Maths Coursework T Shapes
Contents
Introduction  Word Document Version
This document identifies algebra tasks used in year 7 maths lessons in the first half terms of the years 20082009 and 20092010. It attempts to map them to the maths curriculum and suggests which could be used for the different year 7 sets in coming years. Not all aspects of the algebra curriculum are covered. It is intended that some aspects will be covered using other tasks and some will be covered later in the year.
The algebraic skills and techniques to learn in year 7 can be broadly categorised as shown below. These grouping suggest a suitable ‘journey’ for the series of lessons for the year 7 sets.
 Systematic approach, recording data and numerical methods (N*.*, A4.1)
 Formal algebraic fundamentals
 Need for algebra
 Formulae (A4.2, A5.1, A7.1)
 Symbols for unknowns (A4.3)
 Substitution (A5.1, A7.1)
 Collecting terms and simplifying (A5.3)
 Terminology (A6.1, A3.2)
 Functions (A4.3)
 Sequences and patterns (A3.1, A6.6, A7.9)
 Algebraic manipulation
 Solving equations (A5.2, A6.4, A7.2, A7.4)
 Changing the subject (A7.3)
 Factorising/expanding (A5.3, A6.2, A7.4)
 Graphs
 Plotting (A4.4, A6.5, A7.8)
 As tool to solve algebraic problems (A7.7)
 Real life (A6.7, A7.6)
 Properties (A7.10)
 Trial and Improvement (A6.3)
The ‘Suggested scheme of lessons’ section at the end of this document would probably take in the order of 4 to 5 weeks to complete. It is intended that either interlaced with these tasks or otherwise, the remaining time should be spent looking at the Number aspects of the curriculum. Emphasis should be given to enrichment type activities. It is suggested that the Nrich activities identified on the SOW index page be used.
Description of tasks
Magic birthday trick
This is from Jonny Heeley’s Masterclass (from Teachers’ TV http://www.teachers.tv/videos/algebra  at about 1min 15secs in)
Good to use as a ‘hook’ – it may be better to do the trick early in the lesson sequence and later get the students to explain how it is done. It works as follows:
Ask the students to do the following:
 Take the month of the year you were born (1 to 12)
 Multiply by 5
 Add 7
 Multiply by 4
 Add 13
 Multiply by 5
 Add the day of the month
The students then give you their results and you are able to tell them their birthday by breaking the 4 digit result into two 2digit numbers. Subtract 2 from first to get the month and 5 from the second to get the day of the month.
Unknowns: Numbers and animals
This is a teacher lead activity based on Jonny Heeley’s Masterclass (from Teachers’ TV http://www.teachers.tv/videos/algebra  at about 3mins 20secs in). A printable version using animals and letters instead of fruit and vegetables is in resources folder. Give a card to each student (holding back an 8 and a 4). Give out one rabbit, one elephant and one ‘n’. Tell students not to tell each other what they have but get them to follow the process (and to just play along if they have something unusual). They should all get the same answer. You then go on to show how it works with animals and letters.
Resources:
Unknowns  animals and letters.ppt
Summing consecutive numbers
This is a simple little investigation which can be done without formal algebra. Find a rule for summing three consecutive integers. This can be useful to highlight the need to layout numerical ‘trials’ in a logical fashion. Further questions could be:
How does the total vary as we move up to the next three numbers (e.g. compare 1+2+3 to 2+3+4)? Is this always true?
What if we consider numbers that are two apart (e.g. 3+5+7)?
This is a good activity to lead onto the usefulness of symbols for unknowns. It is also a good introduction to the concept of proof (we can show the rule is true for any three consecutives).
NRICH Task: Consecutive Numbers Consecutive Sums Excel Investigation
Me and my brother
This is a task in forming algebraic expressions and can be used at all levels. It would make a good miniwhiteboard activity. Get students to answer the follow kind of questions:
I am n years old. My brother is 3 years older than me. How old is he?
What do you get if you add our ages together?
This can then be revisited as an introduction to solving linear equations.
Grid investigation (or Opposite corners)
This is the well known investigation of taking a 100grid and overlaying smaller (to start with, 3×3) grids. The investigation starts by considering the sum of the numbers in the corners of the smaller grid and looks for patterns depending on its position. This is a good task for introducing a methodical approach to spotting patterns. When approached algebraically it can introduce ‘collecting like terms’. This investigation can be extended by considering different size larger and smaller grids (or even unknown grid sizes).
