PREPARATION FOR MULTIPLICATION 

Color plays an important role in learning.

It aids memory recall and understanding. 

Math is a rich landscape of pattern and relationship.

The rods open a window through which this vibrant world is  visible to children.

Multiplication is simply repeated addition (iteration). It is closely related to division and factors of numbers.

Each multiplication table has a distinct pattern that can be revealed by the rods.

By adding a twist to ‘Cinderella’s Staircase’ children can be introduced to ‘multiplication tables’ .

Simply suggest that Cinderella wishes to change her carpet to red. What would the staircase look like now?

Explain to children that the first step of the staircase will always be the color of the carpet.

It is always interesting to observe how children continue the staircase beyond the orange rod.

Some children will intuitively use the rods that represent  multiples of the first step.

The green (3) staircase can be constructed using only green, dark-green and blue:

               g,     3

               d,     6

               B,     9

         B + g,   12

         B + d,   15

Cinderella’s red staircase. (The two times table).

If necessary construct the first two steps and ask children to continue.

The sequence is:

r, p, d

2, 4, 6 . . .

1 x 2, 2 x 2,

3 x 2 . . .

The difference will always be red (2).

Cinderella’s green staircase.

The three times table.

Again, construct the first two steps if necessary

The sequence is:

g, d, B

3, 6, 9 . . .

1 x 3, 2 x 3, 3 x 3 . . .

 The difference will always be green (3).

 This work also forms the foundation for understanding different number bases.

EXTENDED STAIRCASES

 Staircases can be extended beyond the first ten steps just as numbers can extend beyond ten to infinity.

Ask children to continue their staircase beyond the orange rod,

Some can ‘see’ the next step immediately.

Others will resort to trial and error – very scientific.

Some will be baffled – not a good learning state!

While it is important to present a  challenge once a situation becomes stressful  learning will not take place.

Mental blocks are often the result of imposed stressful learning situations.

Many of us believe we are ‘no good’ at math because we were frequently exposed to formal math situations before we were ready.

The Cockroft report found many professional people, including teachers, felt guilty about their lack of expertise in math.

 Instead why not exercise the imagination. A very powerful learning ally.

We shall call this game:

CINDERELLA’S STAIRCASE

These games and challenges are a preparation for the understanding of  different number bases.

Later children will be led to see how our number system is constructed and also how it is possible to work in bases other than ten.

CINDERELLA’S STAIRCASE

Cinderella has a staircase with a white carpet.

Can you build it?

Once they reach orange suggest they have more carpet left.

Can they continue up the staircase?

STAIRCASES 

Mental Agility

It is important that children never associate a rod with a particular number.

The rods are not a  cumbersome calculating tool. They represent a complete arithmetical model designed to free them to think in abstract terms. 

This is important for later work, for example, with fractions and graphs. 

One way of doing this is getting children to visualize a staircase and name the rods going up and going down. 

In this way, depending on whether the child has built the complete staircase or not , red will be viewed as ‘step 2, going up and ‘step 9’ going down.

Later, once children are introduced to the ‘number names’ of the rods, play RELATIONSHIP GAMES to help increase your child’s mental agility.

The early concept of FRACTIONS – the idea that numbers exist between ‘while numbers’ – can be introduced using this approach.

 Because children have experienced pleasure in using the rods creatively during FREE PLAY they will always adopt a positive attitude to the introduction of new concepts. The material is familiar and associated with positive experiences.

Learning is fun!

Make staircases using the first five colors and ask children to visualize then ‘read’ them going up and down.

Increase the challenge as children get more adept.

e g the first six, seven rods etc.

Remember the ‘flow state’.

RELATIONSHIP GAMES

Play these games regularly once children have been introduced to the ‘number names’ of the rods.

Choose different rods to represent one.

STAIRCASES 

Staircases are very potent mathematical constructions. 

Staircases:

• help fix the mental image of the rods in your child’s mind;
• improve memory recall
• prepare for the introduction of  number and place value;
• can introduce the early concept of fractions. 

Quite probably children will have already begun to construct staircases with the rods during FREE PLAY. 

