1. The tasks follow 4 pathways identified on the CR Matrix.
This is a brief look at possible DOK tasks aligned to the Hess CR Math Matrix.
The tasks follow 4 pathways identified on the CR Matrix.
Pathway 1 includes: Knowledge at DOK-1 and Comprehension at DOK-1.
Pathway 2 includes: Application at DOK-1, Comprehension at DOK-2 and Application at DOK-2.
Pathway 3 includes: Analysis at DOK-1, Analysis at DOK-2, Comprehension at DOK-3, Application at DOK-3, Analysis at DOK-3 and Evaluation at DOK-3.
Pathway 4 includes: Synthesis at DOK-2, Synthesis at DOK-3, Comprehension at DOK-4, Application at DOK-4, Analysis at DOK-4, Evaluation at DOK-4 and Synthesis at DOK-4.

2. Hess Cognitive Rigor Math Matrix
Blooms 
DOK LEVEL 1
Recall and Reproduction
DOK LEVEL 2
Basic Skills and Concepts
DOK LEVEL 3
Strategic Thinking and Reasoning
DOK LEVEL 4
Extended Thinking
Remember
(Knowledge)
Retrieve knowledge from long-term memory, recognize, recall, locate, identify.
Knowledge/Remember
Ra. Recall, observe, & recognize facts, principles, properties
Rb. Recall/ identify conversions among representations or numbers (e.g., customary and metric measures
Understand
(Comprehend)
Construct meaning, clarify, paraphrase, represent, translate, illustrate, give examples, classify, categorize, summarize, generalize, infer a logical conclusion), predict, compare/contrast, match like ideas, explain, construct models.
Comprehend/Understand DOK1
Cc. Evaluate an expression
Cd. Locate points on a grid or number on number line
Ce. Solve a one-step problem
Cf. Represent math relationships in words, pictures, or symbols
Cg. Read, write, compare decimals in scientific notation
Comprehend/Understand DOK2
Cm. Specify and explain relationships
Cn. Make and record observations
Co. Explain steps followed
Cp. Summarize results or concepts
Cq. Make basic inferences or logical predictions from data/observations
Cr. Use models /diagrams to represent or explain mathematical concepts
Cs. Make and explain estimates
Comprehend/Understand DOK3 
CH. Use concepts to solve non-routine problems
CI. Explain, generalize, or connect ideas using supporting evidence
CJ. Make and justify conjectures
CK. Explain thinking when more than one response is possible
CL. Explain phenomena in terms of concepts
Comprehend/Understand DOK4
Cee. Relate mathematical or scientific concepts to other content areas, other domains, or other concepts
Cff. Develop generalizations of the results obtained and the strategies used (from investigation or readings) and apply them to new problem situations
Apply
Carry out or use a procedure in a given situation; carry out (apply to a familiar task), or use (apply) to an unfamiliar task.
Application DOK 1
APh. Follow simple procedures (recipe-type))
APi. Calculate, measure, apply a rule (e.g., rounding)
APj. Apply algorithm or formula (e.g., area, perimeter)
APk. Solve linear equations
APl. Make conversions among representations or numbers, or within and between customary and metric measures
Application DOK 2
APt. Select a procedure according to criteria and perform it
APu. Solve routine problem applying multiple concepts or decision points
APv. Retrieve information from a table, graph, or figure- use it solve a problem w’ multiple steps
APw. Translate between tables, graphs, words, and symbolic notations (e.g., graph data from a table)
APx. Construct models given criteria
Application DOK 3
APM. Design investigation for a specific purpose or research question
APN. Conduct a designed investigation
APO. Use concepts to solve non-routine problems
APP. Use & show reasoning, planning, and evidence
APQ. Translate between problem & symbolic notation when not a direct translation
Application DOK 4 
APgg. Select or devise approach among many alternatives to solve a problem
APhh. Conduct a project that specifies a problem, identifies solution paths, solves the problem, and reports results
Analyze
Break into constituent parts, determine how parts relate, differentiate between relevant-irrelevant, distinguish, focus, select, organize, outline, find coherence, deconstruct (e.g., for bias or point of view).
Analyze DOK 1
ANy. Retrieve information from a table or graph to answer a question
ANz. Identify whether specific information is contained in graphic representations (e.g., table, graph, T-chart, diagram)
ANA. Identify a pattern/trend
Analyze DOK 2
ANB. Categorize, classify materials, data, figures based on characteristics
ANC. Organize or order data
AND. Compare/ contrast figures or data
ANE. Select appropriate graph - organize data
ANF. Interpret data from a simple graph
ANG. Extend a pattern
Analyze DOK 3
ANR. Compare information within or across data sets or texts
ANS. Analyze and draw conclusions from data, ANT. Generalize a pattern
ANU. Interpret data from complex graph
ANV. Analyze similarities/differences between procedures or solutions
Analyze DOK 4
ANii. Analyze multiple sources of evidence
ANjj. Analyze complex/abstract themes
ANkk. Gather, analyze, and evaluate information
Evaluate
Make judgments based on criteria, check, detect inconsistencies or fallacies, judge, critique.
Evaluate DOK 3
EVW. Cite evidence and develop a logical argument for concepts or solutions
EVX. Describe, compare, and contrast solution methods
EVY. Verify reasonableness of results
Evaluate DOK 4
EVll. Gather, analyze, & evaluate information to draw conclusions
EVmm. Apply understanding in a novel way, provide argument or justification for the application
Create
(Synthesize)
Reorganize elements into new patterns/structures, generate, hypothesize, design, plan, produce.
Create/Synthesize DOK 1
SYZ. Brainstorm ideas, concepts, or perspectives related to a topic
Create/Synthesize DOK 2
SYaa. Generate conjectures or hypotheses based on observations or prior knowledge and experience
Create/Synthesize DOK 3
SYbb. Synthesize information within one data set, source, or text
SYcc. Formulate original problem in a situation
SYdd. Develop a scientific/mathematical model for a complex situation
Create/Synthesize DOK 4
SYnn. Synthesize information across multiple sources or texts
SYoo. Design a mathematical model to inform and solve a practical or abstract situation
Hess Cognitive Rigor Math Matrix

