Long Multiplication

Chequer Board  

Material Description:

A board made up of 36 squares.  The squares are colour-coded to correspond to the categories of the decimal system, green for units, blue for tens, red for hundreds.

On the base there is notation in black, right to left for the categories 1 to 100,000,000.  Up the right side there is notation in black for the categories 1 to 1,000.

There is a ledge along the bottom and up the right side for placing out the cards for the multiplicand (bottom) and the multiplier (right side).

A box of coloured bead bars from 1-9 (In tens section, can include loose white and grey cards)

Loose white cards 0-9 for the multiplicand

Loose grey cards 0-9 for the multiplier

1.Laying out all the Bead Bars

Method:

“This is the Chequer Board we use it for multiplication only, it has the same families for as the Bead Frame, (show them) but it also has two new members of the million family”.  (show the children the squares of the simple family) you can see that squares of the same value are on the diagonal” (show them again from the simple to million family).

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“Here I have a bead bar of four if I place it on a ’10’ square what value does it have” [40] (Now give more examples).  “Lets do some combinations” (take two bead bars and put each them on adjacent squares and ask the child to read them” – [a bar of three on a hundred square and a bar of two on a tens square is 320 - place them horizontally, continue making a game out of it.

Introducing the Chequer Board

Method:

“We are going to do is long multiplication, we have white cards to represent the multiplicand and grey for the multiplier” (Lay out four columns of white cards and then, to the right four sets in grey for the multiplier)

“I take my multiplicand and multiplier, watch how I place them” put the cards in front of you to read - 2463   24 - then place the multiplicand (white) along the horizontal and the multiplier (grey) along the vertical.  Read the multiplication of the units, “I take my three, three times”, represent the problem with beads in the unit square, the tens of the multiplicand and the units of the multiplier, the hundreds and thousands of the multiplicand and the units of the multiplier.  Turn the card with the unit multiplier upside down

“There is a trick to this board, when we multiply by ten we add a zero, the special thing with this board is that the multiplication by ten is already done, when we put a number in this square [indicate the tens square] the multiplication is already done”.  When you reach the last number you ask ‘“is the multiplication complete?”, and turn over the tens card.

Bring the second layer of beads diagonally towards the base, collecting beads of the same category together, the you can add or times the beads in the units.  You can carry over one to the tens (keep the ones you take away in your hand for a control later until you have picked up the beads to represent them) keep counting the tens, multiplying or adding, exchange to represent each number with one bead bar.

Turn over the multiplier and read it, multiplicand taken as many times as the multiplier to give the product of 59,112. Continue working at the level of final products for some time

Move the beads to the base of the square to add them.

Aim:

To show the technique of the board

To reinforce the idea of multiplication itself, that you take a given quantity a given number of times.

3. Using the Multiplication Tables

Method:

“I take my multiplicand and multiplier, watch how I place them” put the cards in front of you to read – 3426   34 – then place the multiplicand along the horizontal and the multiplier along the vertical.  “Today, since we know our multiplication tables so well, we will just use what we know.  Begin with – six taken four times is twenty-four. Take a bead bar of two and one of four and place them in the tens and units square. Now I take my tens by my units, thats two taken four times which is twelve, and what are they, tens, so we have twelve tens which is one hundred and twenty”, take a one and a two and put them in the hundreds and tens square, put the carry over beads higher up the square. Stress the category of what you multiply and the category of what you have. Turn the card with the unit multiplier upside down

“The multiplication by ten is already done, when we put a number in this square [indicate the tens square] the multiplication is already done”.  When you reach the last number you ask “Is the multiplication complete?”, and turn over the tens card.

Bring the second layer of beads diagonally towards the base, collecting beads of the same category together, the you can add or times the beads in the units.  You can carry over one to the tens (keep the ones you take away in your hand for a control later until you have picked up the beads to represent them) keep counting the tens, multiplying or adding, exchange to represent each number with one bead bar.

Turn over the multiplier and read it, multiplicand taken as many times as the multiplier to give the product of 59,112. Continue working for some time, after many examples show them how to record

Aim:

Conscious awareness that category multiplication is already made on the board

Recording

Method:

Show the children how to record the problem and answer on squared paper,

Aim:

Recording the answer on paper for the first time.

4. Partial Products

Method:

The changing and recording is the same, emphasising Category Multiplication, through the verbalisation.

