Unit Planning - What Matters
I think the most important element of the unit plan is the big idea, right? What’s the Big Idea? In math, it means a function that is squared. In the real world, it means something that is represented by a parabolic shape, whether that’s the projectile of an object or maximizing or minimizing something like an area or finances. Each lesson needs to be a building block that supports the big idea, creating connections to applications and various forms of representations. Within the study of quadratics, students are learning mathematical vocabulary, such as vertex, domain and range. They learn how these mathematical elements relate to the situations that they represent, and by understanding those parameters, they can then develop values that are realistic to the presented situation. When determining the optimal price for a product, the range of prices must be inline. For example, if determining the optimal price for a song download, no one’s going to pay $100 for a song. That $100 may be appropriate for the cost of shoes though. This sort of reasoning is what requires students to be critical thinkers. It is also an opportunity for teachers to make connections with student’s lives, when choosing a particular scenario to study.
What’s great about this unit is that it brings together learning from previous math lessons, both in this school year and previous ones. Students have to remember the distributive property. They have to remember multiplication pairs. Having strong skills in these areas will prove useful as students develop new skills in working with quadratics. Homework problems present these ideas in a variety of ways, including seeing patterns of squares in series, formatting graphics in quadrants so that students can see how multiplying and adding the same pairs result in a trinomial form, presenting factored form and quadratic form, etc. In my student teaching experience in middle school, I saw that students struggled with their math facts. With quadratics, those same struggles with be present. My CT and I have discussed creating a large multiplication chart for the classroom, so that students can be reminded of not just pairs that work within quadratics, but also the results of common x2, such as 22 = 4, 32 = 9, 42 = 16, 52 = 25, 62 = 36, 72 = 49, etc.
I noticed in comparing the unit goals / learning targets with the Hess matrix, that most (57%) of the goals fell into the lower third of the matrix. Perhaps that is typical of all units? Connecting specific unit goals to my student’s Context for Learning may be more challenging, but certainly connecting the real-world situations that these quadratics equations and expressions represent can be more readily achieved in each lesson within the unit. My students are interested in social media, their friends, sports, shoes, cars, Starbucks, acrylic nails, music, movies, etc. Making connections to those areas of interest, may grab their attention and motivate them to understand the underlying math, more fruitfully than a more arbitrary scenario.