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:
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 […]
When learning how to simplify surds students need to understand the difference between a rational and irrational number. Rational numbers include integers and terminating and repeating decimals. They can be written as a fraction with both the numerator and denominator as integers. An irrational number is a number which, in its decimal form does not […]
There are three common methods for sharing an amount to a given ratio. Depending on the age group and ability range I am teaching I would choose one approach over the other two. The three methods are: Using fractions Unitary method Using a table In this blog I will demonstrate each of the three methods […]