Place Value Introduction & Adding & SubtractingV2.notebook
Place Value Introduction & Adding & SubtractingV2.notebook
March 26, 2015
27/02/15
Year 5 & 6 Maths Workshops Introduction & Welcome Introducing Place Value & the Number System
Make life simple by using effective techniques you can then spend more time on other pursuits!
Analysing techniques for Adding & Subtracting
Analysing techniques for Multiplying and Dividing
Sep 1107:34
Sep 1908:14
Calculate the following: 34 + 17 + 66 + 23
1206 / 3
15 x 18
8007 - 7994
265 / 5
39 x 6
20 x 3.5
3.6 + 3.7
Learning Objective: To read and write numbers in figures and words, and to know what each digit represents
17 x 6 2080 / 4
Nov 208:37
Sep 1107:34
1
Place Value Introduction & Adding & SubtractingV2.notebook
In Japan they use a very logical way of saying the value of any given number e.g. Six hundred and twenty three (623) would be: Six hundreds two tens and three units
Oct 2316:46
H'dred Ten Th. Th Th H T U
.
1
1
10 100
Three thousand four hundred and four (3,404) would be: Three thousands four hundreds zero tens four units
placeValue_1_1.exe
Oct 2316:50
1
Learning Objective:
1000
So what do these particular digits represent in the following numbers: 643 5800 .89 456,789
Grid large
March 26, 2015
To understand the different ways of adding and subtracting.
Sep 1107:34
2
Place Value Introduction & Adding & SubtractingV2.notebook
+10, +100, +1000
Counting on / back
Adding / Subtracting Numbers
Column Addition / Subtraction
March 26, 2015
Many problems occur when presentation is not neat! Alternatively, children do not use their squares to help in the calculation:
479
+ 539
Number Lines
Oct 2316:52
Add 27.7 to 126.56
Feb 2612:16
589 236 But what about 635 478? Or, 704 535? But what about 2004 1997?
Feb 2612:16
Feb 2612:16
3
Place Value Introduction & Adding & SubtractingV2.notebook
Times Tables
Times Tables
Also, once you know one set of information you know at least three other bits of information e.g.
number_dials_04.exe
A key mathematical rule (the commutation law) is that what ever you are multiplying it does not matter in which order you place the numbers.
6 x 4 x 10 = 240 is the same as 10 x 4 x 6
Sep 817:38
.
1
6 x 4 = 24 therefore: 4 x 6 = 24 24 divided into 6 equal groups = 4 in each group 24 divided into 4 equal groups = 6 in each group
Sep 817:38
x10, x100, x1000 H'dred Ten Th. Th Th H T U
March 26, 2015
1
10 100
Doubling and Halving 1 1000
35 x 24 is the same as 70 x 12 = ?
Grid large
Sep 1810:11
4
Place Value Introduction & Adding & SubtractingV2.notebook
Partitioning Numbers & Grid Method As we learned before, you can split a number into its constituent parts e.g. 64 can be thought of as what?
March 26, 2015
Partitioning Numbers & Grid Method This can be extended to more complex numbers e.g. 64 x 32
60 and 4
multiplication_grid_2_2.exe
If I wanted to multiply 64 by 7 I could think of it as 7 groups of 60 added to 7 groups of 4 multiplication_grid_2_2.exe
Sep 817:38
Sep 817:38
8 x 42
Learning Objectives:
To learn and apply the Compact Multiplication method
x
42 x8
40 2
8
﴾8 x 2﴿
42 x8
Sep 13 07:38
﴾8 x 40﴿
Sep 1912:51
5
Place Value Introduction & Adding & SubtractingV2.notebook
March 26, 2015
Now let's try some Compact Multiplication with our partners on our whiteboards:
a﴿ 8 x 37
b﴿ 6 x 57
c﴿ 87 x 7
Sep 1913:49
Let's carry on with trying to make life simple Three steps to successful multiplication, especially relating to larger/complex numbers:
Sep 2011:52
What about when you multiply a 2digit number by another 2digit number?
