10Ticks.co.uk - Level 6 Information

Here you see the contents of the VLE Level 6 Licence. Your order will come on CD-Rom or DVD and will contain each of the pages below as a single page pdf stamped to your school name VLE. The pages are not editable. A searchable page of contents also comes on the disc.

Level 6 Pack 1 Info
Level 6 Pack 2 Info
Level 6 Pack 3 Info
Level 6 Pack 4 Info
Level 6 Pack 5 Info
Level 6 Pack 6 Info
Level 6 Pack 7 Info
Level 6 Pack 8 Info

Level 6 Pack 1 Contents/Teacher Notes

Level 6 Pack 1 Info

Pages 3-8. Algebra 1/2/3.
Traditional text book type activities for Level 6. Directed Numbers; algebra meanings; substitution (positive and negative numbers); like terms; brackets; solving simple equations (two/three terms); solving equations (three terms, three terms and brackets, four terms) and solving any equation. Pages

9/10. Forming and Solving Algebraic Equations.
Taking sentences and turning them into algebraic expressions and solving them. These type of questions are very popular on the SAT's at Key Stage 3.

Pages 11/12. Algebraic Multiplication Grids 1.
Multiplying terms together to generate new expressions.

Pages 13/14. Algebraic Multiplication Grids 2.
As above, negative numbers and expressions with 2 terms are used. An excellent worksheet to introduce factorising processes.

Pages 15/16. Number Magic (or Algebra).
How are those brain-teaser puzzles done "... and the answer is 10" ? A worksheet that follows the numbers and algebra through each question. It is also a subtle way of informally introducing multiplying out a bracket.

Pages 17/18. Puzzling Algebra.
Mensa type problems, requiring pupils to form equations to solve the puzzle.

Pages 19/20. Snakes and Ladders.
A game for 2 - 6 pupils. Cut out the cards, shuffle and turn upside down. Pupils take it in turn to take the top card, work out the answer and move that many places. The card is placed to the bottom of the pile. If calculated wrongly they go forward to the next snake and down it! Normal rules apply. It might be interesting to see if pupils notice that 31 cards only have been supplied, why's that then ?

Pages 21/22. Truncate/Race Track II.
Substitution board games.

Pages 23/24. Some Products (Algebra).
Another practice sheet. Two expressions are given for pupils to multiply and add together. As the sheet progresses pupils have to find the original expressions. This sheet is particularly useful for factorising skills.

Pages 25/26. Finding Equations from Tables.
The Difference Method. Lots of tables of linear functions. The difference method is an easy way for pupils to spot the type of function, as well as to solve linear equations. If the difference between the y numbers is the same, this tells us we have a linear function. This number also becomes the coefficient of x. Hence we know, for example, our equation starts with y = 3x. Now by simple substitution of the x numbers, we can find what we have to add or subtract to find the complete equation to make the y number. This skill in combination with the practical number patterns worksheet is excellent grounding for GCSE coursework for lower ability pupils.

Pages 27/28. Plotting Linear Functions.
This worksheet starts in the positive quadrant, plotting various linear equations and exploring the effect different parts of the equation have on the line. It then progresses to plotting in the 4 quadrants using different types of terminology for the equations.

Pages 29/30. Practical Number Patterns (Linear).
Unstructured linear practical number patterns. Pupils have to find formulae connecting the patterns and use them to solve the problems.

Pages 31/32. Investigations (Linear Equations).
Investigations which generate linear functions.

Pages 33/34. Quadratics.
Number sequences leading from linear to quadratic. Looking at differences in tables to decide on the type of a function. Looking at the graph shapes of the two functions. Solving simple quadratic functions algebraically.

Pages 35/36. Plotting Simple Quadratic Equations.
Although plotting quadratics in this way is not level 6, this sheet is a gentle introduction to the skills required with and without a calculator. The tables are already drawn and partially completed to give confidence. All the questions require answers read off from the graphs. The first part of each question can then be calculated by simple substitution as a check on the accuracy of the graph.

Pages 37/38. Trial and Improvement Techniques (Quadratic).
Solving quadratic equations using trial and improvement. The last exercise solves quite complex cubics with this technique.

Pages 39/40. Practical Number Patterns (Quadratic).
Unstructured quadratic practical number patterns. Pupils have to find formulae or extend tables connecting the patterns and use them to solve the problems.

