Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Purpose and Instructional Strategies
In Math for College Liberal Arts, students represent logical operations, such as AND, OR, NOT,
NOR, and XOR, using logical symbolism to solve problems involving classifying items as
belonging to sets.
- This benchmark builds on MA.912.LT.4.1 and MA.912.LT.4.2 as it involves representing
or translating statements using logical connectives or operations, as well as determining
the truth value of an output given the truth value of the inputs.
- Instruction includes defining of the logic operations as functions.
A search query for romance
- Operators may be in capital or lower case letters. Instruction progresses from using all
capital letters to lower case letters in order to ensure students recognize the operators.
- Instruction includes connections to set operations and Venn Diagrams (MA.912.LT.5.4
and MA.912.LT.5.5) using real-world contexts such as choosing the appropriate logic
operation and writing a search query to identify a subset of a population.
- For example, suppose R is the set of all romance books, and T is the set of all true
crime books in a library database.
A search query for romance AND true crime
- All the books that are an element of the set R.
A search query for romance OR true crime
- All the books that are both a romance and a true crime, which is the
intersection of R and T.
A search query for NOT true crime
- All the books that are a romance, a true crime, or both, which is the union
of R and T. This is the inclusive or.
A search query for romance NOR true crime
- All the books that are not a true crime, which is the complement of T.
A search query for romance XOR true crime
- All the books that are not a true crime and not a romance, which is the
complement of the union of R and T.
- All the books that are a true crime or a romance, but not both. This is the
union minus the intersection, which is the exclusive or.
- Instruction directs students to decide whether an element is a member of resulting set
given the conditions and logic operations (MTR.6.1).
- For example, if given a book that is a true crime romance, students would
determine to which of the operator(s) AND, OR, NOT, NOR or XOR it belongs.
- For example, if given an operator of NOT, does the true crime romance book
belong to that set.
- Students also engage in discussions with their peers, analyzing the mathematical thinking
of others (MTR.4.1), demonstrating their understanding by representing their reasoning in
multiple ways (e.g., Venn Diagram, set operations, specific examples of set elements).
- Instruction mentions that logic operators are used in Boolean Algebra, logic gates and
computer science topics.
- Boolean Algebra focuses on binary variables with truth values being coded as a 0
- Logic Gates is the visualization model of Boolean Algebra. Logic gates can be a
device that acts as building blocks for digital circuits.
Common Misconceptions or Errors
- Students may use the logic operation OR as ‘exclusive or.’ To help address this, make
connection to the set operation of the union to reinforce the meaning of ‘p OR q’ as ‘p or
q or both p AND q.’
- Students may use the logic operation AND to join two sets. To help address this, make
connection to the set operation of the intersection.
Instructional Task 1 (MTR.1.1, MTR.4.1)
- Work with a partner(s) to determine the set of numbers that meet these conditions as a whole.
- Part A. What are some examples of numbers that meet the condition “NOT an odd
- Part B. What are some examples of numbers that meet the condition “less than 20 AND
greater than 1?”
- Part C. What are some examples of numbers that meet the condition “multiple of 3 OR
multiple of 5?”
- Part D. Describe the numbers that meet the following conditions: NOT an even number
AND less than 20 AND greater than 1 AND (multiple of 3 OR multiple of 5).
Instructional Item 1
- Suppose your high school has a database of all students along with many characteristics of
each student such as name, current grade level, intended career path, and many others. A
segment of the student characteristics table is shown.
- Which of the following search queries would generate the list of 12th graders, on a Business
- a. Grade_Level is 12 AND Career_Path is Business
- b. Grade_Level is greater than 11 OR Career_Path is Business
- c. Grade_Level is NOT 9 AND Grade_Level is NOT 10 AND Grade_Level is NOT 11
AND Career_Path is Business
- d. Grade_Level is 12 AND Career_Path is NOT STEM
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.