This lesson is an overview of two days of class, each of which follow the same structure. Class starts with a review opener geared to help kids prepare for the final exam and reflect on what they've learned so far. That's followed by work time. Yesterday's lesson provides an overview and some examples of what the work time might look like. We'll continue with lessons structured just like this for most (but not all!) remaining lessons.
Today's opener takes us back to our work with number lines at the beginning of the year. Students create a "perfectly-scaled number line" and place nine numbers in different representations on it. The first step is to decide where the number line begins and ends. I circulate to check in with kids and coach them to make thoughtful decisions first. "What is the lowest number you see here?" I ask. "Which one is the greatest?" I encourage everyone to check each other's work, which leads to important conversations.
When we finish, often by committee with different students contributing to a solution on the front board, I post the second slide, which says that we just reviewed SLT 1.2, and that anyone who wants extra practice should check in with me.
The next opener is about using algebra to check whether or not a point is on a line. I leave the first slide up for the first five minutes of class. I do not offer help to students. I circulate to take a peek at how everyone is doing, and I encourage students to help each other and discuss the work. When five minutes are up, I skip to the second slide, which gives the solutions. For most students, this is a confidence builder that confirms for them that they know what they're doing. I applaud these students and point out that their hard work is paying off. Some students will still have some clarifying questions, and I'll target these kids with appropriate exercises.
Additional Review Task
On the third slide is a related task that provides a linear equation in two variables and a set of points where only the y-coordinate is given (see the CME Algebra 1 textbook, page 263). I think this is a great task for a review session like this. Students must apply their knowledge of algebraic substitution and the use of variables. For some kids, it's a reinforcement of the still-tenuous idea that a point consists of an x value followed by a y value. There's signed arithmetic and fraction arithmetic, as well as some tricky algebraic manipulation, with all those negative numbers.
Additionally, there's a self-check built into this task. After students find all six values of h, I tell them to plot their six points on the coordinate plane. If they're right about all six, then the points should make a straight line! Sometimes this happens, which leads to a nice conversation about the properties of linear functions, and makes it clear that there are some errors in need of correction.
Finally, I may ask students to rewrite the equation in slope-intercept form, and then to graph that line to ensure that it passes through the points on their graph.
During some of these review lessons, the opener and review task might take a while for some students. I've seen kids take the entire period to finish the pair. If that happens, it's fine - it's exactly what they need. It's important to develop a sense of urgency, but not to rush students into anything. If they're grappling with a task, then it's worth it to let that happen.
The purpose of yesterday's lesson was to set up the kind of work that will continue to happen for the remainder of the year. Each day, I'll post a different review opener as students arrive, and I've shared the next two above.
Following the opener, students will get back to work. Sometimes, the opener will help kids clarify what they need to work on next, and other times they'll be so invested in their current work that they'll just want to get started. Please take a look at yesterday's lesson to see how I structure my classroom, and for some of the assignments that are available.
Here is another example of what the front board looks like after a class like this. I'll teach any mini-lesson that's necessary, but only when students make it clear that it's what they need. The day I took this picture, for example, I'd just spent some of my time helping kids clarify what it means if 6 inches of fence cost $8 (see the back of SLT 1.3 BBK), while helping other students finish some work on completing the square to solve a quadratic equation.