Depth of Knowledge (DOK) I, II, III, and IV High School Examples with Shared Context

The following is a high school example of the MathBits article from Sept. 30, 2018.

The following examples were compiled to demonstrate one way depth of knowledge (DOK) levels I, II, and III may be displayed in a test item (question). Along with each example, a rationale table (reasons why a student may select a particular answer) and the reasoning for the DOK alignment are provided. A DOK IV example is also provided even though DOK IV items/activities are not a part of the Minnesota Comprehensive Assessment (MCA).

The DOK III example was a part of the Optional Local Purpose Assessment (OLPA). The other three items (DOK I, II, and IV examples) were created for this document and not used on any Minnesota Department of Education (MDE) assessment. However, there are released MCA math items (43 new items uploaded on November 15th, 2018) with DOK designations on MDE’s website.

REMINDER: DOK IV items/activities are not a part of the MCA.

DOK I Example

Benchmark: 9.2.4.5 Solve linear programming problems in two variables using graphical methods.

Item Specifications

• Vocabulary allowed in items: constraint, boundary, feasible region and vocabulary given at previous grades

A farmer plants x apricot trees and y pear trees. He plants at most 21 apricot or pear trees on his land. Apricot trees cost $25 each and pear trees cost $30 each. The farmer wanted to spend no more than $600. The inequalities shown represent this situation.

 

x > 0

y > 0

x + y ≤ 21

25x + 30y ≤ 600

The intersection of which two equations describes both the greatest number of apricot trees and the greatest number of pear trees the farmer can plant?

 

A.	x + y = 21 and x = 0
B.	25x + 30y = 600 and y = 0
C.	25x + 30y = 600 and x = 0
D.	x + y = 21 and 25x + 30y = 600

 

RATIONALE A	Choose a pair that looks to maximize the number of pear trees
RATIONALE B	Choose a pair that looks to maximize the number of apricot trees based on price.
RATIONALE C	Choose a pair that looks to maximize the number of pear trees based on price.
RATIONALE D	Correct. Choose a pair that maximizes the number of both trees based on cost.

Reasoning: This is an example of a DOK I item as the student is asked to identify which two equations from a given list without justification.

Note: In full disclosure, it could be “argued” that this is example is actually DOK II due to interpreting the situation in order to select the two inequalities. DOK levels are not always nice clearly defined boxes.

DOK II Example

Benchmark: 9.2.4.5 Solve linear programming problems in two variables using graphical methods.

A farmer had enough land to plant at most 21 fruit trees. Apricot trees cost $25 each and pear trees cost $30 each. The farmer wanted to spend no more than $600. Let x represent the number of apricot trees and
y represent the number of pear trees the farmer could purchase. On the graph, draw the feasible region for the constraints of this situation.

Reasoning: This is an example of a DOK II item because the student is asked to demonstrate graphing a feasible region for a real world situation. The student is required to recall the definition of a feasible region, and then translate the information given into a display of the feasible region for the situation.

DOK III Example

Benchmark: 9.2.4.5 Solve linear programming problems in two variables using graphical methods.

A farmer had enough land to plant at most 21 fruit trees. Apricot trees cost $25 each and pear trees cost $30 each. The farmer wanted to spend no more than $600. Let x represent the number of apricot trees and y represent the number of pear trees the farmer could purchase. Which points are on the boundary of the feasible region for this situation?

Select the points you want to choose.

A. (0, 0) B. (0, 20)

C. (0, 21) D. (5, 12)

E. (6, 15) F. (14, 10)

G. (21, 0) H. (24, 0)

 

RATIONALE A	Correct. Since both constraints are shaded below the lines x + y = 21 and 25x + 30y = 600, the point is on the boundary of the feasible region.
RATIONALE B	Correct. Since both constraints are shaded below the lines x + y = 21 and 25x + 30y = 600, the point is on the boundary of the feasible region.
RATIONALE C	Shaded the constraints in the incorrect direction or confused the largest x- and y-intercept values as being in the feasible region.
RATIONALE D	Chose a point in the interior of the feasible region.
RATIONALE E	Correct. Since both constraints are shaded below the lines x + y = 21 and 25x + 30y = 600, the point is on the boundary of the feasible region.
RATIONALE F	Chose a point outside the feasible region.
RATIONALE G	Correct. Since both constraints are shaded below the lines x + y = 21 and 25x + 30y = 600, the point is on the boundary of the feasible region.
RATIONALE H	Shaded the constraints in the incorrect direction or confused the largest x– and y-intercept values as being in the feasible region.

Reasoning: This is an example of a DOK III item because the student is not given any structure on how to go about solving and must determine the 4 equations and use them to figure out the boundaries and it is not a likely to be something the student has encountered before. The cognitive demands are more complex and abstract than DOK II.

DOK IV Example (not used on the MCA)

Benchmark: 9.2.4.5 Solve linear programming problems in two variables using graphical methods.

Task Description:

The student will research, analyze, and design an orchard on one acre of land to be used for fruit tree production. The maximum amount the student can spend is $1,000 on buying 2 different types of trees. The student will create a write up or presentation showing:

1. The types of fruit trees they will plant based on:

1. cost of the trees
2. amount of land needed for the trees
3. location of the farm
4. potential profits from the fruit

2. Draw a graph to show the feasible region to show the possible amounts of fruit trees they can plant on their farm.
3. Determine the numbers of trees they will plant to maximize fruit variety, the land use, and potential profit and how they came to that conclusion.
4. Show the ideal shape and layout of the land including where trees will be planted where in the farm and why it is the best layout.

Reasoning: This is an example of a DOK IV level task as it is a project-based assessment. The student is required to research, reason abstractly and quantitatively while developing a mathematical model which informs and solves the given situation, and communicate their decisions, analysis, and rationales with others. The task requires the student to make connections within and across content areas and to select an approach among many alternatives on how the situation should be solved.