Transcript 2 by 2 Slides

2 by 2....by more!!!
North Lincolnshire Mathematics Conference
John Leggott College, Scunthorpe
Monday 2nd September 2013
Joe Murray
Association of Teachers of Mathematics
Objectives
2 by 2.........by more!!
 How many themes can you teach or learn with a 2 by 2 grid?
 How can we turn one activity into many?
 ATM support
 Reflection, questions, etc
Problem solving & investigation...
... is at the heart of mathematics
Outstanding teaching & learning will:
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allow children to make decisions
encourage creativity and invention
promote discussion and communication
involve children seeing pattern, connections....... making &
testing hypotheses,
promote reflecting, interpreting, explaining........proving,
encourage ‘what if’ ..........and ‘what if not’ questions;
be enjoyable and contain the opportunity for surprise
offer problems that are accessible …..and extendable
1.
Professional support mathematics community......new CPD package
2.
Professional development work with teachers...branches
3.
Professional identity part of vision for mathematics education
4.
MT journal 6 copies per year; articles by teachers & for teachers
5.
e-News
6.
ATM website
archive of “old” journals, sales,....
7.
Publications
25% discount for members
8.
Annual Easter Conference
9.
Branch meetings
Sheffield 2013, BCME8, Nottingham 2014
10. Tax concessions £65 p.a......£52 after tax effectively £1 a week!!!
Primary school membership is just £65 per year
Chuck the Ted
”use simple formulae expressed in words”
(draft N.C.)
little People...Big Maths
• Children sit in a circle, each child with a number that all can
see.
• Choose a “rule”.
e.g. Find someone with a number 1 more than you
• Each child takes a turn to throw the toy to another child
following the rule.
• Make a new rule and play again.
Addition squares
2
5
4
6
9
9
11
14
• Add pairs of outside numbers
• Add the 4 numbers inside the
square
• Is this total equal to double the
sum of the 4 outside numbers?
40
• Investigate other 2 by 2 squares
• What about 3 by3 squares, 4 by4...?
• What about rectangles??
Multiplication squares
x
4
3
5
20
15
1
4
3
•
•
Multiply pairs of outside numbers
Add these 4 new numbers
What is the connection between the
4 outside numbers and the square
total?
42
•
Investigate other 2 by 2 squares
•
Extend to bigger squares...3 by 3, 4 by 4...
•
What happens with
rectangles?
Monty
Rich Task Maths
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 16 17 18 19 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99
100
Monty Python is a 7square snake on a 1 to
100 grid.
•Make Monty.
•Monty cards.
Monty
Rich Task Maths
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
Monty Python is a 7-square
snake on a 1 to 100 grid.
21 22 23 24 25 16 17 18 19 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99
100
•Longer and shorter Monty.
•Heads and tails.
Find the difference between head
number and tail number.
Biggest?...smallest?
Monty
Rich Task Maths
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
Monty Python is a 7-square
snake on a 1 to 100 grid.
21 22 23 24 25 16 17 18 19 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99
100
•Mystery Monty.
•Monty on a “tables” grid.
Four-ominoes
• These can be made with 4
squares...joined edge to
edge
• Are there any more?
Investigate
• Symmetries, tessellations,
area, perimeter......
• 3-D figures...... with 4 cubes
• Pupil “robots”
What about 5 squares, 6
squares, etc
Four-omino activities
1. Make 4-ominoes
Use 5 squares joined edge to edge, how many different shapes can you make?
2. Names
Find names for all 4-ominoes? Which is a “snake” or the “submarine”?
3. Symmetry
Which have line symmetry? Which have rotational symmetry?
4. Tessellation
Which 4-ominoes will tessellate? Will all 12 tessellate?
5. Area and perimeter
Which 4-omino has the biggest area?........longest perimeter?
6. Joins and perimeter
Investigate the number of joins and the perimeter.
7. Other “ominoes”
Make some shapes using just 5 squares.....or shapes using 6 squares??
8. Using triangle
Use isometric paper to make shapes from 5 triangles
9. LOGO or Roamer
Write a LOGO programme to draw a 4-omino. .......or direct a “pupil robot”
10. 3-D exploration Use 5 multilink cubes to make a 3-D shape.
How many can you find?
Stay-the-Same Numbers
generate and describe linear number sequences (draft N.C.)
8 days a Week
Look at this set of linked number machines
in
x2
-3
out
Which number will go into the machines and come out staying
the same?
Stay-the-Same Numbers
Eight Days a Week
Which number will stay the same now?
in
x2
-7
out
Stay-the-Same Numbers
Eight Days a Week
.....and now?
in
x2
- 23
• Can you generalise? Is there a rule?
• Does this work for any number?
out
Stay-the-Same Numbers
Eight Days a Week
What if the boxes were reversed?
in
-3
x2
out
Which number will go into the machines and come out staying
the same?
Stay-the-Same Numbers
Eight Days a Week
Which number will stay the same now?
in
-5
x2
out
Stay-the-Same Numbers
Eight Days a Week
.....and now?
in
- 17
x2
• Can you generalise? Is there a rule?
• Does this work for any number?
out
Place value
T
U
Roll a dice & enter numbers in the
boxes.
Each player has own table
• Biggest number
• Smallest add
• Biggest take-away

Place your digits and add your numbers together
what if you are allowed to put
numbers in another person’s boxes?
Braille
Your task is to design a new coding system for letters in the alphabet.
• The code is based on a 2 by 2 grid with up to 4 dots in the cells.
• Here are a few......
• How many different “Braille tiles” are there?
• How many have 2 dots, 3 dots, etc....?
• Are there enough for each letter of the alphabet?
• Try some 3-dot, 5-dot, 6-dot........”tiles”
Braille 2
Brill shape
No dots
1 dot
2dots
3 dots
4 dots
5 dots
1
2
1
1
3
3
1
1
4
6
4
1
1
5
10
10
5
1
1
6
15
20
15
6
6 dots
1
Carroll diagram
• Sort shapes by properties
3 sides
red
not red
4 sides
• Sort numbers [odd, prime,
multiples, etc]
• Make sets of criteria cards to
create a variety of problems.
• Use bigger diagrams [e.g. 3 by 3]
Always, sometimes, never...
Always true
Sometimes true
•
•
•
•
Never true
Not sure
•
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Multiples of 3 are odd numbers
Squares have 4 right angles.
A 4-sided shape has a line of
symmetry
An even number cannot be a prime
number
A multiple of 3 cannot be a multiple
of 2.
You can draw a triangle with 2 right
angles
A shape with 4 sides is a square.
Odd one out
7
8
9
1.
Professional support mathematics community......new CPD package
2.
Professional development work with teachers...branches
3.
Professional identity part of vision for mathematics education
4.
MT journal 6 copies per year; articles by teachers & for teachers
5.
e-News
6.
ATM website
archive of “old” journals, sales,....
7.
Publications
25% discount for members
8.
Annual Easter Conference
9.
Branch meetings
Sheffield 2013, BCME8, Nottingham 2014
10. Tax concessions £65 p.a......£52 after tax effectively £1 a week!!!
Primary school membership is just £65 per year
Thank you
For further information about ATM
 Membership
 Publications
 Branches
 Conferences
www.atm.org.uk
or contact Joe Murray at
[email protected]
[email protected]