42 x 87
1.﴿ Estimating 2.﴿ Calculating 3.﴿ Checking Answer against Estimate
Sep 2808:14
Sep 1908:58
6
Place Value Introduction & Adding & SubtractingV2.notebook
March 26, 2015
2. Do Calculation
42 x 87 1. Estimate First:
x
87 42 ﴾2 x 87﴿
0
﴾40 x 87﴿ = ﴾4 x 87 x 10﴿
3. Check against Estimate = 3,600
Sep 1908:58
Sep 1913:19
Now you do one on on your whiteboards! Don't forget to estimate, calculate then check!!
87 x 42 17 4 34 8 0
32 x 48 ﴾2 x 87﴿
1
﴾40 x 87﴿ = ﴾4 x 87 x 10﴿
2
3 654 1
Sep 1913:19
Sep 2007:38
7
Place Value Introduction & Adding & SubtractingV2.notebook
What about larger numbers!
Learning Objectives:
5 9 7
x
3 12
0 0 0
March 26, 2015
(2 x 597) (1 x 597 x 10) (3 x 597 x 100)
To appreciate the various concepts relating to Division
To understand the techniques involved in Division
Let's move on to a subject close to my heart, amely Division!! Mrs. Broom is going tio introduce this.
Sep 2011:52
Sep 1107:34
:10, :100, :1000
Chunking Method
Inverse of Times Tables
Dividing Numbers
Inverse of Times Tables Extended Known Facts
Oct 2316:52
Visualisation is very important for people to understand the concepts of both Multiplication and Division.
For example: Short & Long Division
Nov 1307:46
8
Place Value Introduction & Adding & SubtractingV2.notebook
3 x 7 = 21 (3 lots of 7)
March 26, 2015
Even with Division, we must not forget our known facts!
365 / 12 = 30 5/12
7 x 3 = 21 (7 lots of 3)
We could also use a grid to show the inverse relationship between Multiplication and Division: 21 divided into groups of 3 = 7
4824 / 12 = (4800 / 12) + (24 / 12) = 400 + 2 = 402
21 divided into groups of 7 = 3
Nov 1308:28
Nov 1317:13
Chunking Demonstration
Short Division Demo
﴾repeated subtraction﴿
0 5 7 r 3 8 45 9 4
5
3 or 57 ... and then 8
interpret the result!!
Now you do some:
How many cakes can be made with 324 eggs if each cake needs 5 eggs?
How many cars are needed to transport 126 children if each car can hold 5 children?
Sep 2508:59
Sep 2508:52
9
Place Value Introduction & Adding & SubtractingV2.notebook
March 26, 2015
Chunking Demonstration
Chunking Demonstration
﴾repeated subtraction﴿
﴾repeated subtraction﴿
3 2 r 3 12 3 8 7 ﴾10 x 12 = 120﴿ 1 2 0 2 6 7 2 4 0 ﴾20 x 12 = 240﴿ 2 7 ﴾2 x 12 = 24﴿ 2 4 32 3
Sep 2508:52
Sep 2508:59
(? x 500 = ? )
(? x 500 = ? )
How many pallets (500 bricks on each) are needed for my extension which will use 6250 bricks?
Sep 2508:52
Long Division 0 5 7 r 3 8 4 59 4 0 59 56 3
5 0 0 6 2 5 0
Long Division 3
or 57 8
0 5 7 8 4 59 4 0 59 56 3 3
4 2
2 2 0
Sep 2508:59
10
Place Value Introduction & Adding & SubtractingV2.notebook
When would you use a formal technique like short/long division or chunking?
Long Division 0 25 3 18 4 59 36 9 9 9 0 9 9 1
March 26, 2015
2
5 r 2 2
or 255 18
a) 40 divided by 5 b) 328 / 8 c) How many 13s are in 457? d) 46 / 5 e) 2121 divided by 7
2 0 2
f) 3253 divided by 7 g) 3606 / 6 h) 8,100 divided by 9
Sep 2508:59
Long Division
0 5 7 8 4 59 4 0 59 56 3 3
4 2
2 2 0
. .
Oct 1508:09
1 2 9 6
9 8 1 6 1 6 0
Sep 2508:59
Sep 2011:52
11
Place Value Introduction & Adding & SubtractingV2.notebook
Sep 2011:52
March 26, 2015
Jan 717:22
12
Attachments
placeValue_1_1.exe number_dials_04.exe multiplication_grid_2_2.exe
March 26, 2015
27/02/15
Year 5 & 6 Maths Workshops Introduction & Welcome Introducing Place Value & the Number System
Make life simple by using effective techniques you can then spend more time on other pursuits!