For a set 3 taking just a numeric approach, the sequence of numbers in the larger grid could be replaced with just even numbers, odd numbers etc., use of rectangles for the smaller overlaying grid etc.
The whole investigation can be extended further to cover expansion (A6.2 and A7.4) by summing opposite pairs of corners then multiplying the results (or multiplying then summing).
Resources:
Grid investigation.doc
100 grid  printable.ppt
Smaller grids  printable.ppt
Grids.xls
100 grid  eBeam.emf
Nrich: Seven Squares (http://nrich.maths.org/2290)
Using algebra to answer problems about visual patterns (made using matchsticks). This shows different ways to visualise the constructions of the algebraic expressions.
Nrich; What's it Worth (http://nrich.maths.org/1053)
Complete the solution to find the value of some symbols placed in a square given 6 different starts
Tile Spacers
This investigation is described in the document ‘Tile spacers.doc’. An extract:
“In this investigation, we will start by looking at square tiles, and the three types of spacers we will use are T shaped, L shaped and + shaped.
The investigation is to see how many spacers are needed for different arrangements of tiles.”
This could be delivered over a couple of lesson. The fist would be to teach methodical working, recording of results and identifying simple patterns. The investigation could be revisited later to use it to derive formulae.
Resources:
Tile spacers.doc
Magic Squares
There are three strands to the work that can be done with magic squares. The first is to find ways of constructing them (3x3 to achieve different totals). Folens Y7 T1 U1 p13 is useful here. The second is to practise substitution given a formula. 10Ticks L5 P5 p20 has questions. Lastly, the students could find a, b and c (variables in the formula) given particular magic squares. See 10Ticks L5 P5 p21 for questions. The resources below may be useful for projecting the magic squares.
Resources:
Magic squares.ppt
Magic Squares  eBeam
Blank  eBeam
TShapes Investigation
This is a simplified version of the old GCSE coursework task. It recommended that it is used for assessment for tops sets already having done a similar task (such as the Grid Investigation). The sheet for students (‘T Shapes investigation.doc’) is left very open with some prompts for extension tasks (changing the grid size, changing the size of the T, rotating the T). A selection of grids in emf format (suitable for eBeam) are available for class discussions in the ‘TShapes – eBeam’ folder.
Resources:
T Shapes investigation.doc
Tshape grids  printable.ppt
TShapes – eBeam
Think of a Number
These are the type of problem in which you start with a number, perform a number of functions and always end with the same result. Nrich has a nice task as an introduction to this idea called: “Your number is…” (http://nrich.maths.org/2289). You will need to use your webbrowser’s zoom facility if you are to project these. Exercises for students based on this idea (first numeric then algebraic) can be found in 10Ticks L6 P1 p15,16 (also available as powerpoint slides). See also Folens 7.2 Unit 7 p108 (p126) for work on an algebraic approach to these problems (a lead in to the ‘Pots of Gold’ task below).
Resources:
Think of a Number.ppt
Pots of Gold
This is part of a lesson taken from Folens 7.2 Unit 7 p109 (p127) with worksheet available from p115 (p133). This is a visual approach to expression building.
Calendar Investigation
This is an investigation similar to the Grid Investigation but uses calendars (so the grids are 7 squares wide and the number 1 can be in any column). This is suitable for assessment of set 2 and 3 groups following the Grid Investigation.
Resources:
Calendar.doc
How many squares?
http://www.coolmath4kids.com/math_puzzles/s1squares.html
This is an investigation into counting squares in a larger grid. It starts with a 2x2 grid (which has 4+1=5 squares) then a 3x3 (which has 9+4+1=14 squares) etc.
Suggested scheme of lessons
Note that tasks in italics are not described in the section above.
Set 1
Task  Comment  A 
Magic birthday trick  As a hook. To be revisited later.  6.2 
Unknowns: Numbers and animals 
 4.3 
Summing consecutive numbers  Both numerically algebraically  4.1, 5.3, 6.2 
Me and my brother 
 4.3, 5.3, 6.1 
Algebra terminology 
 6.1 
Simplifying expressions 
 5.3 
Grid investigation  Include extensions  4.3, 5.3, 6.2, 7.4 
Factorising 
 6.2, 7.4 
Magic squares 
 5.1, 5.2, 7.1 
Nrich: 7 squares 
 4.1, 5.1, 6.6 
Nrich: What's it Worth  4.3, (AB.2)  
Linear sequences including termtoterm and nth term 
 6.6 
Think of a number 
 4.3, 5.1 
Magic birthday trick  Revisited  6.2 
Solving linear equations 
 5.2, 6.4 
Tshapes  Individually for assessment 