Pages 41/42. Pen pals. Investigation.
The pen pals investigation is an excellent precursor to the handshakes investigation. In handshakes all the numbers are double the pen pal numbers. Hence by doing this first pupils can spot the 1/2 in the general formula for handshakes. Circles and roads are investigations that bring out triangular numbers. In house of cards the answer is a multiple of 3 to the triangular numbers. Watch out for the general formula, part of it is now n (n+ 1), different from the previous n (n-1).


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Level 6 Pack 2 Contents/Teacher Notes

Level 6 Pack 2 Info

Pages 3/4. Translations.
Translating shapes around a grid. Find the vector that translates an object to an image, then move an object about using vectors.

Pages 5/6. Treasure Island/Island Hopping.
Translation questions set in context of moving about a map. The notation of using a "+" between each vector can be used at a later level whenintroducing vector addition. Find the vector from start to end of journey and then add the "route vectors". Using letters as well as place names means any pupil finising early can quickly be set lots of other routes using the letters.

Page 7. Aliens. A translation game.
Shoot the aliens using vectors to save the earth!

Page 8. Race Track.
A translation game. Use vectors to negotiate a race track.

Pages 9/10. Translate the Joke.
Using vectors to move around a grid and translate jokes.

Pages 11/12. Reflections.
Finding reflections. Finding, by inspection or construction, mirror lines. It would be expected that pupils know equations parallel to the x and y axis, as well as y = x and y = -x.

Pages 13/14. Rotations 1.
Rotating objects through a given number of degrees about a centre of rotation. Tracing paper would be useful here.

Pages 15/16. Rotations 2.
Locating centres of rotation. Instructions how to construct a centre of rotation using the perpendicular bisectors. Describing a rotation given the object and image.

Page 17. Finding Mirror Lines by Construction.
A "disposable" sheet used to construct mirror lines using the perpendicular bisector. Try to get pupils to keep their constructions small as there will be some overlap between different sets of objects.

Page 18. Finding the Centre of Rotation by Construction.
A "disposable" sheet used to construct centres of rotations using theperpendicular bisector. Again, try to get pupils to keep their constructions small as there will be some overlap between different sets of objects. This is adifficult sheet to complete accurately, and may only be suitable for more able pupils at this level.

Pages 19/20. Enlargements 1.
Given an object and image describe exactly the enlargement. All enlargements have a positive integer scale factor. The reverse aspect is finding the image, given the scale factor and centre of enlargement.

Pages 21/22. Enlargments 2.
Given an object and image describe exactly the enlargement. The enlargements now have fractional scale factors. The reverse aspect is finding the image, given the fractional scale factor and the centre of enlargement.

Pages 23/24. Parallel Lines 1.
Revision of general angle properties including corresponding and alternate angles.

Pages 25/26. Parallel Lines 2.
Interior angles, leading to all angle properties of parallel lines. Specialtriangles within parallel lines.

Pages 27/28. Bearings and 6-figure Grid References.
Finding locations of ships by constuction on the sheet. Scales and 6-figure grid references need to be known before this can be attempted.

Pages 29/30. Pirate Trail/Countryside Walk.
Follow the trails, measuring bearings and finding actual distances from thescale as you progress. This and the Bearings Trail have been put into a "real life" context. Bearings and distances are not exact. Pupils will have to make decisions as to which measurement to take. This also introduces scaling up errors, if you are 1mm out, what is this error when scaled up ?

Pages 31/32. Bearings Trail 1/2.
Solve the problems using "real life" bearings and scales.

Pages 33-36. Bearings and Scale Drawings 1/2.
Traditional worded questions that pupil have to translate into scale drawings to be able to answer the questions posed.

Page 37. Using Isometric Paper.
Two different ways of representing 3-dimensional shapes on paper. How to draw solids on isometric paper. When all the solids are made they form a puzzle in themselves. The 7 solids can be put together to form a 3x3x3 cube.

Pages 38/39. Two and Three Dimensional Work.
Using the skills learnt in the previous worksheet, drawing solids on isometric paper. An investigation on polycubes.

Page 40. Plans and Elevations (Solids).
Matching solids to their plans and elevations. The make up of these solids have increased in complexity from the solids in the first plans and elevations sheet at level 5.