Analysing techniques for Adding & Subtracting
Analysing techniques for Multiplying and Dividing
Sep 1107:34
Sep 1908:14
Calculate the following: 34 + 17 + 66 + 23
1206 / 3
15 x 18
8007 - 7994
265 / 5
39 x 6
20 x 3.5
3.6 + 3.7
Learning Objective: To read and write numbers in figures and words, and to know what each digit represents
17 x 6 2080 / 4
Nov 208:37
Sep 1107:34
1
Place Value Introduction & Adding & SubtractingV2.notebook
In Japan they use a very logical way of saying the value of any given number e.g. Six hundred and twenty three (623) would be: Six hundreds two tens and three units
Oct 2316:46
H'dred Ten Th. Th Th H T U
.
1
1
10 100
Three thousand four hundred and four (3,404) would be: Three thousands four hundreds zero tens four units
placeValue_1_1.exe
Oct 2316:50
1
Learning Objective:
1000
So what do these particular digits represent in the following numbers: 643 5800 .89 456,789
Grid large
March 26, 2015
To understand the different ways of adding and subtracting.
Sep 1107:34
2
Place Value Introduction & Adding & SubtractingV2.notebook
+10, +100, +1000
Counting on / back
Adding / Subtracting Numbers
Column Addition / Subtraction
March 26, 2015
Many problems occur when presentation is not neat! Alternatively, children do not use their squares to help in the calculation:
479
+ 539
Number Lines
Oct 2316:52
Add 27.7 to 126.56
Feb 2612:16
589 236 But what about 635 478? Or, 704 535? But what about 2004 1997?
Feb 2612:16
Feb 2612:16
3
Place Value Introduction & Adding & SubtractingV2.notebook
Times Tables
Times Tables
Also, once you know one set of information you know at least three other bits of information e.g.
number_dials_04.exe
A key mathematical rule (the commutation law) is that what ever you are multiplying it does not matter in which order you place the numbers.
6 x 4 x 10 = 240 is the same as 10 x 4 x 6
Sep 817:38
.
1
6 x 4 = 24 therefore: 4 x 6 = 24 24 divided into 6 equal groups = 4 in each group 24 divided into 4 equal groups = 6 in each group
Sep 817:38
x10, x100, x1000 H'dred Ten Th. Th Th H T U
March 26, 2015
1
10 100
Doubling and Halving 1 1000
35 x 24 is the same as 70 x 12 = ?
Grid large
Sep 1810:11
4
Place Value Introduction & Adding & SubtractingV2.notebook
Partitioning Numbers & Grid Method As we learned before, you can split a number into its constituent parts e.g. 64 can be thought of as what?
March 26, 2015
Partitioning Numbers & Grid Method This can be extended to more complex numbers e.g. 64 x 32
60 and 4
multiplication_grid_2_2.exe
If I wanted to multiply 64 by 7 I could think of it as 7 groups of 60 added to 7 groups of 4 multiplication_grid_2_2.exe
Sep 817:38
Sep 817:38
8 x 42
Learning Objectives:
To learn and apply the Compact Multiplication method
x
42 x8
40 2
8
﴾8 x 2﴿
42 x8
Sep 13 07:38
﴾8 x 40﴿
Sep 1912:51
5
Place Value Introduction & Adding & SubtractingV2.notebook
March 26, 2015
Now let's try some Compact Multiplication with our partners on our whiteboards:
a﴿ 8 x 37
b﴿ 6 x 57
c﴿ 87 x 7
Sep 1913:49
Let's carry on with trying to make life simple Three steps to successful multiplication, especially relating to larger/complex numbers:
Sep 2011:52
What about when you multiply a 2digit number by another 2digit number?
