The real number system includes both rational and irrational numbers. Rational numbers can be divided into smaller subsets called integers, whole numbers, and natural numbers. The square roots of perfect squares {1, 4, 9, 16….100} and the cube roots of perfect cubes {1, 8, 27,……1000} belong to the set of rational numbers. The square and cube roots of non-perfect squares and non-perfect cubes belong to the set of irrational numbers. Follow these links to games, videos, and activities that will help you learn the subsets of the real number system.

A perfect square (1, 4, 9, 16, 25,…………100) is the product of a number multiplied by itself. A perfect cube (1, 8, 27, 64, ….1,000) is the product of a number multiplied by itself twice. Square roots of perfect squares and cube roots of perfect cubes are rational numbers. They can be written in fraction form, and they terminate. The square roots and cube roots of all other numbers are irrational. When computed, they produce non-repeating, never ending decimals. We make rational approximations of irrational numbers to locate them on a number line.

**Monday, September 18 **

(Plans carried over from September 15.)

__Common Core Standards and Extended Standards
__8.NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers.

Extended Standard: Apply and extend previous understandings of numbers to the system of rational numbers.

NS.68.4a Solve real-world problems involving positive and negative numbers (e.g., temperatures, elevations, distance from a fixed point (map reading)).

NS.68.5a Recognize the effects of multiplying and dividing with negative numbers (e.g., -2 × -4 = 8).

NS.68.4b Solve problems involving positive and negative numbers using a number line (e.g., temperatures, distances from a fixed point).

NS.68.5b Recognize that the absolute value of a rational number is how far it is from 0 on the number line (i.e., plot a number and its opposite on a number line and recognize that they are equidistant from zero).

NS.68.4c Locate a given positive or negative number on a number line.

NS.68.5c Recognize that addition means move to the right and subtraction means move to the left on a number line.

__Student Objectives
__I can identify rational and irrational numbers.

I can apply order of operations.

__Bellwork
__Students will complete

*Math Minute 10*.

__Lesson__ (Introduction to the Real Number System/Rational and Irrational Numbers/*GoMath* 1.1)

1. Pass back papers. Organize.

2. Super 6 supplies check

3. Guided notes/journal entry presented through modified concept attainment method: rational and irrational numbers-examples, followed by definitions

4. Cooperative practice: Pairs of students sort a bag of rational and irrational number. Discuss criteria students used to sort the numbers.

5. Independent practice: #1-16 from “Rational and Irrational Numbers” worksheet

6. Guided mixed practice with dry erase boards, markers, and a partner

7.

10. Rational and irrational numbers challenge on SmartBoard

11. IXL Module 1 To-Do List

12. IXL Integers To-Do List

13. Extra: order of operations scramble

__Closing
__

__Homework____
__Complete #1-16 on the rational and irrational numbers worksheet.

__Links
__Check out the games and videos on my “Real Number System” page. You can find it by typing “Real Number System” in the search box.

**Tuesday, September 19**

__Common Core Standards and Extended Standards
__8.NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers.

Extended Standard: Apply and extend previous understandings of numbers to the system of rational numbers.

NS.68.4a Solve real-world problems involving positive and negative numbers (e.g., temperatures, elevations, distance from a fixed point (map reading)).

NS.68.5a Recognize the effects of multiplying and dividing with negative numbers (e.g., -2 × -4 = 8).

NS.68.4b Solve problems involving positive and negative numbers using a number line (e.g., temperatures, distances from a fixed point).

NS.68.5b Recognize that the absolute value of a rational number is how far it is from 0 on the number line (i.e., plot a number and its opposite on a number line and recognize that they are equidistant from zero).

NS.68.4c Locate a given positive or negative number on a number line.

NS.68.5c Recognize that addition means move to the right and subtraction means move to the left on a number line.

__Student Objectives
__I can sort rational and irrational numbers.

I can convert a fraction to a decimal and a decimal to a fraction.

__Bellwork
__Students will complete

*Math Minute 11*.

