Gather students to discuss their work with the Number Line Contraption. Have students make their presentations to the class.
Ask questions such as the following:
- What is the same about the numbers on either side of 0?
- What is different about the numbers on either side of 0?
- If the dot starts on a positive number, what do you know about the stopping number?
- If the dot starts on a negative number, what do you know about the stopping number?
- What do you notice about the locations of starting and stopping numbers?
- What kinds of numbers did you work with on the Number Line Contraption?
In the discussion, have students use the dot to show you examples of positive numbers, negative numbers, rational numbers, and integers. Informally bring out the following in the discussion:
- Positive numbers are on the opposite side of 0 from negative numbers.
- Negative numbers are on the opposite side of 0 from positive numbers.
- The opposite of a positive number is negative, and the opposite of a negative number is positive.
- Since the opposite of 0 is 0 (which is neither positive nor negative), then −0 = 0.
- The opposite of the opposite of a number is the number itself.
Introduce the concept of the absolute value of a number as its distance from 0. In this simulation, it is the distance between the dot and the number 0. Students will explore absolute value more in the next lesson.
Have students who did the Challenge Problem share their thinking. Ask class members to evaluate whether their thinking makes sense.
ELL: Be sure that your pace is adequate, and, if needed at any point, present the questions in writing. Provide sentence frames as appropriate, but consider that ELLs might not need them, especially if the questions are shown in writing (students can “borrow” some of the words from the questions to construct their answers).
Allow ELLs to use a dictionary. Repeat the new words at a slower pace, and write them down, asking some of the students to repeat after you. Be sure ELLs feel comfortable with the pronunciation.
SWD: Make sure students understand these domain-specific terms:
- Absolute value
- Positive
- Negative
- Integer
- Rational number
Pre-teach these terms to students with disabilities. Provide a written definition and a visual representation of each term. Post them on a Word Wall or on anchor charts for students to copy into their notebook.
Performance Task
Take notes about how positive and negative numbers are represented on a number line.
As students present, ask questions such as:
- How did you predict where the lever would land?
- How did you know if a number was negative or positive?
- For one swing of the lever, how are the starting number and the ending number alike? How are they different?
- How did you figure out where the lever would land after two swings of the lever?
- What kind of number was the starting number? What kind of number was the ending number? Was it an integer? A rational number? Explain.
FAQs
Answer and Explanation:
The opposite of a rational number is an irrational number. Irrational numbers are numbers that cannot be written as a ratio of two integers. In other words, they can't be written as a simple fraction. The most well-known irrational number is Pi, which is 3.1416...
How do you find the opposite of a rational number? ›
Answer and Explanation:
The opposite of a rational number is an irrational number. Irrational numbers are numbers that cannot be written as a ratio of two integers. In other words, they can't be written as a simple fraction. The most well-known irrational number is Pi, which is 3.1416...
What are opposite numbers Grade 6? ›
The opposite of a number n is the number that is the same distance from 0 as n, but on the other side of 0 on a number line; 0 is its own opposite. A negative number is a number that is less than 0.
What is the opposite of a number in math? ›
The opposite of a number is its additive inverse. The opposite of a number 'a' is equal to '-a', and of a number '-a' is 'a'. For example, the opposite of 20 is -20. Thus, the opposite of a number is the number that is situated at the same distance from 0 but in the opposite direction on a number line.
What is the formula for the opposite of a number? ›
The easiest way to find the opposite number of a number is to simply change the sign in front of it. If it is positive or no sign is present, then add a minus or negative sign. If there is a negative or minus sign, then get rid of it or change it to a positive.
What is opposite number simple? ›
The opposite of a positive number is the negative version of the number. The opposite of a negative number is the positive version of the number. opposite numbers are located in the opposite direction on a number line having the same distance from the origin.
What number is the opposite of 1? ›
To find the opposite, we need to find the additive inverse of one. Additive inverse of a number is a number which when added with the original number gives 0. Therefore, for 1, if we add -1, it gives 0. Therefore, the opposite of 1 is -1.
What is an example of opposite? ›
Examples of opposite in a Sentence
They represent opposite sides of the issue. They ran in opposite directions. Noun “Wet” is the opposite of “dry.” The terms “black” and “white” are opposites. Adverb I sat down and he sat opposite.
What is the opposite rule in math? ›
Inverse means the opposite. So in math, an inverse operation can be defined as the operation that undoes what was done by the previous operation. The set of two opposite operations is called inverse operations. For example: If we add 5 and 2 pens, we get 7 pens. Now subtract 7 pens and 2 pens and we get 5 back.
What does opposite a mean in maths? ›
The logical symbol ∀, has the same shape as a sans-serif capital turned A. It is used to represent universal quantification in predicate logic, where it is typically read as "for all".
Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0. The opposite of 0 is 0. The opposite of 5 is -5. The opposite of -12 is 12.
Does zero have an opposite? ›
The Opposite of zero is zero!
What is the opposite of rational? ›
Opposite of based on, or in accordance with, reason or logic. illogical. groundless. invalid. irrational.
What is the opposite of +(+ 15)? ›
What is the opposite number? Opposite number is the number which has same face value but opposite in sign. For example, if any number has negative sign then their opposite number will contain positive sign. Opposite of 15 = -15.
What rational number is the opposite of 8? ›
Explanation: Opposite of a number means its additive inverse, which means the number added to its additive inverse would be zero. Thus opposite of 8 is -8.
What is the opposite of +(- 40)? ›
In this case, the opposite of +(-40) would be -(-40). When a negative sign (-) is followed by another negative sign, it results in a positive value. Therefore, -(-40) is equal to +40. Hence, the opposite of +(-40) is +40.
