*By Ashli Black, Algebra 2 Lead*

Students need a chance at the beginning of the year to shake off the summer dust. Learn how IM’s curricular design builds in opportunities for review while starting the year with inviting, grade-level mathematics.

One of the things I love about the IM 6–8 Math curriculum and the forthcoming HS curriculum is that none of these courses start with review. While starting with a short unit of review was something I tried when I first started teaching, I later decided on a different route because the review time wasn’t helping my students in any way I could measure. If a student already had graphing and fractions and factoring down, how did the review help? If a student didn’t have those sorts of skills down, how could a single week or two be enough? And how long would the classroom status issues revealed during the review time last?

I eventually changed from review to giving a short quiz during the first week of class. This quiz always had two purposes: to introduce students to what my quizzes looked like and communicate to my classes how I interpret the results of a quiz. Question 1 was always to plot a few points on the coordinate plane. I never had a class get over 80% on the first go. Not even the precalculus classes. Does a result like that mean pausing to spend a day on graphing points?

The next day, after handing back the quizzes—ungraded, comments only—I would display the class average for that question. There was always at least one student who would shout out that they forgot what negatives were, or mixed up $x$ and $y$. Others would then murmur agreement or argue that their brains were still in summer. They would do better next time.

And they did. Always. One thing I know about myself is that it takes time to get back into a groove. The same was true for my students and their mathematical selves. I ask a straightforward question like “plot these points” and then have a discussion about the results to communicate to my students that I knew their brains were still a bit in summer mode and that I wasn’t going to expect they come into class right where they left off at the end of last year. The quiz gave me an opportunity to clearly make the point that review of a variety of skills would be built into our daily work. I also needed that quiz to remind me that the faces I was looking at were not the same as the students I’d last seen sitting in those chairs after a full year of instruction.

The results of that question on the quiz didn’t mean to stop everything and work on that skill, they meant that I needed to look for an opportunity within the grade-level work to highlight things to remember about graphing points. Each course in the IM curricula starts with a unit that has built in opportunities for students to shake off the summer dust and show who they are as mathematicians while keeping the focus on grade-level mathematics. In IM 6–8 Math, that meant a focus on geometry at the start of the year. In Algebra 1 it’s one-variable statistics. In Geometry it’s Constructions and Rigid Transformations. In Algebra 2 it’s Sequences and Functions.

In all of these courses, the first unit gives time to introduce students to the instructional routines they will use throughout the school year, in particular those they are likely less familiar with such as Info Gap Cards. Students have fewer preconceptions about their abilities (and those of their peers) when we focus on new ideas at the start of a year, so these units give an opportunity to set classroom norms for communication, collaboration, and making connections.

In the first unit of Algebra 2, attention was given to the fact that a student who has followed the “traditional” sequence of Algebra 1, Geometry, Algebra 2, may be out of practice with some key algebraic ideas. This unit takes a look at the familiar concepts of linear and exponential functions through the new lens of geometric and arithmetic sequences. The activities ask students to represent relationships using words, tables, graphs, and equations. They learn to define sequences recursively using function notation in a new way, giving contrast to how they have written equations for linear and exponential functions in the past.

As they build new skills while honing older ones, students also get to experience the beginnings of an important part of Algebra 2: modeling. In viewing the IM high school pacing guide, you may notice that Algebra 2 looks a bit shorter than the courses preceding it. This was purposeful to give space for teachers to make use of the modeling prompts that will be part of the course. Here in Unit 1, students address an aspect of mathematical modeling when they make the decision for what input value goes with the first term of the sequence. Often this boils down to choosing 0 or 1, which is highlighted in the task A Sierpinski Triangle. While this choice can appear trivial, making a decision and recognizing the consequences that decision has on different parts of the modeling process is necessary training for students if we want them to be powerful mathematical modelers. And while this is going on, students are plotting points on graphs and thinking critically about equations for linear and exponential functions, blowing summer dust away.

**Next Steps**

- Check out the Unit 1s for the high school courses (Algebra 1, Geometry, and Algebra 2). Where do you see embedded review in these lessons? Where could you build in review to your Unit 1 for the skill practice some students need more time on?
- Give your students an ungraded quiz on something you would expect them to get 100% on. What do you notice about the results?
- Check out the demo of IM 9-12 Math Algebra 1, Geometry, Algebra 2 which is now available on our website. To access the full curriculum, please see our IM
*Certified™*partner page. - See unit 1s for the high school courses. Where do you see embedded review in these lessons? Where could you build in review to your Unit 1 for the skill practice some students need more time on?
- Give your students an ungraded quiz on something you would expect them to get 100% on. What do you notice about the results?

##### Ashli Black

Ashli began teaching over 10 years ago in Washington State. In 2011 she was named Teacher of the Year at her school and earned her National Board Certification in mathematics the following fall. 2011 is also the year she began working for Illustrative Mathematics running social media and helping get more tasks published on the website. Ashli has presented at regional and national NCTM conferences on teacher collaboration, the Math-Twitter-Blogo-Sphere (MTBoS), and creating space in the classroom for students to surprise you. She is an alumna of the Park City Mathematics Institute (2010-2015) as both a participant and staff and has facilitated professional development across the US on middle grades mathematics and teacher professional collaboration. in 2015 she began working for Illustrative Mathematics full time on the 6-8 curriculum where she is the Grade 8 Lead.

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