Acquiring a Working Knowledge of the Multiplication Tables

The young learner first learns to relate the concrete 3D presentation of number value with the related four operations i.e. add, subtract, multiplication and division. A working knowledge and automatic recall of Number Bonds to ten facilitate mathematical operations involving addition and subtraction. A working knowledge and automatic recall of the multiplication tables facilitate mathematical operations involving multiplication and division.
The earlier these skills are established the easier it is to embrace the practical application of further mathematical skills and related problem solving techniques. However, learning the multiplication tables remains an awesome task for many learners who are unable to secure the automatic accuracy required to aid every day and higher mathematical operations. The author has presented in this folder some carefully described descriptions of some of the multi-sensory learning techniques she has invented alongside some of the more recognised supportive scaffolding.
Traditionally the multiplication tables were taught through the dominantly auditory mode of verbal repetition. However the ability to automatically chant a multiplication table, e.g. the two times tables, does not necessarily mean that the learner can automatically recall random elements such as 7×2 or 2×3. For some the answer to 7×2 can only be found by chanting the two times tables form the beginning through to the required seventh element. 1×2=2, 2×2=4, 3×2=6, 4×2=8, 5×2=10, 6×2=12, and 7×2=14! This extended process of recall is time consuming and likely to distract the learner from the mathematical understanding required for successful completion of the task in hand.
Steiner schools place a focus on rote learning of the multiplication tables once the children have entered main school class one at seven plus years. In Steiner schools repetitive rote learning is accompanied by rhythmic movements such as stamping or clapping, catching and throwing together with random participation. This encourages individual children to recall a specific answer without recalling the whole of the multiplication table from the beginning. This combination of repetitive chanting and random recall within a rhythmic structure of movement is considered more beneficial than standard rote learning through repetitive recall of the tables from one times through to ten or twelve times.
The importance of learning is superseded by the nature of enjoyable participation, the development of understanding and later application within a wide range of associated intellectual activity. Multisensory activities are designed to meet the widest possible range of learning and future application. Ideally they may need to present both auditory information and visual information within structural and rhythmic movements and actions with associated kinaesthetic sensory perception. The wide range of examples presented by the author in this chapter are designed to support enjoyable learning and thereby help every learner gain an instant recall of the multiplication tables and a wide spectrum of. understanding. Later development of mathematical skills involves recording this information as 2D drawn numerical symbols and/or written numbers that illustrate sums, mathematical formulas and algebra systems of investigation and resolution.

Poetic Presentations of the Multiplication Tables

The ten times Table

Ten sheep in the pen,
When it is Twenty this field is empty.
Now it is Thirty and my boots are very dirty.
Forty sheep can be very naughty.
Fifty, and the dogs’ eyes are very shifty.
Sixty, too many for our old dog dixy.
Seventy sheep is more than plenty.
Eighty makes me feel high and mighty
Ninety makes the dogs quite flighty
One hundred is far too many sheep to be fed.
And I am so tired I must go to bed and lay down my sleepy head.
Counting sheep will help me sleep 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Sleep tight and good night.

Rhyming Multiplication game

Example:- Three times table (The words in the brackets are optional choices)
One, two, three, (once three is three or 1×3=3), go climb a tree!¬
Four, five, six, (two threes are six) pick up the sticks/now you’re in a fix
Seven, eight, nine, (three threes are nine) lets go out to dine/ the weather it is fine
Ten, eleven, twelve, (four threes are twelve) lets dig and delve.
Thirteen, fourteen, fifteen, (five threes are fifteen) now where have you been!?
Sixteen, seventeen, eighteen, (six threes are eighteen) and what have you seen?
Nineteen, twenty, twenty one, (seven threes are twenty one) did you see Mary’s son?
Twenty two, twenty three, twenty four, (eight threes are twenty four) someone is knocking at the door.
Twenty five, twenty six, twenty seven, (nine threes are twenty seven) is there time to go to heaven?
Twenty eight, twenty nine, thirty, (ten times three is thirty), certainly not you are much too dirty!

There are many creative rhyming answers e.g. either a single word (three/tree) – this could also be a nonsense rhyming word, a short phrase (What can you see?) or a story (It’s time for your tea.). The table rhymes can be created by an individual person or a group and recited either as a single piece of prose or spontaneously created by a group who take it in

turns to add the next line when their turn comes around. The rhyming tables can be spoken and/or recorded in numerical form 3 x 3 = 9 (nine socks on the line) with drawn pictures to represent the rhyming word/phrase at the end of each line. For those who know their tables and can easily recall any element of each table this activity presents a creative verbal challenge, for those that are not expert at their tables this activity also challenges the mind to address automatic recall of the mathematical tables from a new light-hearted perspective.

A Co-operative Game

The following game was designed by Helena as a way of experiencing the recitation of a multiplication table as a co-operative group activity.
Method: a row of chairs is placed in an open space. The number of chairs must be exactly the same as the multiplication number chosen for the game. So if the game is a game based on the three times table then game begins with three chairs with one person sitting on each chair. If the game is going to be based on the seven times table then the game begins with seven chairs and seven people, one sitting on each chair. and a row of spare people sitting on a row of chairs nearby while awaiting their turn to take up the first chair when it becomes empty.
1st person says one then second person says two etc.

7th person says 7 then gets up and rings a bell and says 1×7=7. Then all the seated people move to the chair on their left. This leaves the first chair empty and another person sits on it and says 8 followed by the next person who says 9 etc. until the person sitting on the seventh chair says 14 then gets up rings the bell and says 2×7=14. Then all the seated people move to the chair on their left. This leaves the first chair empty and another person sits on it and says 15 the next person says 16……..next 17 etc until the last on the row says 21