Take the cards 5436   43 and record it in columns on squared paper

We want the children to become more conscious of category multiplication, saying, “I am taking units so my answer will be in units, do six units taken three times is eighteen, eighteen units… I am taking a ten and a unit so my answer will be in tens, three taken three times is nine, nine tens”. At the end of multiplying by the unit I will reduce them by moving the beads to the base  exchange and record.

Now I do my units by tens, (do not record the ‘0’ which records there is no units as this is the result of multiplying by ten.

To emphasise that this is not a unit, we leave the square empty, count the squares till you begin, saying, “No units” etc. (like Mathematicians do).  You add the products on paper, carrying over in your head, review the paper calculation and then check the calculation using the beads on the board.  Then turn the multiplier cards over and review again.

Record on squared paper without the showing those zeros which are not the result of a multiplication

Aim:

Introduce working on squared paper to the children

Further clarification of multiplication

Introduce work beyond the units of millions

Emphases category multiplication (working with tens and powers of ten)

Preparation for the distributive law of multiplication, “That each digit of the multiplicand is multiplied by each digit of the multiplier”

Notes:

The emphasis of long multiplication is category multiplication, because of the structure of the board and the verbalisation the children have the possibility of coming to the realisation that once you have the idea of category multiplication it is simply necessary to know the tables.  At this point the children are receiving the conventional notation of long multiplication for the first time on squared paper.

The children need to do many examples on the board to acquire the concept.

When to give the lesson:

After working with partial products with the large bead frame, when children are able to read large numbers with ease.

Flat Bead Frame (or golden bead frame)

Material Description:

Frame glued to a wooden base.

Colour coded as the large bead frame along the top edge, it completes the millions family (100,000,000).  There are spaces where the comma would go.

There are 9 wires running vertically evenly spaced, one for each category within each family.  The 10 beads on each wire are golden.

Along the right side are 4 colour coded dots, for the first 4 categories up to the 1,000s (green, blue, red, green).

There are 4 black lines leading from each of the coloured-dots on the right, the black line goes across the base of the board to the corresponding category wire.  Along the bottom wood strip below each wire is a red 0.

Beads are kept at the top of the frame when not in use.

Pencil, slips of paper that are cut to fit along the wooden strip with the red zeroes, squared paper for recording problem and answer.

Method:

1.Final Product:

With one child at a time, set up the material as for the chequer board, with the grey cards, but a long white strip of paper, instead of the white cards.

Write the first example on squared paper to show the children how to record this after they have seen it with the chequer board, it is not necessary for the children to record.

Write the multiplicand on a strip of paper on the frames base over the correct position and make the multiplier in grey cards on the vertical axis.  e.g. 3754 x423.

‘Where do we begin?’ (units) ‘Four taken three times is twelve’, move down one ten and two units, continue taking the tens, hundreds and units, mention the category in the question but it becomes laborious to always do this for the answer. ‘We have done the units’, turn over the unit of the multiplier).

‘So we have to multiply by our tens, we have a help on this frame, watch! I move the slip over to the left’, reveal the red zero, ‘it tells us we have multiplied by ten, now all we have to do is multiply by the digit.  We have a little line which tells us where to start’ (indicate the line).  ‘We take four two times’. Continue with the hundred, thousands and tens of thousands.

‘Now all we have to do is the multiplication of our hundreds and I use the trick of the frame (move the slip) I immediately see I have done the multiplication by the hundreds, now all I have to do is multiply by the digit, and look the line shows me where to begin’ (indicate the line).

Lets go back and review what we have (turn the multiplier cards over and move the multiplicand to it’s original position and read the problem.  Transfer the number of beads into the squared paper to read the product.

Give more examples at this level, giving numbers small enough for the frame, the children can use the chequer board or large bead frame to check.

Aim:

Builds a working ability for long multiplication by using the tables and the changes in category.

Repetition through variety, individual work without colour coded so less psychological crutches.

When to give the lesson:

After the large Bead Frame, chequer board, can be done parallel to the chequer rboard

2.Partial  Product:

Now the child must record.

Write the multiplicand on a strip of paper on the frames base over the correct position and make the multiplier in grey cards on the vertical axis.  e.g. 3452 x 346

‘Where do we begin?’ (units) ‘Four taken three times is twelve’, move down one ten and two units, continue taking the tens, hundreds and units, mention the category in the question but it becomes laborious to always do this for the answer. ‘We have done the units’, turn over the unit of the multiplier).  Record the product of the units on the squared paper under the problem.  Clear the board.