3. DOK1 Pathway K1 2 + 2 = 4 ADDING C1 DOK2 Pathway C2 AP1 AP2
= 4
Everything has a name.
What is this called?
Putting Together C1
Everything has a purpose.
What is adding?
DOK2 Pathway
2 + 1 = ___
AP1
Use the rule.
Everything has a rule
Sally has 4 apples in a bowl and 6 apples on the table.
Lupe has 6 apples in a bowl and 4 apples on the table.
2+1= 1+2=
Does the rule change?
What did change? C2
The rule is consistent
Use the rule to solve the problem in a new way.
Who has the most apples?
AP2
The rule guides use

4. DOK3 Pathway AN1 AN2 C3 AP3 AN3 EV3
Two students have different ideas about how to make an addition problem using these three numbers.
DOK3 Pathway
Julie:
Seven cows ate grass. More cows came out to eat grass too. Now there are 13.
Marcos:
I have 13 marbles. Can I share them equally?
Which is the sum?
AN1
Which are the addends?
4 + 5 = 9
Locate the Variables
Why are the addends smaller than the sum?
AN2
4 + 5 = 9
Relationship of Variables C3
Generalize a Concept
Who is right? Are they both right? Show it..
What can you generalize from your answer?
Sam wants to create a story problem using all of the numbers to count library books. What could he do?
Use words, pictures and labels.
AP3
Generalized Concept Guides Use
Justify your answer.
AN3
Organization of Variables
What did you do?
How did you do it?
Which set of numbers can either be addends or sums? Use all of the numbers.
EV3
Verify Reasonableness of Results
John says that the set of numbers
can be either addends or sums using all numbers.
Develop a mathematical argument. Use words, calculations or labeled diagrams to support your thinking.
Is John correct?

5. DOK4 Pathway SY2 SY3 C4 AP4 AN4 EV4 SY4 What can you predict?
I made 9 squares because 9 is the largest number.
Then I counted from 0 to 9 and that made a sum of 9. Now 9 can be an addend or a sum = 9!
Next I counted backward from the 9th square until I go to the number 5.
Then I counted how many squares were left. There were 4.
This showed that = 9.
Now I have used all 4 numbers.
0 + 9 = 9
4 + 5 = 9
Explain your strategy.
Based on my results I can predict or hypothesize.
What can you predict?
Which set did you choose?
I can predict that “If I can make a sum from two numbers in the set and make an addend from the sum and another number in the set, then I know I have the correct set to show that numbers can be either addends or sums.”
Add the smallest numbers together to see if they equaled the largest number.
Then, I took the sum and added it to the smaller numbers to see if it could also be an addend.
SY2
Generate a Hypothesis
Use another strategy to prove you were correct.
SY3
Prove your Hypothesis
I identified and classified variables.
I determined the factors and how to organize them. C4
Conceptualize the Strategy
How can you use your strategy another way? No
Identify and Classify the Variables
fish
bird
reptile
Hard Shelled Eggs
Soft Shelled Eggs
What steps do I take to organize them?
Yes
Determine Factors
How did 5 students solve the problem?
How did 5 students solve the problem?
How did 5 students solve the problem?
AP4
Devise a Way to Solve a Problem
Use your data as supporting evidence.
How did 5 students solve the problem?
What was the common factor in all 5 sources?
Variable
Factors from Sources
Animals
Hard Shelled Eggs
Survival Rate
Soft Shelled Eggs
reptiles 15
85% 20
60%
birds 12
80% 5
45%
fish 25
72% 11
35%
AN4
Find Coherence among Sources
Use a strategy to organize source information.
What impact do hard or soft shelled eggs contribute to an animal’s survival?
Explain why your analysis is correct.
Animals with hard shells have a higher survival rate.
EV4
Evaluate and Justify
How accurate is your analysis?
I will justify my conclusion using other variables.
I will draw a conclusion based on my data.
Did other variables contribute to survival rate?
SY4
Synthesize a New Perspective
How would you solve this problem?
What most impacted animal survival rate?
I will create a mathematical formula for increasing the survival rate of animals with soft shelled eggs.
All sources point to one consistent cause.

6. Keep Moving Forward!! 4 3 2 1
Susan Richmond 2014