding of addition and subtraction through just by working with symbols”.
        Meaningful learning comes from real experiences, not through ‘work’ with symbols.  It is possible for children at this age to be successful with symbols, yet without fully understanding what they represent. 

       This indicates that they do not connect their real-life experiences to the symbols they are working with, and rather memorize the facts and figures instead.  Ditch those worksheets for the moment if this is what you see. 

       For children to clearly understand addition and subtraction, they must be able to see the connection between these processes and the world they live in.  They need to learn that certain words such as add, subtract, total, sum, difference and equals are used to describe things that happen in their lives every day.   

The use of natural language along with the actual objects reinforces the connection between the real world and the mathematics the children are learning.  Children will then regard them as every day events and not something to be heard or done in school only.
 However, children still need to learn to read and write the equations that describe the processes they are working with.  They need to connect their experiences with the symbols used to represent those experiences. They need to see symbols as tools for keeping track of the numbers in the problems and not as the problem itself.
Modifications can be made to these activities to enable your child to reach the next level.  For example, as you present these story problems, provide the opportunity for children to record the actions through pictures or other informal representations and then to conventional symbols.  The symbols should only be introduced as a way of keeping track of the numbers and actions in the stories.
"The most powerful learning experiences have value in being repeated".