Relationships Between Sets of Rational Numbers

7th Grade Relationships Between Sets of Rational Numbers

Mr. Alonzo

Tips for learning

• This presentation is designed to be a lesson that will be teaching you new things. If you rush through it you will fail.

• Do not rush through this slide show.

• Work the questions out on a seperate sheet of paper and take notes.

• Answer each question fully and in complete sentences.

• Ask Mr. Alonzo for help if you don't understand something.

• You may watch the videos provided in this slide show or look at the poster's in Mr. Alonzo's room for help.

Objective

The student applies mathematical process standards to represent and use rational numbers in a variety of forms. Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers.

Classifying Rational Numbers

• A group of items is called a "set".

• A Venn diagram uses intersecting circles to show relationships among sets of numbers or things.

• The Venn diagram below shows how the sets of whole numbers, integers, and rational numbers are related to each other.

• When a "set" is contained within a larger set in a Venn diagram it is called a "subset", the numbers in the smaller set are also members of the larger set.

Classifying Cheat Sheet

• All Whole Numbers  $=$  Whole Numbers, Integers, and Rational Numbers.

• All Integers  $=$  Rational Numbers
  

• Integers  $\ne$  Whole Numbers

• Rational Numbers  $\ne$  Integers or Whole Numbers

Multiple Select

Classify each number by selecting the set or sets to which it belongs. If it belongs to more than one set make sure to check all the sets the number belongs to.
 $-8$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by selecting the set or sets to which it belongs. If it belongs to more than one set make sure to check all the sets the number belongs to.
 $-102.\overline{55}$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by selecting the set or sets to which it belongs. If it belongs to more than one set make sure to check all the sets the number belongs to.
 $\frac{9}{2}$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by selecting the set or sets to which it belongs. If it belongs to more than one set make sure to check all the sets the number belongs to.
 $3$  

• Rational Number

• Integer

• Whole Number

• None of these

Understanding Sets and Subsets of Rational Numbers

• When one set is entirely contained in another set, we say the first set is a subset of the second set.

• You can use the Rational Number Venn diagram to decide whether or not a given set of numbers is a subset of another set.

Open Ended

Jared said that every prime number is an integer. Do you agree or disagree? Explain.

Open Ended

Tell whether the statement “Some rational numbers are integers” is true or false. Explain your choice.

Open Ended

Describe a real-world situation that is best described by the set of rational numbers.

Identifying Sets for Real-World Situations

Numbers in real-world situations can be whole numbers, integers, rational numbers, or some combination of the three sets. When you have a choice of sets to describe a number in a real-world situation, you may be able to choose one that gives a more precise description than the others.

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $5$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $-\frac{3}{14}$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $-23$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $4.5$  

• Rational Number

• Integer

• Whole Number

• None of these

Open Ended

Tell whether the given statement is true or false. Explain your choice.

All rational numbers are integers.

Open Ended

Tell whether the given statement is true or false. Explain your choice.

Some integers are whole numbers.

Open Ended

Identify the set of numbers that best describes each situation. Then explain your choice using sentences.

the number of students in a school The set of _________ best describes the situation because

Open Ended

Identify the set of numbers that best describes each situation. Then explain your choice using sentences.

possible points in a certain board game (...-3, -2, -1, 0, 1, 2, 3,...) The set of __________ best describes the situation because

Open Ended

How can you represent how the sets of whole numbers, integers, and rational numbers are related to each other?

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $-9$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $7.5$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $789$  

• Rational Number

• Integer

• Whole Number

• None of these

Multiple Select

Classify each number by naming the set or sets to which it belongs.

 $5\frac{3}{4}$  

• Rational Number

• Integer

• Whole Number

• None of these

Look at the following Venn diagram

Use a seperate sheet of paper to determine where the whole numbers from 1 to 15 go.

Multiple Choice

How many whole numbers fit inside the divisible by 3 only circle?

• One number

• Three numbers

• Four numbers

• Seven numbers

• Five numbers

Multiple Choice

How many whole numbers fit inside the divisible by 4 only circle?

• Three numbers

• Two numbers

• Four numbers

• Six numbers

• Five numbers

Multiple Choice

How many whole numbers fit inside the very center meaning they are divisible by 3 and 4?

• One number

• Two numbers

• Four numbers

• Three numbers

• Five numbers

Multiple Choice

How many whole numbers fit in the outermost circle and are NOT divisible by 3 or 4?

• One number

• Nine numbers

• Eight numbers

• Three numbers

• Seven numbers

Look at the following Venn diagram

Use a seperate sheet of paper to determine where the whole numbers from 1 to 15 go.

Multiple Choice

How many whole numbers fit in the outermost circle and are NOT composite or odd.

• One number

• Nine numbers

• Eight numbers

• Three numbers

• Seven numbers

Multiple Choice

How many whole numbers fit inside the composite numbers only circle?

• One number

• Four numbers

• Six numbers

• Three numbers

• Seven numbers

Multiple Choice

How many whole numbers fit inside the Odd numbers only circle?

• One number

• Four numbers

• Six numbers

• Three numbers

• Five numbers

Multiple Choice

How many whole numbers fit inside the very center meaning they are Composite and odd?

• One number

• Four numbers

• Six numbers

• Three numbers

• Two numbers

Open Ended

Tell whether the given statement is true or false. Explain your choice.

All rational numbers are whole numbers.

Open Ended

Tell whether the given statement is true or false. Explain your choice.

All whole numbers are integers.

Open Ended

Tell whether the given statement is true or false. Explain your choice.

Some whole numbers are negative.

Open Ended

Tell whether the given statement is true or false. Explain your choice.

No positive numbers are integers.

Open Ended

Identify the set of numbers that best describes each situation. Explain your choice.

possible number of miles you can walk in 1 hour.

Open Ended

Identify the set of numbers that best describes each situation. Explain your choice.

possible number of marbles in a jar.

Open Ended

Identify the set of numbers that best describes each situation. Explain your choice.

Using what you know of rational numbers, describe a real-world situation where a doctor might use the set of rational numbers on a daily basis.

Open Ended

The letters in the Venn diagram represent whole numbers. Describe the numbers you would find in Section c, Section d, and Section e.

Open Ended

Explain how the set of integers differs from the set of whole numbers.

Open Ended

Explain why a mixed number is not in the set of integers or whole numbers.