I pretty-much taught math the way that I did back when I taught a higher-level eighth grade class:
- I front-loaded the vocabulary using a TPR for variable, equation, graph, table and linear relationships. They used social media to discuss things in life that have linear relationships.
- I gave the students a scenario: They had to raise money for a field trip by selling junk food at a school dance. They did quick research on the cost of bags and decided how many they would buy and how much they needed to raise.
- They worked in partners to determine a variable.
- They solved it however they wanted: pictures, tables, multiplying, dividing, estimating, etc. Although the district discourages us to do this, I let them use calculators. I didn't want computation to be a distractor.
- After solving it, they looked at the correct answer and checked if they had it right. Many of them modified their approaches and wrote a shared "common mistakes" document together as a class on Google Drive
- Different pairs compared and contrasted their approaches to the answer algebraically, in graphs, in tables, through repeat addition, etc. In this phase, they also were asked to "prove" their answers using other methods.
- They created their own word problems, graphed the answers (using online graphing), created tables, solved it algebraically and wrote reflections based upon a menu of questions that included the efficiency of methods, the relationships between approaches and how they solved it themselves.