Unit 7
Rational and Irrational Solutions & Sums and Products of Rational and Irrational Numbers
Quadratic Equations
Lesson 20/21
HSA-REI.B.4.b: Solve quadratic equations by inspection (e.g., for πΉΒ² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
HSN-RN.B: Use properties of rational and irrational numbers.
HSN-RN.B.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Expressions and Equations
Warm-up
Unit 7 β Lesson 20/21
Warm-up
Page 254
Page 306
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 7 β Lesson 20/21
Letβs consider the kinds of numbers we get when solving quadratic equations & make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers.
We can explain why sums or products of two rational numbers are rational so that we can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Where were we? Where are we? Where are we going?
Unit 6 β Lesson 20/21
Agenda Review
You are successful today when...,
β You can explain why adding a rational number and an irrational number produces an irrational number.
β You can explain why multiplying a rational number (except 0) and an irrational number produces an irrational number.
β You can explain why sums or products of two rational numbers are rational.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
20.3 Activity: Experimenting with Rational and Irrational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
2 mins individual - 2 minutes group - 4 min class share
pg 307
10 mins Total
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
20.3 Activity: Experimenting with Rational and Irrational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
rational
irrational
Usually irrational
rational
Usually irrational
Usually irrational
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
21.2 Activity: Sums and Products of Rational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
4 mins individual - 3 minutes group - 3 min class share
pg 314-15
10 mins Total
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
21.2 Activity: Sums and Products of Rational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
21.2 Activity: Sums and Products of Rational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
The numerator and denominator are both integers. The product of two integers is an integer, so ad, bc, and bd are all integers. The sum of two integers is an integer, so ad + bc is an integer.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
21.2 Activity: Sums and Products of Rational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
Because the products of integers are also integers, both the numerator and denominator of the product are integers, so the product is a fraction.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
21.3 Activity: Sums and Products of Rational and Irrational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
2 mins individual - 4 minutes group - 3 min class share
pg 316
10 mins Total
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
21.3 Activity: Sums and Products of Rational and Irrational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Lesson Synthesis
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Adding Irrational Numbers
We can make convincing arguments about why the sums and products of rational and irrational numbers are always certain kinds of numbers
8
Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 7 β Lesson 20/21
β I can explain why adding a rational number and an irrational number produces an irrational number.
β I can explain why multiplying a rational number (except 0) and an irrational number produces an irrational number.
β I can explain why sums or products of two rational numbers are rational.
Learning
Targets
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.