Pages 41/42. Plans and Elevations (Finding Solids).
Using plans and elevations pupils have to make a solid then draw it on isometric paper. This is a very difficult sheet. It needs to be attempted from coloured sheets to make it a more accessible to everyone.


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Level 6 Pack 3 Contents/Teacher Notes

Level 6 Pack 3 Info

Pages 3/4. Percentages 1.
There is a huge amount of percentage work to be covered at level 6. This first sheet covers finding percentages of quantities and percentage increases and decreases of quantities. It ends by putting these questions into context with worded questions.

Pages 5/6. Percentages 2.
Finding the original quantity in a question, again putting it into context with worded questions.

Pages 7/8. Percentages 3.
Finding a percentage.

Pages 9/10. Percentages 4.
Percentage increase and decrease.

Pages 11/12. Percentages 5.
Percentage profit and loss. Simple and Compound interest.

Pages 13/14. Vulgar Fractions, Decimal Fractions and Percentages.
Interchanging between these three number systems. The use of the dot above a number is used to indicate recurring numbers. Using trial and improvement to find fractions that are equivalent to recurring decimals is a very difficult skill. Use these sections only with the more able pupils.

Page 15. Fraction Hexagon Puzzle Grid.
The master grid needed for the hexagon puzzle cards.

Page 16. Percentage, Decimal, Fraction Equivalent Hexagon Puzzle Cards.
Place the correct hexagon on the correct spot on the master board. Rotate the hexagons until the adjoining hexagon has the equivalent fraction/decimal/percentage next to it. How many hexagons can you get in place that are fully equivalent?

Page 17. The Decimal Number Line.
A series of questions that lead to deeper understanding of the decimal system. This is a precursor to trial and improvement and the decimal skills needed to attempt this type of question.

Page 18. Investigations with Decimals, Fractions and Percentages.
Some investigations surround the number systems. Some are quite difficult and go beyond level 6, but more able pupils should cope.

Pages 19/20. Rounding Off.
Rounding off to decimal places and significant figures. Page 20 shows numbers that have already have been rounded off and looks at the upper and lower limits that the values could possibly take.

Pages 21/22. Fractions 1.
Revision of improper fractions, cancelling and common denominators.

Pages 23/24. Fractions 2.
Addition and subtraction of fractions. Starting with the same denominators and moving quickly to addition/subtraction by finding common denominators.

Pages 25/26. Fraction Pyramid.
This style of worksheet should be familiar to pupils by now and should need little explanation. To get the fraction above add the two fractions below. As the questions progress subtraction is needed.

Pages 27/28. Magic Squares (Fractions).
Lots of addition and subtraction involved in the magic squares. This sheet is particularly useful for the more able. Question 16 could be used in isolation as a board exercise, with pupils choosing fractions and the class making the magic square.

Pages 29/30. Hit 12/Hit 15.
Shove penny game adapted to fractions. Hit 12 is centred on the fractions 1/2, 1/3, 1/4 and by necessity 1/12. Similarly Hit 15 is centred on the fractions 1/3, 1/6, 1/9 and by necessity 1/18.

Pages 31/32. Addition/Subtraction of Fractions (Worded Questions).
These pages put all the fraction skills learnt to date into context.

Pages 33/34. Multiplication and Division of Fractions 1.
Multiplying fractions by whole numbers. Answers start as whole numbers but graduate to mixed numbers.

Pages 35/36. Multiplication and Division of Fractions 2.
Multiplying fractions by fractions. This leads to cancelling down before multiplying out and multiplying mixed numbers together. Diagrams are used to show the multiplication, this is more clearly demonstrated by repeating the diagrams when folding a sheet of paper. The "overlap" is the answer.

Pages 37/38. Multiplication and Division of Fractions 3.
Division of fractions. Introduction of inverse. Dividing a whole number by a fraction and looking for rules to help with division.

Pages 39/40. Fraction Multiplication Grids.
Again, this style of worksheet should be familiar to pupils by now and should need little explanation. Multiplication and division skills are necessary. Questions 23 and 24 are very difficult and you may want to prompt the class by giving them 1 of the surrounding fractions.

Pages 41/42. Multiplication/Division of Fractions (Worded Questions).
Putting all the multiplication and division skills into context.


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Level 6 Pack 4 Contents/Teacher Notes

Level 6 Pack 4 Info

Pages 3/4. Ratio.
Cancelling down ratios. Cancelling down ratios in different units. Worded questions involving ratio.

