Core Academy Level 1 Day 2
Cognitive Demand and Problem Based Learning
8:30 – 10:00
10:00 – 10:30
Activity (part 1)
 Take a couple of minutes to write your personal definition of “going deeper” as it relates to
 Our focus for today is looking at the concept of cognitive rigor.
 We are going to examine some questions and think of a solution paths, these are questions that you
may see on a test, or that you have written for a test.
 Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the
 What makes them easy for you or more difficult?
 First group of questions – These are examples of fluency types of questions, they lend themselves to
strategies for speed and accuracy
Discussion Points
 Easily solved with an understanding of basic math facts, count by 5’s, time on a clock, flashing 5 on
their fingers
 Understanding of equal groups – 8 x 9 is 9 groups of 8, 80 is 10 groups of 8, and you subtract one
group of 8, making it 9 groups of 8
 Understanding that 49 is 7 groups of 7 and 56 is 8 groups of 7, understand repeated addition or
subtraction to solve multiplication and/or division
 This conceptual understanding makes the fluency faster in all 3 examples
 Relate to Concrete-Representation-Abstract instruction model
Connections to Make
 Relate to Blooms Taxonomy/Hess Cognitive Demand Matrix (Hand out Matrix)
 Have participants place the problems on the matrix
 Connection to Core – which standards by grade ask for fluency? Examine critical areas of different
grade levels.
 What does mastery look like at each grade level
Core Academy 2014
Materials Needed
 Power point
 Hand out with
different types of
questions or include
in power point
 See Appendix for
 Blooms
Cognitive Demand
Activity (part 2)
 Show second set of problems
 Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the
Discussion Points
 Mental math strategy is embedded with the +1
 You would need to compensate (take 1 away from 35) to compute mentally
 (1000 x 200) + (1 x 20) [distributive property, you distributed the 20]
Connections to make
 Connect that the 3 points for discussion above are instructional strategies that can be used in your
classroom to lead to better conceptual understanding and fluency. Different strategies will make
these a different cognitive level.
 Have participants place these problems on the matrix
Activity (part 3)
 Show third set of problems – these are examples of conceptual understanding types of questions,
how and why math works
 Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the
Discussion Points
 Can you use drawings to show combining groups
 2/1; 4/2…..
 Importance of a number line, useful for comparing denominators, differentiation – use a ruler to
help guide students
12:00 – 12:45
12:45 – 2:15
Activity (part 4)
 Show fourth set of problems – these are examples of application types of problems
 Let’s look and discuss (in your groups) what do you notice about the different difficulty levels of the
Discussion Points
 Missing addend problems changes the difficulty of the problem, it is also a fraction problem, which
doesn’t lend itself to always an increase in cognitive demand.
Core Academy 2014
 Second set of
 Third Set of
 Fourth Set of
 Multi-step problem, with multiple entry points. Lends itself to a drawing or algorithm, multiple
solution paths, and opportunities for student explanation. Good discussion for order of operation at
any grade level (work with manipulative, draw a picture, write an equation)
 Critical thinking problem. Opportunity for proving and justifying answer/solution path. Good
problem for generalization. Also good problem for discussion of potential misconceptions and
 SAGE and Depth of Knowledge. What do the DOK levels mean?
Connections to make
 Important to have all, but also to know when to use which level
 How to change any problem from textbook from one level to another
 Creative doesn’t mean a greater depth of knowledge
 What existing curriculum or assessment materials could you re-examine to increase the range of
cognitive rigor?
 What gaps will need to be filled?
 Revisit your definition of Rigor- has it changed?
 Assessing only at the highest DOK level will miss opportunities to know what students do & don’t
know – go for a range; end “high” in selected/prioritized content
 Performance assessments can offer varying levels of DOK embedded in larger, more complex tasks
 Planned formative assessment strategies and tools can focus on differing DOK levels (Karen Hess)
Activity (Practice Standards)
 Review Practice Standards with participants
2:15 – 3:15
 Core Standards from
Day 1
 Chart Paper
Activity – Depth of Knowledge Articles
 Read articles and discuss, use Chalk Talk Protocol
Activity – Textbook
 Participants will go through one unit in their textbook and count how many of each level they find.
Where is it strong? Where is it weak?
 Complete template
End of Day 2
 Write what you learned about, an ah-ha moment, something you want to do differently, etc. using
the vocabulary words: Cognitive Rigor and Depth of Knowledge, each of the four levels
Core Academy 2014
 Journal
 DOK Wheel
 DOK article
 Chalk Talk Protocol
 Template
 Reflection Questions
Core Academy 2014