‘So we have to multiply by our tens, we have a help on this frame, watch! I move the slip over to the left’, reveal the red zero, ‘it tells us we have multiplied by ten, now all we have to do is multiply by the digit.  We have a little line which tells us where to start’ (indicate the line).  ‘We take two four times’. Continue with the hundred, thousands and tens of thousands.  Record the tens product leaving a blank square for the units as no multiplication has taken place, refer to the red zero that has been seen on the chequer board.

Continue for the hundreds and thousands, record each partial product, add it abstractly on the paper in columns to give the answer.  Return to the frame, place the problem in it’s original state and read the problem and solution.  The children should be encouraged to check their working by adding the partial products on the frame.

Follow up work:

This works helps with the abstraction of long multiplication and immediately precedes long multiplication in the abstract, when there is a good chance of success.

Large Bead Frame – Long multiplication

Material Description:

A large bead frame with support for standing upright

The frame has seven wires, each with 10 beads.

  • The beads are colour-coded, green for units, blue for tens, red for hundreds.
  • The LBF begins with the units at the top of the frame.
  • The fourth wire is further from the first three, which begins a new family of thousands.  The same is true for the family of millions.
  • The left side of the frame is painted, white for the simple family, grey for the thousands, black for the millions.
  • The digits are all painted red in the coloured sections next to the corresponding wire.
  • The beads are kept on the left side of the frame when not in use.

Special Notation Paper

  • There is a special notation paper used only for the LBF.  The paper is divided in half vertically by a double-thick black line.  The left side is used for the multiplication problem and the final product, the right side is used for analysis and computation.
  • The names of the families are written at the top of the paper.  Each family is represented by a colour-coded line according to category along which digits are always written.
  • There are small black diamonds between the families.  The diamonds are a reminder of the comma introduced with the WHM.  The diamonds are transformed into commas by the children.

A red pencil and a regular pencil and a skewer for moving beads

All steps should be illustrated on notation paper and titled.

For practice, we use laminated copies that are wiped and re-used but this is NOT used with the children, as they need to keep a record of their work.

Method:

This presentation allows the child to see how the Hierarchical nature of the decimal system allows us to do long multiplication, the process cannot be misrepresented with the Bead Frame as the colour coding, space between the families and the internal hierarchy is fixed.

There are short introductory activities which can be done with a small group, the first is the formation and reading of quantities, the introduction to the symbol, the reading and writing of numbers and the review of short multiplication.  The work here is concrete, the child is still moving through the passage to abstraction at this point.

Work with a group of no more than three at a child, show one of the steps at a time.

  • Preparatory Exercises
  • Formation and Reading of Quantities
  • Introduction of the Symbol – with the notation paper
  • Reading and Writing of Large Numbers
  • Review of Short Multiplication
  • Long Multiplication
  • final products
  • partial products
  • special cases

Preparatory Exercises

Formation and reading of quantities – nothing is written

Do you remember the work we did with the Small Bead Frame, we did addition and subtraction.  Here we have another bead Frame which can be used to do addition and subtraction but we will only use it to do Long multiplication. Here are the units, tens, hundreds and thousands, just like the small bead frame.  We also have some more categories which we have looked at with the Wooden Hierarchical Material (the ten-thousand etc).  We have the colours down the sides, can you read the numbers, we have a gap between the 100 and thousands, the hundred-thousands and millions, to show us we are moving into categories, Relate each category to the Wooden Hierarchical Material, you describe it, these units are the same as the green cube of a unit etc (this is done to associate, not pair, the WHW is not shown)

Count, “I am going to count from the unit to one million” showing how you make changes, count to ten moving one green bead to the right each time, ask the child how do you think we should keep going, move ten over, replace greens, count in tens, at the end ask what you should do, continue to one million.  “now I am at a million, we have counted from one to one million”

(Stress the counting from 10,000 because this is what is new.)

Put over some units, ask the child to read, now add some terms and ask the child to read continue adding one category at a time, say, “We read up the categories” When you get beyond the families, stress “We have to say the name of the family”

(Continue as necessary as a game; making the number and asking the child to read it, ask the child to make a number and another child to read it,dictate a number in its entirety repeating a number in it’s entirety, but not one category at a time.  Emphasise the members of the family and then the family itself.)