Pages 5/6. Ratio Revision.
Need some more practice ? Another sheet of questions. This can be used as a general revision sheet for GCSE candidates.

Pages 7/8. Menus.
A slightly different approach to ratios. All questions are part of genuine recipes. A good way of generating display work if pupil produce their own menus from recipes they may have used in school.

Pages 9/10. Golden Numbers.
Practical ratio work. Starting with the Golden Rectangle and how to construct one of varying sizes. Links with the Fibonacci sequence and finishing by constructing the Golden Section Spiral.

Pages 11/12. Proportion 1.
Solve worded questions using the unitary method.

Pages 13/14. Value for Money.
Finding best values for money with different items. When attempting the first side it is best to use the unitary method. On the second, try to get pupils to "cancel" down to a common denominator, rather than all the way down to 1.

Pages 15/16. Proportion 2.
This might be best done at a later date than the Proportion 1 sheet as the ideas are distanced. Rather than using the Unitary method now we are using fractions/decimals to solve the worded questions.

Pages 17/18. Number Work Revision.
Revision of some of the number work from level 5. This includes long multiplication/division, LCM, HCF, Prime Numbers, powers and roots and estimation.

Pages 19/20. Missing Multiplications/Divisions.
More number familiarity work without a calculator.

Page 21. Four in a Row (Estimation).
A game using estimating skills.

Page 22. Hex-an Estimating Game.
A game using estimating skills.

Page 23. Powers of 10 (Multiplication/Division).
Graduated mental exercise multiplying and dividing by powers of 10.

Page 24. Number Work (Estimating).
Multiplying and dividing by 2, 3 and 4 digit numbers and mentally working out an estimate.

Page 25. Cricket (Estimation).
A game for two players using estimation.

Pages 26/27. Trial and Improvement.
Solving, mainly linear equations, by trial and improvement. Sections A and B are primarily for those pupils who struggle to solve these equations by the usually algebraic method. Section C is where the Trial and Improvement technique is really tested out.

Pages 28/29. Golf Practice Holes/Royal Idiotdale.
An idea that came from a Brian Bolt book that practices Trial and Improvement techniques. Pupils have to guess the answer inside the par. All guesses are to be recorded. Good wall display material. Get every pupil to make up one hole and draw it. Put them together and have a whole class golf course wall display.

Pages 30. Glennsparrows.
The second, harder Trial and Improvement golf course.

Pages 31/32. Compass and Ruler Constructions.
Constructing a triangle given all three side lengths and bisecting an angle.

Pages 33/34. Nets.
This sheet should be attempted by the majority of pupils without the aid of polydron. The focus is to be able to visualise the nets becoming solids. To recap the worksheet you may wish that polydron be handed out and pupils spot their own mistakes.

Pages 35/36. Construct Your Own Calendar.
Construction of nets that can build up into a calendar.

Pages 37/40. Calendar Nets.
More complicated nets (Square-based Pyramid, Glueless Hexagonal prism, dodecahedron and the Truncated tetrahedron). These can be photocopied onto coloured card and made into calendars for the next year. They will have to be used in conjunction with the calendar sheets page. A good end of year activity.

Page 41. Santa's Grotto.
This puzzle originates from an Australian detergent manufacturer who used it as a sales gimmick. Here we have adapted it for Christmas. Use it with or without a calculator. Especially good to fill up the back of your Christmas News letter! Very quick to check if set as a competition.

Page 42. Christmas Investigations.
Four Investigations with a seasonal twist.


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Level 6 Pack 5 Contents/Teacher Notes

Level 6 Pack 5 Info

Pages 3/4. Real Life Graphs.
Exploring a variety of real life situations and the graphs that they produce.

Pages 5/6. Correlation 1.
Exercises looking at the connections between two variables. Direct and indirect correlation linked to scatter graphs. Interpreting scatter graphs.

Pages 7/8. Correlation 2.
Plotting scatter graphs and using them to give estimates. Some practical exercises that pupils can carry out which generate scatter graphs.

Pages 9/10. Speed 1.
Converting minutes to fractions of hours ready for distance/time calculations. Calculations involving finding the average speed and the distance travelled.

Pages 11/12. Speed 2.
Converting decimals and fractions of hours into hours and minutes. Calculations finding time taken for journeys. Worded questions covering the topic.

