Lesson title | Description (objectives) | Lesson Worksheet | Calculator required | Problem Solving Questions | Problem Solving Worksheet |
---|---|---|---|---|---|
Solving quadratic inequalities | To be able plot inequalities on a graph, by plotting quadratic graphs. Extending to re-arranging inequality in form $ax^2 + bx + c > 0$ | ![]() | ![]() | ||
Solve inequalities with one or two variables | To be able solve inequalities. Beginning with 1 step equations, then 2 step equations, followed by double inequalities. Extending to using negative numbers. | ![]() | ![]() | ||
Solving quadratic equations by factorising | To be able solving simple quadratic equations by factorising into 2 brackets (coefficients of x is always 1). Extending to re-arranging equation to form $x^2 + bx + c = 0$ first. | ![]() | ![]() | ||
Expression, Equation, Identity and Formula | To be able to identify expressions, equations, formulaes and identities | ||||
Solving quadratic equations by using the formula | To be able to accurately use the quadratic formula to solve equations | ![]() | ![]() | ![]() | |
Simplifying Expressions | To be able to add and subtract terms with common unknowns, and to be also able to multiply out simple terms . | ![]() | ![]() | ||
Use Trial and Improvement to find approximate solutions of equations | To be able to apply trial and improvement method to find solution to specified decimal placing, starting with 1dp moving to 2dp, extending to 3dp. | ![]() | |||
Parallel and perpendicular lines | To be able to calculate perpendicular gradient, given just gradient (using $m_1$x $m_2$ = -1), leading onto finding equations of perpendicular lines to given a linear equation on the point of intersection, then finding equations of perpendicular or parallel lines | ![]() | ![]() | ||
Change the subject of a Formula | To be able to change the subject of the formula by re-arranging, leading onto working with powers and then re-arranging formulas with unknowns on both sides. | ![]() | ![]() | ||
Factorising using difference of two squares | To be able to factorise expressions using the difference of 2 squares | ![]() | ![]() | ||
Find the equation of a straight line from gradient and co-ordinates | To be able to find the equation of a line initially given a gradient and a co-ordinate, leading onto finding the equation from 2 co-ordinates, not given the gradient. | ![]() | ![]() | ||
Find the gradient of a straight line graph from 2 points | To be able to find the gradient of a line given 2 co-ordinates, extending to 2 co-ordinates which involve negative numbers | ![]() | ![]() | ||
Find the gradient of a curve and area under a curve | - To be able to calculate the gradient of a curve at a point - To be able to calculate the average gradient of a curve - To be able to calculate an estimate of the area under a curve | ![]() | |||
Find the mid-point and length of a line | To be able to find the midpoint of a line from a drawn line, extending to finding midpoint between 2 co-ordinates. To also be able to calculate the length of a line from a drawn line, leading onto between 2 co-ordinates. | ![]() | ![]() | ![]() | |
Understand and plot points in four quadrants | To be able to plot co-ordinates in different quadrants, leading to any quadrant, followed by reading co-ordinates in all quadrants. | ![]() | ![]() | ![]() | |
Geometric sequence (Common Ratio) | To be able to identify a common ratio of a sequnece, followed by being able to find a term given first number and common ratio. | ![]() | ![]() | ||
Co-ordinates in one quadrant | To be able to plot co-ordinates in the 1st quadrant, followed by reading co-ordinates in the 1st quadrant | ![]() | ![]() | ![]() | |
Solving quadratic equations by completing the square | To be able to complete the square with co-efficients of $x^2$ as 1, extending to completing the square where the co-efficient of x is not 1 | ![]() | ![]() | ||
Completing the square of quadratic expressions | To be able to re-arrange equations by completing the square, leading onto equations which have co-efficients of x, and extending to re-arranging equation to form $x^2 + bx + c = 0$ first. | ![]() | ![]() | ||
Solve equations that include brackets | To be able to solve equations which contain brackets. Expanding brackets prior to re-arranging and solving. | ![]() | ![]() | ||
Solve equations that include powers | To be able to solve equations which containing powers - a short lesson (used as an add ont) | ||||
Working with Algebraic Fractions | To be able to add and subtract algebraic fractions, moving onto simplifying - followed by multiplying and dividing | ![]() | ![]() | ||
Solving Fractional equations | To be able to solve equations which involve algebraic fractions with more than one unknown. | ![]() | ![]() | ||
Solve equations with unknown on both sides including negative numbers | To be able to solve multiple step equations with unknowns on both sides, with differing order of operations. | ![]() | ![]() | ||
