1. These are the easiest facts to learn
Level 4 Module 1
Multiplication Number Facts: Strategies for 2x, 5x, 10x, 1x and 0x

3. © Professor Pete's Classroom. All rights reserved.
Index
Think Bubble Mathematics: Level 4
Module 1
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4. Think Bubble Math: Level 4 Overview
Module 1:
243731_TBM401_Mult_facts _Strategies_I.pptx
Module 2:
243736_TBM402_Mult_facts _Strategies_II.pptx
Module 3:
243741_TBM403_Mult_facts _Strategies_II.pptx
Module 4:
241710_TBM404_Fractions _equivalent.pptx
Module 5:
241801_TBM405_tenths.pptx
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5. Level 4 Lessons & Practice Sets
Module 1: x2
x5, x10 x3
x1, x0
Lessons 1-4
Practice Set 1
Subsets A-E
Module 2: x4 x9 x6
revision
Practice Set 2
Subsets F-J
Module 3: x8 x7
x11, square numbers
x12 (optional)
Practice Set 3
Subsets K-O
THIS MODULE
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6. Think Bubble Math Worksheets:
Many lessons are supported by corresponding worksheets
Purchasers:
Included in zip file for download
Members:
Access via profpete.com in TBM section
Some lessons recommend that students use hands-on materials
243504_TBM102_WS_Counting_on_back_1_2_3
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7. Navigating in Think Bubble Math on a Computer
Return to Index
Go to other slide:
Right-click screen, click “See All Slides”
Navigate forward & back: click right & left arrows
Start presentation:
Double-click file name or icon
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8. Using Think Bubble Math on a Tablet or Phone
Download free PowerPoint app in iTunes or Google Play:
iPhone or iPad:
Android:
Save Think Bubble file to your device
You may find it helps to install Microsoft OneDrive, to save and find files
If you see a warning about “unsupported content”, you can safely ignore it
We include special fonts to improve the presentation’s appearance
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9. Navigating in Think Bubble Math on a Tablet or Phone
Start presentation:
click “play” button in top bar
Navigate to other slide:
rotate device to portrait, click slide thumbnail at bottom of screen
Navigate forward & back: swipe left & right
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10. Multiplication Facts Strategies I
ACMNA075:
Recall multiplication facts up to 10×10…
ACMNA076:
Develop efficient mental strategies… for multiplication…
(c) Professor Pete's Classroom, All rights reserved.

11. Assumed Prior Knowledge
Students should already be able to:
Understand multiplication as an array
Instant recall of the addition facts to 20 (see level 3: modules 1, 2, 3)
3 x 4 groups of
3 x 4 array
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12. The Value of Memorizing Multiplication Facts
Children should memorize all multiplication facts because knowing the facts:
is necessary for efficient processing of algorithms
avoids interruptions to thinking while using a calculator or table of numbers
allows for quick estimations of answers when working with a calculator
empowers students as they work with more and more complex numbers and calculations
opens the door to mental strategies with larger and smaller numbers
4 x 8 = 32
3 x 8 = 24
9 x 5 = 45
6 x 7 = 42
7 x 4 = 28
8 x 8 = 64
9 x 8 = 72
5 x 8 = 40
4 x 2 = 8
6 x 3 = 18
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13. Strategies vs Rote Learning
Practising strategies strengthens students’ thinking about the numbers and their understanding of mathematical relationships
Rote learning relies on parroting verbal statements until they are memorized, without any understanding
If the student forgets a multiplication fact then a strategy can be applied allowing the student to work out the answer
If rote-learned facts are forgotten, they must be re- learned all over again
Strategies may be used to mentally check if the answer is correct
With rote there is no method for checking if the answer is correct or not
Strategies may be extended to multiplying larger numbers
Rote-learned facts are a dead end
Knowing powerful mental strategies makes solving problems much easier
A rote learner has no way to develop mental strategies for other problems
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14. © Professor Pete's Classroom. All rights reserved.
Arrays 10
Arrays are the most efficient way of showing every single element in a multiplication fact
They provide a visual prompt of the multiplication strategy for simple reference 10
100
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15. © Professor Pete's Classroom. All rights reserved.
Strategies Poster
There is a poster provided in your Level 4 Think Bubble Mathematics bundle for printing and display
The poster illustrates all the recommended strategies for multiplication facts
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16. x2: Doubles with Ten Frames
Doubling is best displayed with two ten frames
Students should be able to subitize both the pairs and rows layouts
We display the number to be doubled as two rows, split over the first columns of both ten frames
The same number of counters is then shown in a second colour, making an easy-to-recognise number
For doubles >10, a teen number is clearly visible
Point out that doubling always results in an even number. Why?
2 x 8 = 16
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17. © Professor Pete's Classroom. All rights reserved.
x5: Half of x10
6 x 10 = 60
x5 is half of x10
It is easy to multiply by 10
Finding half is easy for those numbers with an even number of ten
8 x 5 = 40
Finding half of numbers with odd tens is more difficult
7 x 5 = half of 70
half of 70 think half of 60 =
This strategy, which presents as more complicated than just counting in 5s, is very useful when used on larger numbers such as
26 x 5 = half of 260 = 130 5 10 6 30 60
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18. © Professor Pete's Classroom. All rights reserved.
x3: Double + one more set 2
6 x 2 = 12 3
x3 is double + one more set
Doubling needs to be an instant recall fact
Adding one more set (not adding 3) is a little more tricky, but once students become fluent with addition of simple number in their heads, this strategy allows for the checking of their answer
6 x 3 = 6 x 2 + 6
As the answer is a multiple of 3 all answers must add to a multiple of 3 (3, 6 or 9)
24 (2 + 4 = 6 yes!)
27 (2 + 7 = 9 yes!)
21 ( = 3 yes!)
6 x 3 =
12 + 6 18 6 12 18 +6
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19. Supporting Resources:
Resources at profpete.com
Gadgets Interactive Software
Multiplication Facts: Double 2x
Multiplication Facts: Place Value & Halving 5x 10x
Multiplication Facts: x 2 : Double Plus One More Set 3x
Multiplication Facts: Double Double 4x
Multiplication Facts: “Multiplication Madness” Game
Multiplication Division Facts Games: Multiplication & Division Fact Family Deck of Cards
Multiplication Strategies Posters (A3)
Gadgets Number Facts: Multiplication x2 Double
Gadgets Number Facts: Multiplication x5 & x 10
Gadgets Number Facts: Multiplication x3 Double plus 1 More Set
Multiplication Flashcards for the x2 tables
Multiplication Flashcards for the x3 tables
Multiplication Flashcards for the x5 tables
Multiplication Flashcards for the x 10 tables
Multiplication Facts Daily Practice Set I [PowerPoint TBM401P]
Number Facts Gadget:
Fact families
Strategies
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20. (c) Professor Pete's Classroom, 2017. All rights reserved.
Lesson 1 x2: Double
ACMNA075:
Recall multiplication facts up to 10×10…
ACMNA076:
Develop efficient mental strategies… for multiplication…
(c) Professor Pete's Classroom, All rights reserved.