Pages 13/14. Density.
Density calculations using the units g/cm3 and Kg/m3. Finding the density, mass and volume in a variety of situations.

Pages 15/16. Distance/Time Graphs 1.
Describing journeys from graph shapes. Calculating velocity from graphs.

Pages 17/18. Distance/Time Graphs 2.
Drawing lines that represent speed on a distance/time graph. Interpreting simple distance/time graphs.

Pages 19/20. Distance/Time Graphs 3.
Interpreting and taking readings from more complex distance time graphs. Constructing graphs given the relevant information.

Pages 21/22. Rectilinear Areas.
Revision of the level 5 shapes. Introduction of the kite, rhombus and trapezium. The rhombus is already defined as a parallelogram and can be found with that formula. As a link to quadrilateral properties the kite and rhombus have the common property of perpendicular diagonals and can both use the area formula 1/2 product of diagonals. The sheets end with compound areas involving all the formulae already used.

Pages 23/24. Cubes, Cuboids and Triangular Prisms 1.
Finding volumes of the above.

Pages 25/26. Cubes, Cuboids and Triangular Prisms 2.
Given the volume now try to find the missing dimension. The section ends with putting these into context with worded questions.

Pages 27/28. Polygons 1.
Defining a polygon and discovering the sum of interior angles. Using the newly found formulae in problems.

Pages 29/30. Polygons 2.
Finding exterior angles and formulae. Using the formulae in problems. Some links with Logo, tessellating shapes and a construction.

Pages 31/32. Polygon Perimeters and Circles .
Introducing pi and the formulae for circumference and area. Some interesting facts about pi and 1 000 000 pound coin problems.

Pages 33-36. Circles 1/2.
Using the formulae for the circumference and area of a circle. Questions where measurements from diagrams have to be taken. The circle formulae put into contextual questions.

Pages 37/38. Circles 3.
A mixture of questions using all the skills from the previous sheets. Given the area and circumference finding the radius. Worded questions of this type.

Pages 39/40. Quadrilaterals/Properties.
A cloze procedure exercise looking at quadrilateral properties.

Pages 41/42. Discovering Diagonals.
Through construction, an exercise looking at diagonal properties in quadrilaterals. Very good revision for some of the constructions pupils should know.


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Level 6 Pack 6 Contents/Teacher Notes

Level 6 Pack 6 Info

Pages 3/4. Stem and Leaf Diagrams.
Introducing "stem and leaf" diagrams. Calculating the mode, median and mean from "stem and leaf" diagrams.

Pages 5/6. Two Way Tables.
Taking readings from two way tables. Pupils will need knowledge of fractions, percentages, ratios and probability to carry out the subsequent calculations.

Pages 7/8. Inequalities.
Using inequalities on a number line. Looking at integer solutions to sets of inequalities. This has been placed here as a precursor to grouping continuous data into class intervals.

Pages 9/10. Grouping Continuous Data using Equal Class Intervals.
Grouping discrete data into class intervals was covered at level 4. Continuous data needs the introduction of inequalities so that the class intervals don't overlap or have gaps. A lot of work will need to be done with inequalities first to cover this concept. Check also that pupils are making class interval sizes the same. This type of "bar chart" has been titled a "Frequency diagram forContinuous Data". It could also be titled a "Histogram with Equal ClassIntervals". Both names are used at examination level so try to interchange between the two.

Pages 11/12. Pie Charts 1.
Pie charts drawn from tables. Questions 1-15 give exact answers. Questions 16 onwards are more life like and need to be rounded off. Some after rounding may add up to 361 or 359, and this needs talking through with pupils.

Pages 13/14. Pie Charts 2.
Six pie charts are presented. Each angle needs to be measured from the pie charts and from this information the questions answered.

Pages 15 - 18. Statistical Investigation 1/2.
Notes and guidelines on presenting and carrying out questionnaires etc.

Page 19. Questionnaire.
A spoof questionnaire. Find all the mistakes.

Pages 20/21. Statistical Investigations.
Typical short GCSE questions on Data Collection Sheets and Questionnaires. Some investigations for the class to perform.

Pages 22/23. Single Event Probability.
Revision of single event probability from level 5, moving onto the sum of all mutually exclusive events.

Page 24. The Grand National .

Page 25. Motorway.

Page 26. Dice Difference.

Page 27. Home Time.

