KS3 Level

Algebra

Projected KS4 Grades

6

I can expand and factorise single brackets at all difficulties. I can simplify expressions with indices and have looked at discovering the index laws. I can construct linear equations with unknowns on both sides and with brackets (+ve and ve coefficients). I can construct formulae for two step real life situations. Ex; higher charge, bills, delivery costs, etc. I can derive a formula (from mathematics or other subjects) and change its subject then apply to real life contexts to solve problems. I can solve linear equations with fractional/decimal coefficients and unknowns on one side, both sides all with and without brackets using appropriate methods.

I can solve more complex linear inequalities in one variable and represent the solution on a number line. I can apply the effect of multiplying/dividing by a negative when solving inequalities. I can use trial and improvement or iteration to determine the approximate solution to an equation. I can determine two unknown integers that satisfy simple worded problems that represent two simultaneous equations. I can construct a pair of simultaneous equations to represent a mathematical problem. I can apply efficient methods to solve a pair of simple simultaneous equations (no manipulating/rearranging needed first)

9

5

I can recognise and use sequences of cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences I can interpret, deduce and justify how the nth term for linear sequences work including those generated by a pattern or practical situation. I can apply function notation and construct functions to describe mappings. You understand how to calculate with two successive functions.

I can generate points and plot graphs of linear functions where y is given implicitly in terms of x (e.g. ay+bx=0, y+bx+c=0). I can identify and interpret a gradient from an equation ax+by=c. I can select and use graphical methods to identify and interpret gradients and intercepts of linear functions. I can determine the equation of a line using two points, one point and a given gradient or perpendicular line.

8

4

I can use the rules of Algebra to add, subtract, multiply and divide terms. I can simplify expressions by collecting like terms with 1, 2 or 3 unknowns I can expand harder single brackets and extend this to show equivalences within brackets and true/false type questions I can construct expressions for a given situation. I can construct linear equations with and without simple single brackets where the unknown is only on one side. I can substitute values into more complex formulae involving those with brackets, indices and more than one operation.

I can change the subject of a formula and rearrange equations. I can solve a linear equation which has an unknown with an integer coefficient on one side or both sides. I can solve a linear equation with and without brackets . I can solve a linear inequality which has an unknown with an integer coefficient on one side or both sides. I can solve a linear inequality equation with and without brackets . (not multiplying or dividing by a negative)

7

3

I can determine pairs of positive integers that satisfy an equation with 2 unknowns • I can investigate pairs of numbers (including fractions/negatives/decimals) that satisfy an equation with 2 unknowns • I can investigate lists of combinations of possibilities that will satisfy a worded problem with 2 variables, eg a list of combinations of teas and coffees I can buy for £2, giving reasoning to explain your answers I can generate terms of linear sequences using the nth term rule from patterns and practical situations

I can interpret, deduce and justify the general (nth rule) for linear sequences I can generate a quadratic sequence using a position to term rule. I can express simple functions algebraically. I can use function machines to generate an algebraic function. I can find the inverse of a linear function. I can interpret the output to input process as the inverse function.

6

2

You can explore and identify the key features of linear graphs in the form y=mx + c You can explore and determine the features of the graphs of y=a and x=a. You can recognise and explore straight line graphs parallel to the x and y axis. You can determine the gradient of lines given by the equation of the form y=mx + c. You can understand what the gradient of a line actually means both in abstract and real life contexts.

You can determine approximate solutions to linear equations using graphs. You can investigate features of positive and negative gradients of linear graphs. You can investigate the features of the equations of parallel lines and perpendicular lines You can describe and draw a simple distancetime graph. You can interpret information from straight line graphs in real life situations.

5

1

I can use the rules of Algebra to add, subtract, multiply and divide letters. I can simplify algebraic expressions by collecting like terms. e.g. 8x + 4y – 2x simplifies to 6x + 4y. I can expand single brackets, by multiplying the exterior term by all of the interior terms. I can construct algebraic expressions to represent problems. e.g. 3 pens and 5 pencils is 3p + 5q. I can construct linear equations without brackets and unknowns only on one side. E.g. 3 pens and 5 pencils cost £1.20 is 3p + 5q = 120.

I can define substitution and explain its application in algebra. I can substitute positive whole numbers into simple expressions with one or more unknown. You know standard mathematical formulae and can substitute values into them, including expressions with small powers.

4

WT+

I can solve linear equations with an unknown on one side and using integer values, this is with and without brackets. I can solve linear inequalities with an unknown on one side and using integer values, with and without brackets.
I can generate terms of a simple sequence given a written rule.
I can express simple functions in words, and then use symbols. I can interpret simple expressions as functions with inputs and outputs.
I can discuss and interpret graphs of functions, with the use of function machines to find coordinates.

I can determine pairs of positive integers that satisfy an equation with two unknowns.
I can describe a sequence in words. I can reason a term to term rule from a linear sequence. I can generate terms of a linear sequence using a term to term rule.
I can determine coordinate pairs that satisfy a simple linear rule. I can Plot and draw graphs of linear equations with and without a table of values. I can understand how to label and scale an axis correctly. I can interpret information from straight line graphs in real life situations.

3

WT

2

WT

1