Call the rods by their color names.  

Later, when all the signs have been introduced, children will write sentences using the letter-names of the rods. 

Explain that because the color names begin with a certain initial letter they will be given that letter name.

We call brown ’tan’ because we already have a black (b) and a blue (B).

Because blue is bigger we write the initial letter in upper case.

Tan becomes ’t’.

 There is an important link to language development here that we will look at later. 

If children have not made any staircases ask them to make a set of stairs starting with the smallest rod (white) and finishing with the largest (orange).

Children will quite possibly have already made a staircase like the one below.

The sequence is:

w, r, g, p, y, d, b, t, B, o

1, 2, 3, 4, 5, 6, 7, 8, 8, 10 

Once we have introduced the ‘number names’ of the rods the white will, most of the time but not always, represent 1.

It is vital that the rods are not seen to represent a particular number.

For example when introducing fractions we may decide to call red ‘one’.

We will look at this next.

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CARDINAL NUMBER 

Formal approaches to the teaching of number tend to focus exclusively on one to one relationships. 

This can often result in children having to count on fingers to calculate the answer to a problem. They are unable to ‘see’ numbers as a whole group. 

Through FREE PLAY, DIRECTED ACTIVITIES and TOUCH GAMES children naturally view numbers as complete groupings. 

They will know that green is equivalent to three whites while  perceiving it to be a ‘number’ in its own right. 

The concept of cardinal number has been naturally acquired through play. 

Having a firm grasp of CARDINAL NUMBER  helps children develop the ability to SUBSTITUTE ONE TERM FOR ANOTHER – crucial to understanding in Math. 

NUMBER BOND GAMES can consolidate this ability and give children a firm grasp of number bonds even before ‘number names’ are introduced.

Children view green (3) and red (2) as complete objects (groups) that combine to make another complete object (group), yellow (5):

    g + r = y

    3 + 2 = 5

and not as separate objects combined: 

   (w + w + w) + (w + w) = 5w

   (1 + 1 + 1) + (1 + 1) = 5

(Don’t worry – we will deal with brackets later) 

Choose one of the rods and ask  children to name two rods that end to  end will be the same length as it.

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THE LEARNING EQUATION: 

              L = U + M 

Learning equals understanding plus memory. 

This programme is built upon the foundation of understanding and not learning by rote. 

The kinesthetic approach afforded by the rods provides the understanding.

This must be consolidated by memory recall. 

We remember via our senses.

You can begin to increase children’s capacity for recall now by engaging his/her senses in every activity. 

We have all experienced an occasion when a smell, a sound, a color, or a particular taste triggers memories we often did not know we possessed. 

The smell of leather transports me back to my first day in school. I see murals on the wall that have long since disappeared. Experience once again the panic of being abandoned by my mother for a whole day! 

Color, for example, is a greater stimulus for memory recall than verbal cues or objects (Backman et al and Allen) 

If your children want to build a fairy tale castle with the rods then ask them to imagine themselves standing outside the castle first.

What might they see, smell, hear, taste?

Get them to ‘see’ the object they are about to create in their mind.

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Funding sources are available to provide a Power Pumper at no cost to most children who need them. See if your child qualifies.

The Power Pumper Helps Children Develop:

IMPORTANT WORDS AND PHRASES:

end to end

train

pattern

big

small

side by side

above

below

long

short

All children need to know this vocabulary. 

For young children it can be introduced during FREE PLAY or DIRECTED  ACTIVITIES. 

Because young children are more naturally kinesthetic learners introducing the vocabulary this way will ensure they understand and retain  it. 

This is also true for older children or adults who, for whatever reason, did not understand these concepts the first time around. 

Adults have found this approach very liberating especially as, often for the first time, they are able to ‘see’ patterns and relationships that traditional teaching methods had ’hidden’ from them.      

“I hear and I forget,

I see and I remember

I do and I understand.” 

Chinese Proverb     

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If any of you are interested in getting one for your child, you can visit their website using the link below for more information.
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Thanks

Phil Rowlands