Topics not covered above (levels 5 and 6) for later in the year: A6.3, A6.5, A6.7
Set 2
Task  Comment  A 
Tile spacers  First part  4.1 
Linear sequences including termtoterm and nth term  Generating sequences only  4.1, 5.1 
Tile spacers  Revisit  4.2, 5.1 
Grid investigation  Summing only  4.3 
Think of a number 
 4.3, 5.1 
Pots of gold 
 4.3 
Nrich: What's it Worth  4.3, (AB.2)  
Expanding brackets 
 5.3 
Grid investigation  Next part  5.3 
Solving linear equations 
 5.2 
Calendar Investigation  Individually for assessment 

Topics not covered above (levels 4 and 5) for later in the year: A4.4
Set 3
Task  Comment  A 
Supporting number work  Adding and multiplying 

Number patterns (even, odd, multiples, squares, etc.) 
 3.1, 4.1 
Grid Investigation (summing)  Numeric approach only  3.2, 4.1 
Think of a number 
 4.3, 5.1 
Pots of gold 
 4.3 
Magic squares  Constructing and substitution only  5.1 
Substitution games 
 5.1 
Formulae in words 
 4.2 
MyMaths: Function Machines 
 3.2, 4.3 
Calendar Investigation  Individually for assessment 

How many squares?  For assessment 

Topics not covered above (levels 3  5) for later in the year: A4.4, A5.2, A5.3
Task Mapping to National Curriculum Levels
Investigating the Relationship Between Ttotals and Tnumbers
 Length: 701 words (2 doublespaced pages)
 Rating: Excellent
Investigating the Relationship Between Ttotals and Tnumbers In my maths coursework I will be focusing on TNumbers. I will be investigating the relationship between Ttotals and Tnumbers. In my investigation I will also try and find out the relationships between the grid size and the transformations. The Tnumber is always the number at the bottom of the T shape and the Ttotal is always all the numbers inside the T shape added together. 1 2 3 10 11 12 19 20 21 [IMAGE] 9 By 9 Grid: 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 26 27 28 29 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 The total of the numbers inside the Tshape is 1+2+3+11+20=37 this is called the Ttotal. The number at the bottom of the Tshape is called the Tnumber. How to Cite this PageMLA Citation:  Length  Color Rating  

