# Algebra Lessons

Lesson titleDescription (objectives)Lesson WorksheetCalculator requiredProblem Solving QuestionsProblem Solving Worksheet
Solving quadratic inequalitiesTo 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 factorisingTo 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 FormulaTo be able to identify expressions, equations, formulaes and identities
Solving quadratic equations by using the formulaTo be able to accurately use the quadratic formula to solve equations
Simplifying ExpressionsTo 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 equationsTo 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 linesTo 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 FormulaTo 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 squaresTo be able to factorise expressions using the difference of 2 squares
Find the equation of a straight line from gradient and co-ordinatesTo 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 pointsTo 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 lineTo 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.
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.
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 bracketsTo be able to solve equations which contain brackets. Expanding brackets prior to re-arranging and solving.
Solve equations that include powersTo be able to solve equations which containing powers - a short lesson (used as an add ont)
Working with Algebraic FractionsTo be able to add and subtract algebraic fractions, moving onto simplifying - followed by multiplying and dividing
Solving Fractional equationsTo be able to solve equations which involve algebraic fractions with more than one unknown.
Solve equations with unknown on both sides including negative numbersTo be able to solve multiple step equations with unknowns on both sides, with differing order of operations.
Re-arranging & solving simple one step equationsTo 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 fractionsTo be able to solve simple two step equations, with differing order of operations.
Use elimination or substitution to solve simultaneous equationsTo 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 xÂ² + yÂ² = rÂ² 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 FormulaTo be write or derive expressions, equations, formulaes and identities from given information.
IterationTo be able to use iteration to find roots of equations
Quadratic Simultaneous EquationsTo be able to solve simultaneous equations, where one equation is a a quadratic, and the other is linear.
Turning PointsTo be able to find the turning point of a quadratic equation / function
Triple BracketsTo be able to expand triple brackets - with varying degrees of difficulty
Finding the Equation of a LineTo be able to find the y-intercept, the gradient 'm' followed by the whole equation of a line
Required
Factorising Linear ExpressionsTo be able to factorise expressions, starting from integer factors, then algebraic factors leading onto combined factors
Expanding Single BracketsTo be able to expand and simply brackets, starting with 1 bracket moving onto 2 brackets
Expanding Double BracketsTo 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 BracketsTo be able to factorise quadratics, starting with $x^2$ moving onto quadratics with coefficient of x more than one.
Drawing Straight Line GraphsTo 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