Upload
grace-benson
View
219
Download
0
Embed Size (px)
Citation preview
Concrete Stage: Addition
Concrete stage: with real objects
putting together two sets of objects, with a number sentence:
3 + 2 = 5
Concrete Stage: Subtraction
Concrete stage: with real objectstaking a set of objects away from a larger
set, with number sentence
4 – 2 = 2
Counting Forwards (Addition) and Backwards (Subtraction)
Counting forwards along labelled number tracks or lines, with number sentences:
3 + 4 = 7
Counting Forwards (Addition) and Backwards (Subtraction)
Counting backwards along labelled number tracks or lines, with number sentences:
5 – 2 = 3
Expanded Vertical Layout
For addition: For subtraction:
47 + 327 – 116
76 300 20 7 -
13 (7+6) 100 10 6
110 (40 + 70) 200 10 1
123 = 211
Subtraction Using The Expanded Vertical Layout With Decomposition:
53 – 28 =
50 3 - 40 13
20 8 20 8
20 5 = 25
Multiplication
Concrete stageputting together equal sets, with counting:
1 2 3 4 / 5 6 7 8 / 9 10 11 12
Multiplication
Drawing stagerepresenting the concrete stage in pictures,
with repeated addition:
5 + 5 = 10
Multiplication
Counting forwards in jumps of greater than 1, both mentally and along labelled number tracks or lines, or on the hundred square, with number sentences written as repeated addition:
3 + 3 + 3 = 9
Multiplication
Introducing the multiplication symbol as a shorthand form of recording:
2 + 2 + 2 = 6
or 3 x 2 = 6
5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
or 7 x 5 = 35
Multiplication
Recognising equivalent multiplication, e.g. using arrays:
2 x 4 = 8 * * * *
* * * *
4 x 2 = 8 * * * *
* * * *
Multiplication
Place Value: Multiplying by 10 and multiples of 10, using 0 as a place holder:
5 x 10 = 505 x 100 = 5005 x 1000 = 5000
Multiplication
Multiplication using partitioning:
e.g. 38 x 7 = (30 x 7) + (8 x 7)
124 x 6 = (100 x 6) + (20 x 6) + (4 x 6)
Multiplication
Vertical method for multiplication: 38 x 124 x 7 6 210 (30 x 7) 600 (100 x 6) 56 (8 x 7) 120 (20 x 6) 24 ( 4 x 6) 266 744
Division
Concrete stage : sharing
sharing a set of objects between a group of people:
4 shared between 2 people gives 2 each.
Division
Drawing stage : sharingrepresenting the concrete stage in
pictures, recording using the division symbol.
e.g Sharing 6 sweets between 3 friends:
Joe Lucy Lee
* * * * * * 6 : 3 = 2
Division
Concrete stage: grouping
making groups or sets of a certain number:
e.g. 15 grouped into 5s gives 3 groups:
# # # # # # # # # # # # # # #
Division
Division as repeated subtraction:Counting backwards in jumps of greater than
1 along labelled number tracks or lines, or on hundred squares, with number sentences:
8 -:- 4 = 2
Division
Division as repeated subtraction without the number line, continuing until 0 (or a remainder) is reached, e.g. for 18 -:- 6:
18 – 6 = 12 – 6 = 6 – 6 = 0 I took 6 away three times, and so
18 -:- 6 = 3
And for 20 -:- 6: 20 – 6 = 14 – 6 = 8 – 6 = 2 I took 6 away 3 times, leaving 2 at the end,
so: 20 -:- 6 = 3 remainder 2
Division
Division using ‘chunking’ Chunking means subtracting larger groups, or
chunks, of the divisor number. This saves time and reduces the length of the repeated subtraction:
e.g. for 72 -:- 6 72 – 60 (10 X 6) 12 – 12 (2 X 6) 0 So, 72 -:- 6 = 12
Division
Short formal written method for division:
12
6 72
and with remainders:
20 r 4 or 20.5 8 164