Course No. / 27.09720 / Course Name / GSE Analytic Geometry
Grade / 10 / Unit # / 4 / Projected
Timeline / 3 weeks
Unit Name / Extending the Number System
Unit Overview
In this unit students will:
• operate with polynomials with an emphasis on expressions that simplify to linear or quadratic forms.
• rewrite expression involving radicals
• understand that the basic properties of numbers continue to hold with polynomials
Unit Curriculum Map
Unit Standards / MGSE9-12.N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents (i.e., simplify and/or use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots).
MGSE9-12.N.RN.3 Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.
MGSE9-12.A.APR.1 Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
Content Learning Progression # 1
Topic _1__ out of _2_ / Polynomials
(2 weeks)
Standards in this learning progression: / MGSE9-12.A.APR.1
Connections to other standards (Standards for Mathematical Practice, Literacy, etc: / 1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Resource 1:
Resource 2:
Terms students should learn and use with precision in this unit and progression: / Binomial, degree of a polynomial, expression, leading coefficient, monomial, polynomial, term, trinomial
(Refer to your textbook glossary for definitions)
Materials and tools students should use with precision in this unit and progression: / Pencil, paper, calculator (graphing or scientific), Algebra-Tiles
**Online AG Milestone provides an online graphing calculator similar to the TI-84
Know – Understand – Do
(KUD)
By the end of this learning progression, students will be able to…
UNDERSTAND
Big Ideas, Essential Understandings, or Generalizations
Operations with polynomials are similar to operations with integers.
KNOW
Facts and Procedural Knowledge / DO
Skills
- Know how to add, subtract and multiply polynomials.
- Perform operations on polynomials.
- Explain how performing operations on polynomials is similar to performing operations on integers.
Content Learning Progression # 2
Topic _2__ out of _2_ / Rational and Irrational Numbers
(1 week)
Standards in this learning progression: / MGSE9-12.N.RN.2
MGSE9-12.N.RN.3
Connections to other standards (Standards for Mathematical Practice, Literacy, etc: / 1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Resource 1:
Resource 2:
Terms students should learn and use with precision in this unit and progression: / Index, irrational number, nonzero rational number, radical, rational number
(Refer to your textbook glossary for definitions)
Materials and tools students should use with precision in this unit and progression: / Pencil, paper, calculator (graphing or scientific)
**Online AG Milestone provides an online graphing calculator similar to the TI 84
Know – Understand – Do
(KUD)
By the end of this learning progression, students will be able to…
UNDERSTAND
Big Ideas, Essential Understandings, or Generalizations
- How to rewrite expressions involving radicals and use operations with radicals.
- The sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.
KNOW
Facts and Procedural Knowledge / DO
Skills
- Know how to rewrite radicals (NOT rational exponents)
- Know how to simplify radical expressions.
- Know how to add, subtract, and multiply with radicals
- Know how to add and multiply rational and irrational numbers.
- Rewrite expressions involving radicals. (NOT rational exponents)
- Explain why the sum or product of rational numbers is rational.
- Explain why the sum of a rational number and an irrational number is irrational.
- Explain why the product of a nonzero rational number and an irrational number is irrational.