Re-arranging & solving simple one step equations | To be able to solve simple one step equations split between adding & subtracting, dividing and multiplying with a fraction. | ![]() | ![]() | ||
Solve two step equations with unknown on one side and involving fractions | To be able to solve simple two step equations, with differing order of operations. | ![]() | ![]() | ||
Use elimination or substitution to solve simultaneous equations | To be able to solve simultaneous equations by elimination or subsitution. Solve by adding or subtracting, extending to having to multiply one or both equations. | ![]() | ![]() | ||
Using number sequences & describe a rule of a sequence | To be able to spot the linear sequence, the term to term rule and find then create a sequence knowing a specific rule. | ![]() | ![]() | ||
Substitute Numbers into Formula | To be able to substiute numbers into increasingly challenging formulas. | ![]() | ![]() | ||
Substitute Numbers into Expressions | To be able to substiute numbers into increasingly challenging expressions, including mixed variables and extending to negatives | ![]() | ![]() | ||
Find & Use the nth term expression for a sequence | To be able to use linear nth terns to find a specific term in a sequence and then to be able to find the nth term of written linear number sequences. | ![]() | ![]() | ||
Find the nth term expression for a quadratic sequence | To be able to use quadratic nth terms to find a specific term in a sequence and then to be able to find the quadratic nth term of a written quadratic number sequences. | ![]() | ![]() | ||
Circle equations in the form x² + y² = r² | To be able to work out equation of a circle given it's radius and centre, leading onto being able to find equation of a tangent given centre and co-ordinate on a circle. | ![]() | ![]() | ||
Forming Expressions, Equations or Formula | To be write or derive expressions, equations, formulaes and identities from given information. | ||||
Iteration | To be able to use iteration to find roots of equations | ![]() | ![]() | ![]() | |
Quadratic Simultaneous Equations | To be able to solve simultaneous equations, where one equation is a a quadratic, and the other is linear. | ![]() | ![]() | ||
Turning Points | To be able to find the turning point of a quadratic equation / function | ![]() | ![]() | ||
Triple Brackets | To be able to expand triple brackets - with varying degrees of difficulty | ![]() | ![]() | ||
Finding the Equation of a Line | To be able to find the y-intercept, the gradient 'm' followed by the whole equation of a line | ![]() | ![]() | ![]() | |
Quadratic Graphs | To be able to plot quadratic graphs, find the solution from quadratic graphs - leading onto solving simultaneous equations involving a quadratic graph | Graph Paper Required | |||
Factorising Linear Expressions | To be able to factorise expressions, starting from integer factors, then algebraic factors leading onto combined factors | ![]() | ![]() | ||
Expanding Single Brackets | To be able to expand and simply brackets, starting with 1 bracket moving onto 2 brackets | ![]() | ![]() | ||
Expanding Double Brackets | To be able to expand double brackets using either grid method or combination method. Questions extending to brackets with coefficients of x | ![]() | ![]() | ||
Factorsing Quadratics into 2 Brackets | To be able to factorise quadratics, starting with $x^2$ moving onto quadratics with coefficient of x more than one. | ![]() | ![]() | ||
Drawing Straight Line Graphs | To be able to draw straight line graphs using a table or otherwise, extending to solving simultaneous equations by drawing graphs | ![]() | |||
Exponential Growth and Decay | - To be able To plot exponential growth and decay graphs | ![]() | ![]() | ![]() | |
Function Machines | - To be able To find the output of a function machine - To be able To find the input of a function machine - To be able To find the missing rule of a function machine | ![]() | ![]() | ||
Proofs | - To be able To use algebra To prove a statement | ![]() | ![]() | ||
Functions (including Composite & Inverse) | - To be able To understand and use function notation - To be able To find composite functions - To be able To find inverse functions | ![]() | ![]() | ||
Double Function Machines | - To be able To find the output of a double function machine - To be able To find the input of a double function machine - To be able To find the missing rule of a double function machine | ![]() | ![]() | ||
Inequalities on a graph | - To be able to represent inequalities and it's regions on a graph | ![]() | ![]() | ![]() | |
Inequality notation | - To understand inequality notation - To be able to list integers that satisfy inequalities | ||||
Inequalities on a Number Line | - To be able to plot a simple inequalities on a number line - To be able to plot more complex inequalities on a number line | ![]() | ![]() |