ALEX Learning Activity

  

Complex Numbers

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: Kristy Lacks
System:Marshall County
School:Douglas High School
  General Activity Information  
Activity ID: 2283
Title:
Complex Numbers
Digital Tool/Resource:
Complex Numbers Google Doc
Web Address – URL:
Overview:

This learning activity will be used at the end of a lesson on complex numbers. The student will use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

This activity results from the ALEX Resource Development Summit.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra II with Statistics
1. Identify numbers written in the form a + bi, where a and b are real numbers and i² = -1, as complex numbers.

a. Add, subtract, and multiply complex numbers using the commutative, associative, and distributive properties
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Produce equivalent expressions in the form a + bi, where a and b are real for combinations of complex numbers by using addition, subtraction, and multiplication and justify that these expressions are equivalent through the use of properties of operations and equality
Teacher Vocabulary:
  • Complex number
  • Commutative property
  • Associative property
  • Distributive property
Knowledge:
Students know:
  • Combinations of operations on complex number that produce equivalent expressions.
  • Properties of operations and equality that verify this equivalence.
Skills:
Students are able to:
  • Perform arithmetic manipulations on complex numbers to produce equivalent expressions.
Understanding:
Students understand that:
  • Complex number calculations follow the same rules of arithmetic as combining real numbers and algebraic expressions.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGII.1.1: Define real and complex numbers, commutative, associative, and distributive properties.
ALGII.1.2: Apply commutative, associative, and distributive properties to using multiplication with complex numbers.
ALGII.1.3: Apply commutative, associative, and distributive properties to using addition and subtraction with complex numbers.
ALGII.1.4: Use commutative, associative, and distributive properties.
ALGII.1.5: Identify imaginary numbers.

Prior Knowledge Skills:
  • Review laws of integers.
  • Apply commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
  • Review commutative, associative, and distributive properties.
  • Recall solving one step equations and inequalities.
  • Calculate a solution or solution set by combining like terms, isolating the variable, and/or using inverse operations.
Learning Objectives:

I can use the relation i2=-1.

I can use the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
  Strategies, Preparations and Variations  
Phase:
After/Explain/Elaborate
Activity:

This activity will be used at the end of a lesson on complex numbers. Students will complete the activity Complex Numbers.  This activity provides the teacher and students with a final check to assess complex numbers. Students will complete this activity individually.

Assessment Strategies:

The activity Complex Numbers can be used to access the student's ability to use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Advanced Preparation:

Students will need to know how to use the relation  i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. The teacher can add the activity to Google Classroom for the students to view.  The teacher can copy the activity Complex Numbers for the students to write on and turn in.
Variation Tips (optional):

The learning activity Complex Numbers can be shortened to use the questions as exit slips.
Notes or Recommendations (optional):

This activity is best when students complete the activity individually.  The teacher can assess the student's ability on an individual basis.
  Keywords and Search Tags  
Keywords and Search Tags: associative, commutative, complex numbers, distributive, i