42 x 87
1.﴿ Estimating 2.﴿ Calculating 3.﴿ Checking Answer against Estimate
Sep 2808:14
Sep 1908:58
6
Place Value Introduction & Adding & SubtractingV2.notebook
March 26, 2015
2. Do Calculation
42 x 87 1. Estimate First:
x
87 42 ﴾2 x 87﴿
0
﴾40 x 87﴿ = ﴾4 x 87 x 10﴿
3. Check against Estimate = 3,600
Sep 1908:58
Sep 1913:19
Now you do one on on your whiteboards! Don't forget to estimate, calculate then check!!
87 x 42 17 4 34 8 0
32 x 48 ﴾2 x 87﴿
1
﴾40 x 87﴿ = ﴾4 x 87 x 10﴿
2
3 654 1
Sep 1913:19
Sep 2007:38
7
Place Value Introduction & Adding & SubtractingV2.notebook
What about larger numbers!
Learning Objectives:
5 9 7
x
3 12
0 0 0
March 26, 2015
(2 x 597) (1 x 597 x 10) (3 x 597 x 100)
To appreciate the various concepts relating to Division
To understand the techniques involved in Division
Let's move on to a subject close to my heart, amely Division!! Mrs. Broom is going tio introduce this.
Sep 2011:52
Sep 1107:34
:10, :100, :1000
Chunking Method
Inverse of Times Tables
Dividing Numbers
Inverse of Times Tables Extended Known Facts
Oct 2316:52
Visualisation is very important for people to understand the concepts of both Multiplication and Division.
For example: Short & Long Division
Nov 1307:46
8
Place Value Introduction & Adding & SubtractingV2.notebook
3 x 7 = 21 (3 lots of 7)
March 26, 2015
Even with Division, we must not forget our known facts!
365 / 12 = 30 5/12
7 x 3 = 21 (7 lots of 3)
We could also use a grid to show the inverse relationship between Multiplication and Division: 21 divided into groups of 3 = 7
4824 / 12 = (4800 / 12) + (24 / 12) = 400 + 2 = 402
21 divided into groups of 7 = 3
Nov 1308:28
Nov 1317:13
Chunking Demonstration
Short Division Demo
﴾repeated subtraction﴿
0 5 7 r 3 8 45 9 4
5
3 or 57 ... and then 8
interpret the result!!
Now you do some:
How many cakes can be made with 324 eggs if each cake needs 5 eggs?
How many cars are needed to transport 126 children if each car can hold 5 children?
Sep 2508:59
Sep 2508:52
9
Place Value Introduction & Adding & SubtractingV2.notebook
March 26, 2015
Chunking Demonstration
Chunking Demonstration
﴾repeated subtraction﴿
﴾repeated subtraction﴿
3 2 r 3 12 3 8 7 ﴾10 x 12 = 120﴿ 1 2 0 2 6 7 2 4 0 ﴾20 x 12 = 240﴿ 2 7 ﴾2 x 12 = 24﴿ 2 4 32 3
Sep 2508:52
Sep 2508:59
(? x 500 = ? )
(? x 500 = ? )
How many pallets (500 bricks on each) are needed for my extension which will use 6250 bricks?
Sep 2508:52
Long Division 0 5 7 r 3 8 4 59 4 0 59 56 3
5 0 0 6 2 5 0
Long Division 3
or 57 8
0 5 7 8 4 59 4 0 59 56 3 3
4 2
2 2 0
Sep 2508:59
10
Place Value Introduction & Adding & SubtractingV2.notebook
When would you use a formal technique like short/long division or chunking?
Long Division 0 25 3 18 4 59 36 9 9 9 0 9 9 1
March 26, 2015
2
5 r 2 2
or 255 18
a) 40 divided by 5 b) 328 / 8 c) How many 13s are in 457? d) 46 / 5 e) 2121 divided by 7
2 0 2
f) 3253 divided by 7 g) 3606 / 6 h) 8,100 divided by 9
Sep 2508:59
Long Division
0 5 7 8 4 59 4 0 59 56 3 3
4 2
2 2 0
. .
Oct 1508:09
1 2 9 6
9 8 1 6 1 6 0
Sep 2508:59
Sep 2011:52
11
Place Value Introduction & Adding & SubtractingV2.notebook
Sep 2011:52
March 26, 2015
Jan 717:22
12
Attachments
placeValue_1_1.exe number_dials_04.exe multiplication_grid_2_2.exe