Investigating the Relationship Between the Ttotals and the Tnumber Essay  Investigating the Relationship Between the Ttotals and the Tnumber To show the relationship between Ttotals and the Tnumbers I will use a nine by nine grid to explain. There is a shape in the grid called the Tshape. This is shown below highlighted in the colour red. 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 26 27 28 29 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... [tags: Papers]  2568 words (7.3 pages)  Strong Essays  [preview]  
TTotals Investigation Essay  TTotals Investigation Aim I am investigating the different relationships between the Ttotal and Tnumber of the Tshape by translating it to other positions on the grid. First I am going to use 9×9 grid then go on to smaller sizes like 8×8 7×7 6×6 5×5 to investigate whether the size of grid affects the Ttotal and Tnumber. This can be done by rotating it and then use vectors to find out if there is any relationship if it is translated. Mr. Zaman Contents Title Page and Aim Page 1 Contents Page 2 9×9 Grid Investigation Page 3 8×8 Grid Investigation Page 5 7×7 Grid Investigation Page 7 6×6 Grid Investigation Page 9 5×5 Grid Investiga... [tags: Papers]  6491 words (18.5 pages)  Strong Essays  [preview]  
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Essay on TTotals and TNumbers  TTotals and TNumbers [IMAGE] This is a Tshape. It allows us to gather information into algebraic formulas to explain the relationships between numbers. [IMAGE]This is the TNumber. It is the central part of our research. If you add up all the numbers in the T, you will find the TTotal. For the T above, the TTotal will be 1 + 2 + 3 + 9 + 16 = 31. 2) Using algebra, we can work out a formula for this T. On a 9x9 grid a T would look like this: [IMAGE] From this we can see that if: T number = n 1 = a 2 = b 3 = c 11 = d 20 = n [IMAGE] a = n19 From this we can see that the TTotal b = n18 will equal: c = n17 d = n... [tags: Papers]  1878 words (5.4 pages)  Strong Essays  [preview]  
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TTotals Investigation Essay  TTotals Investigation Introduction If you look at the 9x9 grid with the Tshape, you can see that the total of the numbers added together is 37 because it is1+2+3+11+21 which equals 37. This is what we call the Ttotal (37) And Tnumber is the number at the bottom of the Tshape which in this case is 20 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 My tasks The tasks I have been set are: 1) Investigate... [tags: Papers]  2195 words (6.3 pages)  Strong Essays  [preview]  
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Essay about TTotals  TTotals Introduction Looking at a grid of 9*9, with a tshape you can see that the totals inside the Tshape.=37 E.g.1+2+3+11+21=37. This is called a Ttotal =37 And Tnumber is the number on the Tshape =20 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Task ==== I have been set a task to:  1) Investigate the relationship between the Ttotal and the Tnumber.... [tags: Papers]  1656 words (4.7 pages)  Strong Essays  [preview]  
Ttotals Essay examples  Ttotals Introduction For my Ttotals maths coursework I will investigate the relationship between the Ttotal and Tnumber, the Ttotal and Tnumber and grid size and the Tshape in different positions. 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 26 27 28 29 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 7... [tags: Papers]  1209 words (3.5 pages)  Strong Essays  [preview] 
Related Searches
Ttotals Numbers Relationship Tnumber Shape Maths Grid Added Always
For
the tshape in red the Tnumber for this Tshape is 20. When you take
the other numbers in the TShape away from the TNumber you get
something like this:
N17
N18
N19
N9
N
When you get the Tshape like this you can see that the centre numbers
always go up by 9's because of the table size, with the table set out
like this a formula can be worked out to find the formula to find any
TTotal on this size grid. This can be achieved by using this below:
TTotal =A
TNumber =N
Ttotal = N19+N18+N17+N9+N
So the formula for this grid is: 5N63
The Testing Process for grid 9x9:
Testing the formula can be done using the variables A and N.
TTotal =A
TNumber =N
(I have used the number 5 in the formula to multiply N because there
are 5 grid boxes in one T shape on any grid)
(Example Tnumber = 20)
A = 5N63
N = 20
A = 5x20
= 10063 = 37
I will now test to see if this will work any were on the 9x9 grid.
N=43
A=5x43 24+25+26+34+43=152
24
25
26
34
43
A=21563
A=152



N=49
====
A=5x49 30+31+32+40+49=182
A=24563
30
31
32
40
49
A=182
I have fully tested the formula for three different Tnumbers and the
formula works any were correctly on a 9 by 9 grid.
The full formula for this size grid is: A=5N63
6 By 6 Grid:
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
26
27
28
29
30
31
32
33
34
35
36
If you take the other numbers in the TShape away from the TNumber
you get a TShape like this.
TTotal =A
TNumber =N
N13
N12
N11
N6
N
When you get the Tshape like this you can see that the centre numbers
always go up by 6's because of the table size, with the table set out
like this a formula can be worked out to find the formula to find any
TTotal on this size grid. This can be achieved by using this below:
TTotal = N13+N12+N11+N6+N
= 5N42
The Testing Process for grid 6x6:
Testing the formula can be done using the variables A and N.
TTotal =A
TNumber =N
(I have used the number 5 in the formula to multiply N because there
are 5 grid boxes in one T shape on any grid)
A = 5N42
N = 14
A = 5x14
= 7042 = 28
I will now test to see if this will work any were on the 6x6 grid.
N=22
A=5x22 9+10+11+16+22=68
9
10
11
16
22
A=11042
A=68



N=35
====
A=5x35 22+23+24+29+35=133
A=17542
22
23
24
29
35
A=113


N=32
====
A=5x32 19+20+21+26+32=118
A=16042
19
20
21
26
32
A=118
I have fully tested the formula for three different Tnumbers and the
formula works any were correctly on a 6 by 6 grid.
The full formula for this size grid is: A=5N42
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