Students who finish early will complete an XtraMath lesson.

__Lesson__ (Fraction and Decimal Conversions)

1. Go over Schoology discussion questions: “Expressions of 36” and “Order of Operations Challenge”

2. Schoology discussion question: “Which type of number do you see more often, fractions or decimals? Which do you prefer to use? Why?”

3. Journal entry: ratios

4. Foldable book/journal entry: fraction to decimal conversions, decimal to fraction conversion

5. Distribute conversions “cheat sheet.”

6. Direct instruction with examples, questioning, and calculator tips: expressing rational numbers (fractions and mixed numbers) as decimals

7. Direct instruction with examples, questioning, and calculator tips: expressing decimals as fractions (rational numbers)

8. Direct instruction with examples, questioning, and calculator tips: expressing repeating decimals as (fractions)

9. Early bird game: guided mixed practice with dry erase boards, markers, and a partner using problems from worksheet below

__Closing
__

__Homework__

__Complete the conversions on the front page of the irrational and rational numbers worksheet. The student information form in Schoology (basic information folder) is due on Friday. Ask your parent to help you complete it.__

__Links__

Check out the games and videos on my “Real Number System” page. You can find it by typing “Real Number System” in the search box.

**Wednesday, September 20 **

__Common Core Standards
__8.NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers.

Extended Standard: Apply and extend previous understandings of numbers to the system of rational numbers.

NS.68.4a Solve real-world problems involving positive and negative numbers (e.g., temperatures, elevations, distance from a fixed point (map reading)).

NS.68.5a Recognize the effects of multiplying and dividing with negative numbers (e.g., -2 × -4 = 8).

NS.68.4b Solve problems involving positive and negative numbers using a number line (e.g., temperatures, distances from a fixed point).

NS.68.5b Recognize that the absolute value of a rational number is how far it is from 0 on the number line (i.e., plot a number and its opposite on a number line and recognize that they are equidistant from zero).

NS.68.4c Locate a given positive or negative number on a number line.

NS.68.5c Recognize that addition means move to the right and subtraction means move to the left on a number line.

__Student Objectives
__I can sort rational and irrational numbers.

I can convert decimals and fractions.

__Bellwork
__Students will complete

*Math Minute 12*.

__Lesson__ (Sets of Real Numbers/*Go Math* 1.2)

1. Pass back order of operations quiz.

2. Go over answers to homework.

3. Footloose game with a partner: converting fractions and decimals with a calculator

4. Journal entry: rational and irrational numbers-examples and definitions presented through modified concept attainment method

5. Guided practice: selected items from “Rational & Irrational Numbers” worksheet, teach calculator method for finding square and cube roots

6. Assess understanding by giving students a bag of rational and irrational numbers to sort with a partner. Discuss criteria students used to sort the numbers.

7. Journal entry/”foldable”-subsets of real numbers, definitions, examples and nonexamples from Math=Love

8. Independent practice with Chromebooks: real number systems links on teacher’s web page

9. Video wrap up-student choice

__Closing
__

__Homework
__

Links

Check out the games and videos on my “Real Number System” page. You can find it by typing “Real Number System” in the search box.

**Thursday, September 21**

__Common Core Standards
__8.NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers.

Extended Standard: Apply and extend previous understandings of numbers to the system of rational numbers.

NS.68.4a Solve real-world problems involving positive and negative numbers (e.g., temperatures, elevations, distance from a fixed point (map reading)).

NS.68.5a Recognize the effects of multiplying and dividing with negative numbers (e.g., -2 × -4 = 8).

NS.68.4b Solve problems involving positive and negative numbers using a number line (e.g., temperatures, distances from a fixed point).

NS.68.5b Recognize that the absolute value of a rational number is how far it is from 0 on the number line (i.e., plot a number and its opposite on a number line and recognize that they are equidistant from zero).

NS.68.4c Locate a given positive or negative number on a number line.

NS.68.5c Recognize that addition means move to the right and subtraction means move to the left on a number line.

