Multiplication Mental to Written Parent Workshop

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Multiplication Mental to WrittenParent Workshop
X

• L.Barratt D.K.Hyde

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Point of the workshop

• To identify the progression from mental to
  written methods of calculation in multiplication
  by
• identifying the key prerequisites, knowledge and
  skills that children need if they are to use
  written methods with confidence,
• demonstrating helpful models to give children
  when teaching multiplication.

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Lets play a game of Bingo to get us started.
RULES!

• Listen to the multiplication or division
  calculation.
• Work out the solution to the calculation.
• See if you have the answer on your bingo card, if
  you have cross it off.
• AIM OF THE GAME.
• Get a line or a full house to win.

This is a fix, Mr Bates has all the numbers!!!
Oh dear, I havent got that answer on my Bingo
card!
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Warm Up

• Left Overs!
• Aim
• To score as many points as possible (the
  remainder from each
• throw of the die becomes your ongoing score until
  all 5 throws
• of the die have been taken).
• Rules
• Write down 5 different two-digit numbers up to
  50. Roll the
• die, if the die lands on 5 decide which of your
  numbers will give
• the highest remainder. These are your points.
• spinner

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Left Overs!
Okay, so lets write five, 2 digit numbers up to
50.
Wait for the spinner.
It landed on a 4, so which number will you get
the largest remainder from?
32 4 8 41 4 10 rem 1 22
4 5 rem 2 48 4 12 17 4 4
rem 1
This number gives the highest remainder, so cross
this off first.
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Supporting the learning of multiplication facts

• We expect pupils to derive and recall
  multiplication facts
• Year 2 the 2, 5 and 10 times tables
• Year 3 the 2, 3, 4, 5, 6 and 10 times tables
• Year 4 tables up to 10x10
• Year 5 recall quickly tables up to 10x10
• Hit the button

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Hit the button GO Mrs Cross!!!

• Choose a multiplication table you have been
  learning (X2 X3 X4 X5 X6 X7 X8 X9 or X10).
• Play the game making note of how many questions
  you answer in 1 minute.
• Repeat the game for the same table at a later
  date to see if you can improve your score.

Its not fair, its not working, I know my 7 x
table!
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• Recall of facts
• Children need to recall (know) number facts
  quickly so that
• they can use and apply them to derive (work out)
  new
• facts and explore patterns and relationships in
  numbers
• that will help them when carrying out
  calculations, both
• mental and written.

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What are the missing facts?How did you work it
out?
A
B
C
D
Show me the missing numbers with your fans.
32.1.. show.
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Have a go at Race Against the Clock
How many squares can you fill in within 5 minutes?
This will be 3 x 1
This is tricky!
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Recalling number facts and mental calculations

• Know by heart all multiplication facts up to
  10x10 and derive (work out) quickly
  corresponding division facts.
• Multiplying and dividing by 10, 100, 1000.
• Doubles and halves.
• Multiply and divide a single digit number by a
  two digit number.

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Progression towards written method

• Establish mental methods, based on a knowledge of
  tables and
• an understanding of place value.
• With more difficult calculations, approximate
  first, using
• mental methods e.g. 128 X 6 becomes 130X 5
• Show children how to set out written calculations
  using
• jottings.
• GRADUALLY refine the written method into a more
  efficient
• method.
• Extend to larger numbers and to decimals.

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IMPORTANT TEACHING PRINCIPLE If, at any stage, a
child is making a significant number of errors,
they should return to the stage they understood,
until ready to move on.
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Progression in Multiplication
At school when we teach your children all about
Multiplication this is the order we follow to
ensure children have a good understanding of the
concept taught-

• Repeated addition
• Use of Arrays
• Grid Multiplication

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Repeated Addition/working towards an array
How many fingers would we have if 6 hands were
wearing a glove?
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Question Time What are the repeated additions
or multiplication sums for these arrays?
C
A
B
Now A is 5 rows of 8 or 8 x 5 thats 40.
D
E
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Moving from an array to a number line
10 X 7 5 X 7
0 70 105
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Moving from an array to the grid method
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Question Time What is 13 X 6?

• Can you estimate the answer to this?
• What would the array look like?
• How would you partition the numbers?
• What would the answer be?

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Multiplication

• Grid method of multiplication

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3
10
60 18 78
60
18
6
6
13 x 6
78
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Moving from the grid method to a more formal
written method.
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Question time

• Can you use what you know to answer these related
  questions?
• 7 X 6
• 70 X 6
• 0.7 X 6
• 0.7 X 0.6
• Would you work out the answers to these
• mentally or would you use a written method?

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Key Messages

• Mental strategies need to be taught
• The links to division need to be explicit
• number dials
• A game we played-
• What times table could
• this be?
• (32 and 28 are in 2X and 4X tables)

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What can you do to help?

• Use some of the activities from the pack
• Play Race Against the Clock
• Reinforce the link between X and
• Look for arrays for food packaging and get
  children to make the links to multiplication/divis
  ion facts.
• Ask multiplication questions of children.
• e.g- How many socks altogether if there are
  13 children?
• e.g- If there were 30 oranges in 6 crates
  how many would there be in 1 crate?
• Talk to your children about their targets and
  what they need to be able to do to achieve it.
• Talk to the teacher about any questions you have.
• Make Maths fun and enjoyable for you and your
  child.

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Here are a few more activities you can carry out
with your child/children.
Domino Doubles

• Each person has six dominoes.
• Play as normal dominoes but at the matching ends
  you have to find a half or a double of the end
  number. If you cannot match one, then another
  domino is taken from the pile.
• The winner is the first to use all their
  dominoes. If the end becomes blocked and no one
  can go the winner is the one with the lowest
  total.

Double 3 6 Half of 6 3
Cant go END BLOCKED!
Double 1 2 Double 1 2
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Calc Busters
Player B
Player A
Player A
Player B
How to play Player A chooses a hexagon on the
grid and uses estimation / approximation to
decide which two numbers in the box on the right
will multiply together to make the chosen number.
Player B checks this on the calculator. If player
A is correct he can cover that hexagon with a
counter. If Player A is incorrect then play
passes to player B. The winner is the first
player to cover a pathway from one side of the
board to the other.
3.5 10.4 14.4 13.2
16.9 20.1 11.6 11.7
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Missing Number Squares
These can be completed by children as a race
against the clock activity or one large one can
be drawn on the board and children can use digit
boards, fans or whiteboards to show what number
they think goes in each square. Children should
be encouraged to explain why they think the
number they have chosen is correct.
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Three in a row
A game to play in pairs You need a set of 3 10
digit cards, a dice marked with 2, 5 and 10, two
sets of different coloured counters and some
multilink if needed The first player turns over a
digit card and then rolls the dice The digit card
tells you how many times you have to add the
number shown on the dice Write down the number
sentence. E.g. if 3 was shown on the digit card
and 5 shown on the dice This means we need to
add 5 three times. The number sentence would be
recorded like this 5 5 5 15 The answer can
now be recorded on the game board by covering it
with a counter Play continues until a player has
3 counters in a row, column or diagonal
Repeated Addition
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Remainders Game

• RULES
• Use a 6-sided dice
• Play like connect 4 (4 in a row) or
  blockbusters (side to side)
• Ask pupils to choose and write a number between
  30 and 50.
• Roll the dice. Divide the chosen number by the
  dice number.
• Take turns to cover up the remainder.
• Repeat until 1 player has 4 in a row or has gone
  side to side

Extension Use other dice such as a 10 sided dice
to practice division by larger numbers, but you
will need to extend the grid to use numbers
between 0 and 9.