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).

 

Level 6 Pack 2 Info