21. 12 x 2 : Double 2 x 6 = Look at the double ten frame:
2x facts (doubles) are the easiest to recognize and remember
Look at the double ten frame:
6 = 5 + 1
Think about double 6:
double 6 = double 5 + double 1
2 x 6 = 2 x x 1
double 6 =
2 x 6 = 12
Point out that 6 is made up of 5 plus 1
Talk about doubling 5 and doubling 1
Discuss why doubling always gives an even answer
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22. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Look at the double ten frame:
8 = 5 + 3
Think about double 8:
double 8 = double 5 + double 3
2 x 8 =
2 x 8 = 16
Note that 8 is 5 plus 3
double 5 is 10
double 3 is 6
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23. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Think about double 7:
double 7 = double 5 + double 2
2 x 7 =
2 x 7 = 14
Note that when doubling an odd number the answer is still even
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24. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Double 10 is easy!
Two full ten frames show 2 tens, or twenty
10 x 2 = 20
Turnaround fact
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25. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Think about double 9:
double 9 = double 5 + double 4
2 x 9 =
Or think of doubling ten, then take away double one;
20 – 2 = 18
9 x 2 = 18
This is also a nines fact, so can be thought of as 2 tens – 2 ones
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26. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Double 5 fills the ten frames nicely:
2 x 5 = 10
It is also a rainbow addition fact:
5 + 5 = 10
2 x 5 = 10
Double 5 is best shown in the left hand ten frame as it shows the 1 ten 0 ones
This is also the foundation for the doubles greater than 5, where double 5 is shown on the left
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27. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Double 3
2 x 3 = 6
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28. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Double 4
4 x 2 = 8
Doubles less than 10 are shown in the right-hand ten frame to match place value digits
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29. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Double 2
2 x 2 = 4
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30. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
Double 1
1 x 2 = 2
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31. (c) Professor Pete's Classroom, 2017. All rights reserved.
Lesson 2 x5, x10
ACMNA075:
Recall multiplication facts up to 10×10…
ACMNA076:
Develop efficient mental strategies… for multiplication…
(c) Professor Pete's Classroom, All rights reserved.