1. The Introduction to the symbol – introduces notation paper with pencil and red pen

In Elementary the quantities are introduced with their symbols (not separately like in Casa)

Describe the notation paper, “Here we have a green line for the units, a blue line for the tens and red line for the hundreds, above it tells us the names of the families, the simple family, the thousands family and the millions family, can you see the little diamond here, this is where we put the comma.  Today what I am going to do is count, do you remember when we counted to the millions before, but this tome we are going to record as we count.  Here have we unit, look we have to write it across the line” (Do not complete the number with zeros yet. Write the numbers on the right hand side – the left is for analysis – on the green line of the units family keep pushing the bead, count and write, stop after 9) “Now we need to keep going, what should we do (we change) yes, push over a blue bead”, say “ten” and change, recording a one on the blue line, continue to do this.  Encourage the child to make the link between changing from one category to the next, when they are able let them take over with the counting and moving and even the  writing, depending on the child, staying with them till they reach one million.

  • We can make a number and the children read it out-loud and record it.

Repeat the counting, using the reverse of same sheet of paper, this time writing the zeros on the line, to emphasise the effect of the zero in keeping the place to all children and to give extra support to children who are unsure.  The child can count and you write do the same to write up to nine, then record the unit of ten, say, “Today we are also going to record our unit bar, what is on the Unit bar?  Yes, nothing, so we write a zero on the green line”, now keep going.  At one hundred “We record one hundred”,  writing a one on the red line, “And how many do we have on the blue bar?” (write a zero) “On the green bar?” “ (write a zero) Continue depending on the child’s interest and willingness to take over… saying “Now look how many zeros we have when we write a million”.

The reading and writing of numbers  – (now we use the left side of the paper)

Ask the child to suggest what they would like to make, compose it on the Large Bead Frame

Starting with the highest category, record it on the left side of the notation paper, putting in the comma for the first time, saying the numbers.  Clear it and make other numbers and record them, leaving a line in between to indicate that you are not adding them.

Variations – repeating without labouring it because the children need to be able to read large numbers from now on.  The emphasis is on read and record numbers beyond the thousands in a conventional way:

  • Make a game of it and encourage the child to do it more and more quickly.
  • The children can make a number, record it and read it to you.
  • The child can write it on the paper, the frame and then tell you what they made.
  • Dictate a number for the child to record and make on the frame

2. The review of short multiplication

The aim here is to review the language of short multiplication.  Start with a unit above thousands in the multiplicand, we avoid using a multiplier of five as it gives zero.

“I am going to take a multiplicand of 3,437, I write it on the left side of the page and the multiplier will be 4, write it beneath the unit.  What does this really mean, we want to take 3,437 four times.” Write the problem on the left hand side and analyse what you do on the right side of the paper, writing them category by units first, with the units, a bracket and writing, ‘x 4’

Begin with the units, “I will take seven units, three tens, four hundreds and three thousand, and I will multiply them by four.  

Seven taken four times is twenty eight (put the two tens and eight units across), now I have thirty taken four times, I don’t know what that is but I do know that three taken four times is twelve, but these are tens (indicate the tens) so three tens taken four times must be twelve tens, which is the same as one hundred and two tens (move a red bead and two blue ones).

Now we have four hundreds taken four times, I know four taken four times is sixteen, these are hundreds so four hundreds taken four times must be sixteen hundred, which is the same as one thousand and six hundreds (move one green thousand bead and six red beads.)

Now we have three thousands taken four times, I don’t know what that is, three taken four times is twelve, so three thousand taken four times must be twelve thousand with is the same as one ten thousand and two thousands” (push across one ten thousand blue bead and two green thousand beads)

Record the number you have made, underneath, “So three thousand, four hundred and thirty seven taken four times is thirteen thousand, seven hundred and forty eight”

Notes to short multiplication review:

  • You always finish with the child reading the product from the paper and checking that that is what they have with the frame.
  • Language is important, multiplicand, multiplier and product.
  • Give a dynamic example, include the thousands because they represent the unit of another family, initially avoid giving zeros

3. Long Multiplication – final products

Excluding the preliminary exercises, long multiplication uses a multiplier with two or more digits; it includes final products (accumulating all of the products on the frame and the additions) partial products (where the individual multiplications are recorded and the additions.

On squared paper review

2×10=20, ask “Are the ‘2’s the same?” (no, one is a unit and the other is a ten, give more examples by ten)

“When we look at them what does it seem we do when we multiply by 10?” (add a ‘0’)

Now try multiplying by ‘100’, “What does it seem we do when we multiply by ‘100’? We add two ‘0‘s.  Lets keep that in mind”.

