KS3 Level

Algebra

Projected KS4 Grades

7

I can expand double brackets. I can simplify expressions using fractions. I can construct simple linear equations with fractional and decimal coefficients I can solve problems by rearranging formulae. I can solve quadratic equations by factorising I can solve a pair of simultaneous equations

I can determine an approximate solution to simultaneous equations using a graph and interpret the answer. I can interpret, deduce and justify generalisations for the nth term of a quadratic sequence. I understand how to find f(x) + g(x), 2f(x), 3f(x) etc. graphically I can explore and use graphical methods to identify and interpret roots, intercepts and turning points of quadratic functions

9

6

I can represent an inequality graphically on a set of axes I can generate, plot, interpret and explore graphs of functions of the form y=x^n and recognise their characteristic shapes. I can generate, plot, interpret and explore graphs of functions of quadratic and cubic functions I can explore how quadratic graphs can be used to find approximate solutions to quadratic equations.

I understand how to solve an inequality by representing the solution sets as a region on a graph. I can solve linear inequalities and represent the solution graphically. I can interpret and analyse graphs arising from complex real life situations I am able to interpret the gradient in distance/time and speed/time graphs. I can use graphs to calculate measures including unit price, average speed, distance, time

8

5

I can expand and factorise single brackets I can simplify expressions with indices I can construct linear equations with unknowns on both sides and with brackets I can construct formulae for two step real life situations I can derive a formula (from mathematics or other subjects) and change its subject I can solve linear equations with fractional coefficients and unknowns on both sides

I can solve 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 equations. 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 I can apply efficient methods to solve a pair of simple simultaneous equations

7

4

I can recognise and use sequences of cube numbers, arithmetic progressions, Fibonacci type sequences, quadratic sequences I can interpret how the nth term for linear sequences work I can apply function notation and construct functions I 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 I can identify and interpret a gradient from an equation I can 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.

6

3

I can use the rules of Algebra to add, subtract, multiply and divide I can simplify expressions by collecting like terms I can expand single brackets I can construct expressions I can construct linear equations with and without simple single brackets I can substitute values into 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 or both sides. I can solve a linear equation I can solve a linear inequality which has an unknown on one or both sides. I can solve a linear inequality equation with and without brackets

5

2

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 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.

4

1

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

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

3

WT+

I can use the rules of Algebra to add, subtract, multiply and divide letters. I can simplify algebraic expressions by collecting like terms. I can expand single brackets I can construct algebraic expressions to represent problems. I can construct linear equations with unknowns on one side. I can define substitution and explain its application in algebra. I can substitute positive whole numbers into simple expressions with one or more unknown. I know standard mathematical formulae and can substitute values into them

I can solve linear equations with an unknown on one side and using integer values I can solve linear inequalities with an unknown on one side 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 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.

2

WT

1