32. x 5 : Half of x 10
4 x 10 = 40
4 x 5 = 20 5 10
Multiplying by ten is easy:
4 tens = 40
4 x 10 = 40
5 is half of 10
so x 5 is half of x 10 4 20 40
X 5 facts are easy if you think of X 10 and find half
The “half of x 10” strategy is preferable to counting in 5s on fingers, which is time consuming and can lead to inaccuracies
Discuss the x 10 array and is relation to the x 5 “half array”
This method can be used when multiplying any number by 5:
e.g. 26 x 5 = 260 ÷ 2 = 130
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33. © Professor Pete's Classroom. All rights reserved.
x 5 : Half of x 10
3 x 10 = 30
3 x 5 = 15 5 10
We know 3 x 10:
3 tens = 30
3 x 10 = 30
So 3 x 5 = half of 30 3 15 30
Discuss ways to mentally halve three tens
e.g. 30 = 2 tens + 10
Half of 30 = 1 ten + 5
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34. © Professor Pete's Classroom. All rights reserved.
x 5 : Half of x 10
8 x 10 = 80
8 x 5 = 40 5 10
x 10
x 5 8 40 80
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35. © Professor Pete's Classroom. All rights reserved.
x 5 : Half of x 10
5 x 10 = 50
5 x 5 = 25 5 10
x 10
x 5
To halve 50 (think halve 40 and halve 10) 5 25 50
To halve 50 (where there is an odd number of tens), halve the even number less than it, then halve the ten
This works with large numbers such as 5 x 45:
half of 45 tens = half of 44 tens + half of 10 = 220+5
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36. © Professor Pete's Classroom. All rights reserved.
x 5 : Half of x 10
9 x 10 = 90 5 10
9 x 5 = 45
x 10
x 5 9 45 90
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37. © Professor Pete's Classroom. All rights reserved.
x 5 : Half of x 10
6 x 10 = 60
6 x 5 = 30 5 10
x 10
x 5 6 30 60
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38. © Professor Pete's Classroom. All rights reserved.
x 5 : Half of x 10
7 x 10 = 70
7 x 5 = 35 5 10 7 35 70
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39. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
2 x 5 = 10
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40. Lesson 3 x3: Double +One more set
ACMNA075:
Recall multiplication facts up to 10×10…
ACMNA076:
Develop efficient mental strategies… for multiplication…
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41. x 3 : Double Plus One More Set2
To multiply by 3, first multiply by 2 (double) then add one more set 3
4 x 2 = 8 4
If you know the doubles, you can work out x 3 facts 8 12 +4
4 x 3 =
8 + 4 12
Multiplying by 3 is multiplying by 2 and adding one more of the other multiplicand
Students need to have instant recall of addition facts to us this strategy efficiently
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42. x 3 : Double Plus One More Set2
To multiply by 3:
double the number
add the number (one more set)
6 x 3:
6 x 2 + 6
12 + 6 18 3
6 x 2 = 12
6 x 3 =
12 + 6 18 6 12 18 +6
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43. x 3 : Double Plus One More Set2
8 x 3:
8 x 2 + 8
16 + 6 24 3
8 x 2 = 16
8 x 3 =
16 + 8 24 8 16 24 +8
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44. x 3 : Double Plus One More Set2
Turnaround fact: use the same strategy 3
2 x 7 = 14
3 x 7 =
14 + 7 21 7 14 21 +7
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45. x 3 : Double Plus One More Set2 3
3 x 2 = 6 3 6 9 +3
3 x 3 =
6 + 3 9
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46. © Professor Pete's Classroom. All rights reserved.
x 2 : Double
2 x 3 = 6
These facts have already be learnt with an earlier strategy
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47. x 3 : Double Plus One More Set2 3
2 x 9 = 18
3 x 9 = 27
18 + 9 9 18 27 +9
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48. © Professor Pete's Classroom. All rights reserved.
x 5 : Half of x 10
3 x 10 = 30
3 x 5 = 15 5 10 3 15 30
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49. (c) Professor Pete's Classroom, 2017. All rights reserved.
Lesson 4: x1, x0
ACMNA075:
Recall multiplication facts up to 10×10…
ACMNA076:
Develop efficient mental strategies… for multiplication…
(c) Professor Pete's Classroom, All rights reserved.

50. x 1 : Special Case
X 1 and X 0 facts are special cases: think carefully about each one 1
Multiplying by one means that we have just one set of that number:
9 x 1 = one set of 9
9 x 1 = 9
9 x 1 = 9 9 9
These facts may present as very easy but students sometimes make mistakes such as believing that x 1 always gives an answer of 1
Have students think about what is being represented by the number fact
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51. © Professor Pete's Classroom. All rights reserved.
x 0 : Special Case 1
1 x 6 = 6
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52. © Professor Pete's Classroom. All rights reserved.
x 0 : Special Case 1
Multiplying by zero means that we have zero sets of that number:
9 x 0 = zero sets of 9
9 x 0 = 0
When multiplying by zero there is nothing at all!
9 x 0 = 9
x 0 results in there being nothing at all
Ask students to think of receiving nothing 9 times – they will still have nothing
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53. © Professor Pete's Classroom. All rights reserved.
x 1 : Special Case 1
7 x 1 = 7 7 7
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54. © Professor Pete's Classroom. All rights reserved.
x 1 : Special Case 1
5 x 1 = 6 5 5
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x 0 : Special Case 1
8 x 0 = 8
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56. © Professor Pete's Classroom. All rights reserved.
x 1 : Special Case 1
1 x 4 = 4 4 4
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