Grade Band: 6-7

1. Grade Band: 6-7 Domain: Ratio and Proportional Reasoning

2. Why this domain is a priority for professional development • Grades 6 and 7-8 teachers are VERY different from one another. • Their preparation (in most states) is very different (namely grades 6 are elementary trained, and the 7th are actually 7-12 trained) • Proportional reasoning is a linchpin, a fundamental domain into many high school concepts

3. Why this domain is a priority for professional development • Language (technical and precision): • Translate between old to new (crosswalk) • teachers feel uncomfortable about the language as it is different • More challenging to get Ts to understand the language/terminology of the the new standards • Quality difference: • Problems/concepts in textbooks versus quality in standards and problems used to talk about the standards • Especially useful since tasks/problems are a good way to set the tone for what we mean about the topics

4. Key standards in this domain that pd should focus on • Understand “versus” Solve/Find • How can Ts be prepared to identify when understanding occurs (in say, formative assessment) • Keep the big picture in tact and not get bogged down in the minutia (conceptual vs. procedural) • Interconnectivity: • You really lose something integral if you isolate one component instead of all of them • Tie to past and future standards • Tasks matter • E.g. traditional textbooks do not have rich problems • “don’t cook the problem”

5. Key standards in this domain that pd should focus on • Consistency across grade levels • Conceptual understanding to be able to make decisions about what to focus on… • Graphically/symbolically representing R&P is new to 7th grade. • Modeling and Applications • Modeling is already intimately entwined with fractions as well as ratio/proportion • Scaling down to unit rate can lose the idea of scaling up. Flexibility • Extension to geometry • Context of unit rates

6. Existing resources that support these domains and standards • Multimodal representation (rule of 4 to ratio and proportion- can help enrich the understanding of the topic) • (video data) Leverage point: kids on video is very powerful. It busts teacher preconceptions • Intel Math- source for finding rich mathematical tasks

7. Existing resources that support these domains and standards • More Specific Resources: • NCTM focus on R&P (does a nice job putting this together, namely: ratio -> slope -> linear -> general linear) • Content courses aligned with standards incorporating student work • Essential understanding (NCTM) • CMP- Stretching and Shrinking • Examples of teachers enacting rich problem • Hard to teach hard to learn • Fractions and Ratios • Mark Driscoll (D.C.)- Habits of mind

8. Key ideas to keep in mind while considering what pd should focus on • Need to overcome: teachers make decisions about which Ss to incorporate as “those that will get it” versus “those that just never will”. It is our responsibility to establish that these concepts are attainable to all. We need to engage all of our kids. • Decisions about pace of the course [slowed down to focus on mechanics hang-ups which loses the big picture]