In Part 4 of this series, I will explore multiplying linear expressions and factorising quadratic expressions. Often in tests, these sorts of questions are put into ‘throw’ the students. Although there are mathematical conventions for writing expressions, students need to work with examples written in unconventional ways. In the above example, the variable has been written after the constant term. Another example with the variable on both sides One more example of solving a linear equation. A gallery walk is a great way to do this. Allow the students time to explain their methods to the class to discuss which method works ‘best’ and why. Same equation, different methodīy encouraging students to solve in more than one way, they can begin to discover which methods are more efficient. Here is the same equation solved in a different way. Solving a linear equation with the variable on both sides of the equals sign In the next few examples, I demonstrate how to use Algebra Tiles to solve linear equations with variables on both sides of the equals sign. Make sure you mix it up a little by not having the variables always on the same side of the equals sign! Linear equations with variables on both sides of the equals sign Solving a liner equation with negative values In this example, I have introduced negative values. When they put in tiles to make zero-sum pairs and then annotate that the reasoning behind the algorithm for solving equations becomes more apparent. This also allows them to see where the standard algorithms come from. Having a surface where students can easily erase errors will encourage them to ‘give it a go’, to try ideas that they are not confident with. I really like to annotate what I am doing as I work. ![]() Solving a simple linear equation using Algebra Tiles I have used conventional x rather than b. In the video below, I show how I would solve the above problem using Algebra Tiles. ![]() Once the problem is set up, you can begin to discuss how to solve the problem. In this case, the question would probably be: There is still no question being asked – ask the students what they think the question is. Here are some possible abstract representations: Maybe ask them to illustrate it using Algebra Tiles. Now you can ask the students how they could write this problem down. In the other basket, some apples are evenly divided into 3 bags and there are 5 loose apples. I now add in some numbers to the scenario: What has this added to the problem? what questions might the students have now? What might the problem be? In the other basket, some of the apples are in bags. In one of the baskets, the apples are loose. Then add a little more detail to the scenario: There is no problem yet, maybe ask the students what they think the problem might be. Each basket has the same number of apples.Īsk the students what they notice and wonder. This allows students to think about the problem before you introduce the numbers. In order to help students I would start with Numberless Word problems (see this link and the Padlet for examples). ![]() Students have to be comfortable with the notion that the variable an unknown amount. Using Algebra Tiles, and the zero-sum pair concept can help students understand why we ‘add/subtract the same from both sides’. One of the most common will be using a balance to demonstrate that both sides of an equation must remain the same (in balance) as you manipulate the variables and constants. There are several ways you can draw diagrams to illustrate this process and also different concrete materials you can use. ![]() In this post, I will look at how to use Algebra Tiles to solve Linear Equations.
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