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 introduce solving two step equations using the balance method.
The start of the lesson recaps solving one step equations. At this stage it is important students understand y/3 means y divided by 3 and 7y means 7 multiplied by y. Next, we discuss inverse operations, i.e., the opposite of dividing by 3 is multiplying by 3 and the opposite of multiplying by 7 is dividing by 7. I will often use function machines to demonstrate this.
When solving two step equations using the balance method we arrange the terms, so the unknown is on one side of the scale and the numbers on the other. Using scales as part of the working helps students to see how the equation remains balanced throughout this process. Function machines help students identify the individual operations but, in my opinion, lack the perception of balance.
The terms move according to the inverse of the order of operations. For instance, with 6x + 2 = 26, the addition of 2 is moved to the other side before the multiplication of 6. The equation remains balanced by doing the same operation to both sides of the scale (or equals sign).
As we progress through the lesson I consolidate and extend the learning by increasing the level of challenge. I do this by:
These mini-extensions all help to develop student’s algebraic fluency.
In the plenary students match the equation to its solution. This involves attempting a variety of questions across the ability range. This activity takes about 10 minutes with students working independently on mini-whiteboards. I assess student’s progress against these differentiated learning objectives:
In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]
Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]
Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]