Page 28. The Hare and the Tortoise.
Games where strategies can be thought through by looking at the possibility space. To start with, just play the game and then look at the probabilities through possibility spaces. You may want to start off looking at the probabilities with the later games before you start playing them. Page 29. Roll a Pound. At this level pupils will not be able to work out the theoretical probabilities for this game. Through possibility spaces pupils should be able to see which direction you will be more likely to move towards.

Pages 30/31. Yachts (Permutations/Lists 1).
Exploring permutations by looking at patterns.

Pages 32/33. Filing Cabinets (Permutations/Lists 2).
Less structured activity exploring permutations by looking at patterns.

Pages 34/35. Books (Permutations/Lists).
Make your own books. Work out all the permutations. Notice the similarities with the last three sheets!

Pages 36/37. Lists and Probability.
Putting lists together logically. Using the lists to find probabilities of events.

Pages 38/39. Possibility Spaces (Sample Spaces).
How to draw out a possibility space and use it to find probabilities.

Page 40. Probability Obstacle Course.
To get through the obstacle course pupils will need luck and a good knowledge of probability!

Page 41. Blank Probability Obstacle Course.
Set up your own obstacle course. A good source of wall display material.

Page 42. Win, win, win !!!
An interesting puzzle that looks difficult to solve. It is broken down in to stages for pupils to follow the mathematics. It surprises some pupils that the odds are only slightly in favour of Beth. It leads to good discussion on Casinos. It is similar in so much that the odds are slightly in favour of the Casino but over the millions of bets going on the Casino will always come out on top.


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Level 6 Pack 7 Contents/Teacher Notes

Level 6 Pack 7 Info

Pages 3/4. Addon-agons with Fractions.
Addition and subtraction of fractions in preparation for the algebraic fractions section later on.

Pages 5/6. Fraction Wheels.
More fraction addition and subtraction familiarity exercises.

Pages 7/8. Some Products (Fractions).
Addition and multiplication of fractions. The sheet differentiates by fall out. The later questions become quite difficult.

Page 9. Four in a Line - Fractions.
Traditional four in a line game using fraction addition and subtraction skills.

Page 10. Hex-an Adding and Subtracting Game (Fractions).
Traditional hex game using fraction addition and subtraction skills.

Pages 11/12. Decimal Multiplication Grids.
Multiplying and dividing decimals mentally. Pupils will have previously completed similar worksheets based on multiplication grids and will need little explanation of the task.

Pages 13/14. Decimal Calculations.
Pen and paper techniques for multiplying and dividing decimals. Multiplying decimals incorporates grid and long multiplication, whilst dividing decimals is based on long division.

Pages 15/16. Indices.
Multiplying by powers of 10 in index form. Addition rule of indices, negative indices and utilising the xy button.

Pages 17/18. Number Work with Factors.
Factorising numbers to enable easy multiplication. Using prime factors to find square and cube roots. Using prime factors to find HCF's and LCM's.

Pages 19/20. More Number Work.
Revision of number work and introduction of nested brackets. Using the calculator efficiently.

Pages 21/22. Inequalities.
Revision of inequalities. Changing worded questions into inequalities. Rearranging inequalities, including multiplying/dividing by a negative number. Identities.

Pages 23/24. Multiplying Brackets with Grids 1.
The worksheet starts by multiplying out brackets through multiplication grids. It expands this skill and introduces the skills of factorising.

Pages 25/26. Multiplying Brackets with Grids 2.
Pupils are expected to deal with more complex terms. The sheet finishes with multiplying out two sets of brackets. This skill is not expected at this level, but it is a simple progression using grid multiplication.

Pages 27/28. More Algebra.
Previous skills such as multiplying out brackets, solving 2, 3 and 4 term equations are furthered through the introduction of fractions and decimals.

Pages 29/30. Algebra Fractions.
Cancelling down algebraic fractions and finding equivalent algebraic fractions. Introducing algebraic addition through breaking down fraction addition into the component parts. It is important that pupils are competent at fraction addition before attempting this worksheet.

Pages 31/32. Complex Substitution 1.
No calculator is allowed for this work sheet. Numbers have to be substituted into increasingly complex expressions. This covers a wide range of the mental arithmetic skills needed at level 6.

Pages 33/34. Complex Substitution 2.
Calculators are allowed for this worksheet and it is important pupils can use them efficiently. Again numbers have to be substituted into increasingly complex expressions.

