Translating a line

I will never forget one of my students telling me after a district exam, "One of the questions asked me to translate a line - what does that mean, write it in Spanish?" I thought I had done just a great job on the linear functions unit, but I had totally missed connecting the idea of translations for them. I had always waited until quadratic functions to talk about shifts in the parent function as transformations, but when I looked into the standards I realized I was missing a key part of linear functions. CCSS.MATH.CONTENT.HSF.BF.B.3: Identify the effect on the graph of replacing f(x) with f(x)+ k, … for specific values of k (both positive and negative); find the value of k given the graphs. 

So I created some doodle notes that compare various graphs to the parent function. Each graph already had y = x graphed, so seeing the transformation is easier. 

The standard specifically addresses translations, but I also wanted students to see that changing the slope is actually a dilation and making it negative is a reflection. 

After finishing the notes, we completed a dominoes activity to practice translations. I love these dominoes because they have an answer bank to work from. They start with the line y = x and perform the vertical translations up or down. Students match the graph and then perform the next translation.

For extra practice I had them write the equation of each line, again reinforcing the idea that the constant is the only thing changing in the equation. 

Both sheets made up a two-page spread in our interactive notebooks. 

I wrapped things up with this "Try It" question too. I know that before this lesson, my students would have had no idea how to even tackle it, but they were so confident in their answers. With any luck, when they see questions about "translating" on the next test, it will no longer think of a foreign language.