These notes represent one approach to introduce solving equations. I would typically teach this to year 8 students, who have previously studied fractions, decimals, and negatives. Discussion of these problems and their strategies will often yield the following; trial and improvement, collecting terms, cancelling from both sides, and checking solutions by substitution. Things I emphasise are correct use of equals sign, equations as statements of equality, and solutions as values of variables that make statements true. I also think this approach sets up algebra as a construct for solving problems. The lesson numbers are only to give a sense of possible timings, this is not intended to be prescriptive in anyway.
The problem below is posed with no explanation, this works well displayed with students working on whiteboards so they can change values easily. I have found many students will complete with different values in the boxes, I will then pose it as a challenge to complete using same number in each empty box.
Students are encouraged to articulate their thoughts at this stage, prior to group discussion. Whilst facilitating this discussion I would be aiming to attention towards; the meaning of equals sign, the process of checking solutions, and the definition of a solution.
Students work through the following tasks, interspersed with discussions and opportunities for students to write reflections. Again I emphasise are correct use of equals sign, equations as statements of equality, and solutions as values of variables that make statements true. During this lesson I circulate providing extension, this is often in the form of posing problems to introduce another concept (such as fractions, negative coefficients, indices) and support, often by drawing attention to method in previous questions. I will have resources for all lessons printed so students can move on at different paces.
Discussion following these needs to include why boxes are ambiguous (may represent different values), hence use of letter where same letter means same value within a question.
Collecting of terms made explicit at this stage to students.
Mixed questions, often used as self assessment for students, also aids in making the previous links more explicit.
Practice at this stage will be a mixture of students generating questions, questions provided, and students explaining their thinking.
Tasks that encourage students to form equation. Although many students will be able to solve some of these without forming an equation, I ask students to do so.
Here is flipchart for these.