Choose a multiplicand and write it on the left, e.g.8437 x 34, analyse it on the right in two parts, first by 4 and then again by 30.

“I need to multiply by ten, I already know how to multiply by 10, I just add a zero”.  With the red pen mark a ‘0’ in the units column and continue analysing the problem, “what happens to my (unit e.g.7) it becomes (ten e.g. 70)” in pencil beneath beginning with the units, verbalise the whole process. Say, “Now it is only necessary to multiply by ‘3’”. Cross out the multiplication by ’30’.

Multiply the top analysis 4 on the frame as usual, leave the answer on the frame, don’t record anything and begin the second analysis by ‘3’, then record the final answer only, on the left side of the paper under the original problem, putting in commas.  Read out the total problem and check it on the frame.

Repeat, doing another example with the children.  Separating each problem with a decorated line, celebrating an achievement.  They can practice for some time, show them how to use a three digit multiplier, analysing the units, tens and hundreds of the multiplier, converting then with the red pencil as before.

4. Long Multiplication with partial products

Use a number with a three digit multiplier, begin as before analysing and show the units on the chart.  Say, “This is the new part, we are going to record the multiplication by the units”. Then record the units under the problem on the left and clear the frame.  “Now we will do the next part, we will take the number ten times”. The record the analysed tens. “Lets start with the units, there is nothing, because we multiplied by ten, it’s special so lets’s record it in red”. Record the tens multiplication – the bar for the units will be clear, record the ‘0’ in the units, and the numbers for the bars with beads in pencil, under the product of the units, “To remind myself that I am multiplying by tens I am going to write in red”. Clear the frame and make the hundred and thousand product and recording them the same way. Saying, “What did we multiply by?, so how many zeros do we have, lets write them in red”.

Add all the partial products together keeping the number being carried forward in abstract, “Keep it in your head” (this builds intelligence and imagination, like a point of interest, it builds their skills and awareness).

Now ask the child how they can check their answer, do the addition on the bead frame.

Give many examples, allow children to make up their own.

5. Long Multiplication with Special Cases

Deal with these when they naturally arise from the children’s work.

With a multiplier with a zero in the tens, e.g 473 x 204

Analyse this as before, when you multiply by ten, you will write it out with one ‘0’ in red and times it by nothing.  “Now lets do our multiplication by tens, but look if I multiply by zero what will I have (nothing) I need to record my answer so I write a row of zeros”, with the units ‘0’ in red, and the rest in pencil.

Exploration:

Multiplying by ten and the powers of ten

To gain an ease with the reading and writing of large numbers

Aim:

Main aim – long multiplication

Emphasise that the addition of zeros is a change of category – isolated in red

Notes:

  • You can count the beads in twos and small groups as you move them from right to left.
  • As variations, you can add in columns as well as horizontally, put the units on the frame first, you can show them how to add in tens.
  • Use the comma in the workings on the left, it makes it easier to read the numbers.

When to give the lesson:

Ideally this is where the work at Elementary begins after the Key Lesson with the Wooden Hierarchical Material, we are presuming the children know dynamic addition and subtraction, the small Bead Frame and that they have internalised the multiplication tables.

The Large Bead Frame can be used with children familiar with the short Bead Frame who knows the multiplication tables.

Once the child is familiar with Short Bead Frame the Long Multiplication can begin

After the lesson:

The colour coding of white for simple, grey for thousands and black for millions is continued with the racks and tubes.

The Bank Game

Material Description:

The box contains:

  • A series of colour-coded hierarchical cards representing the multiplicand.  The categories are from 1 to 1,000; the digits are from 1-9 in each category; the digits are written in black. (multiplicand)

  • A series of grey cards representing the multiplier.  There are 3 sets of single digits from 1-9 in each category; there is a card with a single 0 and a 00 and a 000. (multiplier)

  • A series of white cards with colour-coded digits representing the product.  The categories are from 1 to 100,000,000; the digits are from 1-9 in each category. (product)

Method:

This is a game for a group of children, it should be fun.

With a single multiplier

Lay out the number cards in a similar way as the cards for the group games for maths in the Casa, with the coloured ones on the left, grey in the middle and white background ones on the right.

One child is the teller or cashier, this would be the child with the strongest understanding, another child is a customer and a third could be supervisor or bank manager, or help to identify the money the cashier needs. For the presentation the adult plays the banker.

First time, explain what each type of card is for and give a multiplicand for the child to form and a single digit multiplier, 657 x 4.

