GRADE BAND: 6-7
Domain: Ratio and Proportional Reasoning
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
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
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”

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

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
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

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]