Blogs about Algebra

Blogs about Algebra

Solving Two Step Equations using the Balance Method

An equation is when one expression, or term, is equal to another.  To solve an equation means to find the value of the variable (represented by a letter) that makes the two expressions equal.  There are two types of equations for secondary school mathematics, linear and none-linear.  In this blog I write about how I […]

Plotting Quadratic Graphs on Cartesian Axes

In recent examiner reports it is noted how important it is for students to understand the properties of a parabola  when plotting quadratic graphs on Cartesian axes.  Students who have a secure understanding of parabolas can use them to correct miscalculated values in their table of results and are more likely to attain full marks […]

Equation of Straight Line Graphs

To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis.  Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they […]

Arithmetic and Geometric Sequences

Students learn how to generate and describe arithmetic and geometric sequences on a  position-to-term basis.  Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term. This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs. Arithmetic […]

Proving Geometrical Relationships using Algebra

Back in May 2017 maths teachers around the country eagerly awaited the first exam for the new GCSE Mathematics syllabus.  Proving geometrical relationships using algebra featured at grade 9.  In Paper 1 of Edexcel’s test paper the last question of the higher tier looked like this. Edexcel wrote about student’s performance on this question in […]

Factorising algebraic expressions with powers

When factorising algebraic expressions with powers students often struggle to identify the highest common factor when it involves an algebraic term. For example, factorising 3h + 12 as 3(h + 4) is attempted correctly much more often than factorising 3h2 + 12h as 3h(h + 4). In this lesson students learn how to identify the […]

Extending transformations beyond shapes on a grid

While I was teaching a higher GCSE class about  Reflections, Rotations and Translations  I wanted to explore extending transformations beyond shapes on a grid to include transforming straight line graphs. About forty minutes into the lesson on reflections the majority of the students were quietly working their way through the activities.  The class were well […]

nth term of a geometric sequence

GCSE foundation and higher maths students are now expected to find the nth term of a geometric sequence. When I teach the nth term of geometric sequences I ask the class to work in pairs to categorise a range of sequences into two groups and present their solutions on mini-whiteboards. The students can decide what the […]

Simultaneous Equations through Elimination

Being able to solve a pair of simultaneous equations through elimination is a key topic for GCSE students.   With the new criteria focusing more on problem solving and application of knowledge it is much less obvious for students when simultaneous equations is being assessed. It’s important students are exposed to the types of questions they […]

Teaching Algebraic Notation

There is thought amongst students that teaching algebraic notation involves the students haveing to memorise a set of abstract rules unique to the topic and separate from the rules of arithmetic.  If, on the rare occasion they see the two overlap this is simply by coincidence. My ambition when first introducing algebraic notation to students […]