__Student Objectives
__I can sort rational and irrational numbers.

I can convert a repeating decimal into a fraction.

I can locate rational approximations of irrational numbers on a number line.

__Bellwork
__Students will complete

*Math Minute 13*. Schoology discussion: “Can a number be…..?”

__Lesson__ (More Subsets of Real Numbers)

1. Go over homework.

2. Discuss evacuation drill procedures.

3. Video

4. Rational and irrational numbers organizer (SAVE)

5. Shopping bag extension activity from PDF below to give students a more concrete example of how subsets fit together

6. Guided practice:

7. Guided practice: workbook page 12, #1-12, and remaining items on the top portion of the rational and irrational numbers worksheet

8. Google drive organization-teacher will demonstrate and assist students in organizing their Google drive

9. Teacher introduction to “Grouping Subsets Project”-rubric and template in Schoology, examples of finished projects on teacher website

10. Work time-homework, grouping subsets project, real number system links on teacher web page

__Closing
__

__Homework
__Grouping subset projects will be due next Friday. This Friday there will be a quiz over the subsets of the real number system. Complete #1-10 on page 18 and #14-19 on page 10 in your math workbook.

__Links
__Check out the games and videos on my “Real Number System” page. You can find it by typing “Real Number System” in the search box.

**Friday, September 22**

__Common Core Standards
__8.NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers.

Extended Standard: Apply and extend previous understandings of numbers to the system of rational numbers.

NS.68.4a Solve real-world problems involving positive and negative numbers (e.g., temperatures, elevations, distance from a fixed point (map reading)).

NS.68.5a Recognize the effects of multiplying and dividing with negative numbers (e.g., -2 × -4 = 8).

NS.68.4b Solve problems involving positive and negative numbers using a number line (e.g., temperatures, distances from a fixed point).

NS.68.5b Recognize that the absolute value of a rational number is how far it is from 0 on the number line (i.e., plot a number and its opposite on a number line and recognize that they are equidistant from zero).

NS.68.4c Locate a given positive or negative number on a number line.

NS.68.5c Recognize that addition means move to the right and subtraction means move to the left on a number line.

__Student Objectives
__I can sort rational and irrational numbers.

I can convert a repeating decimal into a fraction with my calculator.

I can locate rational approximations of irrational numbers on a number line.

__Bellwork
__Students will complete

*Math Minute 14*.

__Lesson__ (Introduction to Perfect Squares & Cubes/Sets of Real Numbers*/*Rational Approximations*)*

1. Go over homework.

2. Review real number subsets. Students will place numbers in the correct section of a real number system organizer projected onto the SmartBoard.

3. Real Numbers Jeopardy

4. Generate interest by giving students a small piece of graph paper. Ask students to draw a 1 by 1 square, a 2 by 2 square,……..as many squares of different sizes as they can on the piece of paper of graph paper. Ask students to label the side lengths for each square. (OR-Gizmos Student Exploration: Square Roots)

5. Review how to square and cube numbers on the calculator. Demonstrate how to take the square and cube root of a number on the calculator.

4. Journal entry/foldable: perfect squares and square roots with flashcards

5. Guided practice: roots practice worksheet

6. Discuss grouping subsets project. Answer questions. Share another example.

7. Demonstrate how to log into my.hrw.com. Have students write usernames and passwords on the inside cover of their math journal and on their passwords form in their math binder.

8. Independent work:

-real numbers, integers, and order of operations links on teacher web page

-work on grouping subsets project

-GoMath Personal Math Trainer 1.1 and 1.2

__Closing
__Schoology discussion question: “Explain the difference between rational and irrational numbers. Give at least 2 examples of each type of number.”

__Homework
__Your subsets project is due next Friday. Tomorrow, you will have a brief quiz over the subsets of the real number system. Complete the “Rational Approximations of Irrational Numbers” worksheet.

Links

Check out the games and videos on my “Real Number System” page. You can find it by typing “Real Number System” in the search box.