Pages 35/36. Shove Penny (Substitution 1/2).
The teacher sets the targets and the value to be substituted, start off with x at 2. To keep the interest going vary the target and the x value. This will make different areas of the grid more/less valuable. Decisions will have to be made such as are scores truncated, rounded to 1 dp, will x be whole, decimal, fraction etc. What happens when x is between 0 and 1, or below 0 ?

Pages 37/38. Useful Formulae 1.
Formulae that pupils should meet around school.

Pages 39/40. Useful Formulae 2.
Substituting into formulae then rearranging to find the unknown quantity which isn't the subject of the formula.

Pages 41/42. Rearranging Simple Formulae.
A worksheet that increases in complexity. To make life easier for the rearrangement some subjects may be powers, e.g. i2. This can be taken a step further by making i the subject, square rooting both sides, if the class is competent.

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Level 6 Pack 8 Contents/Teacher Notes

Level 6 Pack 8 Info

Pages 3/4. Sequence Notation.
Term-to-term rules and term-to-position rules. The worksheet uses the notation T(1), T(n) etc.

Pages 5/6. Mapping Diagrams.
Mapping diagrams of linear functions and their inverse. The inverse will need talking through. Draw tables of the function and then test the inverse function to see if it works.

Pages 7/8. Mapping Diagrams (Pupils' Sheet).
All the questions from the Mapping Diagrams sheet can be answered on this. It will save pupils time in drawing their mapping diagrams.

Pages 9/10. Plotting More Linear Functions.
Revision of plotting linear functions. Looking at equations and lines to discover which part of the equation affects the line, leading to y = mx + c. Sketching linear equations.

Pages 11/12. Linear Functions and Mid-points.
Rearranging linear functions in the form "y = " then plotting the line. Comparing the size of fractions through gradients. Finding the half way point of two numbers. There are four possible formulae that can be used. Why do they work ? Which is the easiest to use ? This leads to finding the coordinate that is the mid-point of a line segment.

Pages 13/14. Linear Functions and Gradients.
Finding the gradient of a straight line. Given two coordinates finding the gradient of the line segment that connects them.

Pages 15/16. Routes and Pathways (Loci).
Describing pathways and familiar routes. It can be fun describing a route through a maze. Pupils may want to define 1 step forward as a way of describing the distance travelled. You may ban this! After pupils have attempted the exercise draw the mazes on the board and close up the exit. Follow pupils instructions and see if they find the exit. Pupils may want to make up their own mazes. Possibly use Logo instructions to get through them! Discovering basic loci rules. Loci in two and three dimensions.

Pages 17/18. More Logo.
Writing procedures that rotate various polygons. Recursive programs.

Pages 19/20. Transformations.
Creating new shapes through transformations. Moving a shape through two transformations. Creating tessellating patterns with transformations.

Pages 21/22. Combined Transformations.
Comparing multiple and single transformations.

Pages 23/24. Proofs.
Looking at simple problems and finding proofs using algebra. The last two questions introduce the notion of counter example - find one example that disproves the conjecture.

Pages 25/26. Geometric Proofs and Constructing Triangles.
Basic geometric proofs. Discovering criteria for construction of unique triangles. The geometric proofs are continued in the level 7/8 packs.

Pages 27/28. Constructions.
Revision of the basic constructions needed at this level. Constructing scale diagrams from a series of worded questions. Taking measurements from the scale drawings to solve the problems.

Pages 29/30. Solids.
Constructing nets of more complex models. Constructing a model from a plan, side and front elevation. Exploring planes in solid shapes.

Pages 31/32. Scale Drawing.
Converting measurements through more complex scales than at level 5.

Pages 33/34. Metric Conversions.
Converting between the metric units of area and volume.

Pages 35/36. Calculating the Mean/The Mean (Worded Questions).
Using an assumed mean to calculate the mean. More complicated mean questions involving median, mode and range. Pages 37/38. Population Pyramids. Reading information from a population pyramid. Making comments on a variety of shapes of population pyramids.

Pages 39/40. Statistical Tasks.
The tasks may be carried out as part of an ongoing course or as a coursework assignment appropriate to this level. Many of the tasks would be suitable at higher levels, differentiated by the pupils input.

Pages 41/42. Statistical Diagrams.
Taking readings from a variety of statistical diagrams. Looking at misleading diagrams.


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