The afternoon mathematics session, “Bridging the Gap,” led by Jill Dinitz from Common Core Inc., was a great, powerful presentation on how to assess and remediate students’ prerequisite knowledge and conceptual understanding of key mathematical ideas and how to further develop their mathematical fluency. The remediation strategy presented was in three parts: assess, discuss, and repeat.

Jill introduced a great instructional tool that helps to assess where a student is in terms of their conceptual knowledge by having them create their own word problem to model a computational one.

**Example:** Write a problem that would require you to compute 12 divided by ½ to solve the problem.

Participants looked at how visual models like tape diagrams and arrays/area models can be used to help students transition from the concrete, pictorial to the abstract. They covered the four basic operations, focusing especially on division. How we ask the division question is important (i.e., twelve divided by ½ vs. how many ½’s are in twelve). The answer, “24,” jumps out in the second questioning technique.

Participants spent time going over various fractional situations that students encounter through grade 8. They did a very cool paper folding exercise that involved finding two shapes, each with an area of ½, but different shapes, utilizing one post-it note. Participants were highly motivated and involved, so one can just imagine the potential for the engagement in a classroom doing this exercise.

Participants also took a look at operations with negatives, which is another tricky area for students. Jill demonstrated how to prove that the product of two negatives is always positive through the use of mathematical properties, as well as through area models, both excellent instructional ideas.

The session ended with a presentation of a systems of equations problem found in pre-calculus. Due to timing, the session had to quickly end, but it would have held interest for a much longer time frame if allowed. Lots of great ideas were presented here this afternoon, and participants went home with excellent strategies to use in their districts/classrooms.

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