Overlay the the multiplicand at first, then analyse, saying, ‘We must take seven, four times, fifty, four times and six hundred, four times’, putting the cards  under each other as in work on paper with columns. Move the multiplier ‘6’ down, adjacent to the units of the multiplicand.

Ask the child for the product of seven and four, take the white product cards, ’20′ and ’8′, and place them under their categories beneath the product cards, leaving a distinct gap. Now move the multiplier up to the tens multiplicand and ask the child for their product, take the white product cards and place then below.  Continue for the hundred and thousands, putting each subsequent category below the first.

Add up the products, in their categories, beginning with the units.  Replace multiple cards with a single one for each category of the product, it might be necessary to exchange.

Ask the child for the multiplicand (she will need to overlay them first)  and the multiplier, overlay the cards for the product, and read it.

No recording is done.  It can be checked on any piece of work the children have previously worked with. Repeat this process with a single digit multiplier, the child as the customer and yourself as the banker, Begin as before with the child analysing the number and requesting the product, ask the child to verify that what you have given her is right.

With a multiplier in the tens

As above, only to make the multiplier put a single digit ‘0’ beneath the units multiplier card.

After analysing it, put the units multiplier by the multiplicand and find the products of each category. Keep the tens multiplier at the base of the table.

Then turn over the units card

Proceed with the tens, asking, ‘What do we know about multiplying by tens?’ (we add a zero) transfer the ‘0’ of the tens multiplicand cards.  Then continue as above.

Reform the multiplicand, multiplier and product to read the process.

With a multiplier in the hundreds and thousands

The child’s own work, this is not shown.

Aim:

Social, communication and mathematic

Further elaboration on the process of multiplying by ten and the powers of ten

Notes:

This resembles processes which occur in a bank.

When you first do this you can supervise both roles, then model being the banker so the children know how to run the bank themselves.

It gives the child a complete vision of the aspects of long multiplication, with an emphasis on rapid long multiplication and category multiplication.

When there are not enough cards you will need to exchange them, ask the child for solutions on what to do.

When to give the lesson:

After the presentation for the flat bead frame is given and worked parallel with it, as yet multiplication is not yet done completely in the abstract.

When the children have a good command of the addition and multiplication tables, it also needs good social skills.

After the lesson:

This is a material that can be left out on a table, as older children do not enjoy taking out and putting it back again.

Follow up work:

This is the last piece of work on long multiplication, the children are revealed of writing, it is a stage beyond writing the calculation but just previous to complete abstraction.

The Geometrical aspect of Long Multiplication

Material Description:

Squared paper, hierarchically coloured pencils, lead pencil, ruler

Method:

‘Today we are going to do long multiplication on paper, it’s as if we are going to make a picture of long multiplication, our example will be 3,432 multiplied by 43’

‘I will draw a horizontal line which will represent my multiplicand.’

Mark off the multiplicand along the horizontal, on squared paper, the number of squares used represents the units value in each category. make a dot by the end of each category to help construct the internal shape later.

‘I will draw a vertical line which will represent my multiplier.’

In the same way, draw the multiplier along the right, enclose it in a box and divide it internally, in relation to the multiplier, then the multiplicand and record. Add values along the base and right side

‘I will begin with the multiplication by the units, remember we are painting a picture. What will units by units give me? (units) that will be coloured green’. Colour it. Ask, ‘Two taken three times, what will that be?’ (6) ‘So thats six units,’ Write the multiplication and the answer on the square you have coloured, e.g. ‘2 x 3 =6’.

Continue with the units working left.

‘I will now do the multiplication with my tens, I have units by tens, what will this give me? (tens) so I will colour it blue, now we take two taken forty times, what will that give me? (8)

Continue with the tens working left.

‘In the units I have six.  In the tens I have 90, I also have 80.  In the hundreds I have 1,200, I also have 1200, In the thousands I have 9,000, I also have 16,000 and in the tens of thousands I have 12,000’.  As you say this write a column addition.

The check is to write a multiplication

Aim:

This exercise helps with category multiplication, binomial multiplication.

It prepares for the squaring of numbers and helps to rekindle interest in long multiplication

Notes:

Series of short steps done with a group of children, modelled by the adult

Choose multiplications which will produce squares, not rectangles.

When to give the lesson:

After the children have worked with the chequer board and are comfortable with the idea that units by units give units, they should also know the Laws of Multiplication.

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