Representing Rational Numbers: Plotting on a Number Line
In this lesson, students will learn how to represent positive and negative rational numbers on a number line to solve mathematical and real-world problems. The content covers identifying opposites, ordering, and comparing rational numbers through engaging activities and discussions.
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Presentation Transcript
Lesson Representing Rational Numbers
[OBJECTIVE] The student will understand positive and negative rational numbers as quantities of opposite directions or values and plot these values on a number line in order to solve mathematical and real-world problems.
[MYSKILLS] Ordering and comparing positive rational numbers
[ESSENTIALQUESTIONS] 1. What is the opposite of a positive value? What is the opposite of a negative value? 2. Describe specific situations that could be represented with a positive value. 3. Describe specific situations that could be represented with a negative value.
[Warm-Up] Begin by completing the warm-up for this lesson.
SOLVE Problem Introduction REPRESENTING RATIONAL NUMBERS
[LESSON] SOLVE Travis and Sonia are creating a matching game and want to identify a number that is equal to 35. Travis suggests that they write 35 on a card as the match, but Sonia argues that the card should show ( 35) to be equal to 35. Who will create the correctly matched card? Explain your answer using a number line.
[LESSON] SOLVE S Study the Problem Underline the question.
[LESSON] SOLVE Travis and Sonia are creating a matching game and want to identify a number that is equal to 35. Travis suggests that they write 35 on a card as the match, but Sonia argues that the card should show ( 35) to be equal to 35. Who will create the correctly matched card? Explain your answer using a number line.
[LESSON] SOLVE S Study the Problem Underline the question. This problem is asking me to find the person who correctly matched the number value of 35.
IDENTIFYING OPPOSITES ON A NUMBER LINE
Identifying Opposites on a Number Line Up Left Hot Day In Enter Fast Wet Happy Soft Loud Long Large Above
Identifying Opposites on a Number Line What do you see in the left column of the table? It is a long list of words. Write the opposite of each of the words. For example, if the word provided is east, then the opposite would be west. For the bonus, create your own set of opposites that aren t already listed in the table.
Identifying Opposites on a Number Line Down Dry Up Left Hot Day In Enter Fast Wet Happy Soft Loud Long Large Above Right Sad Cold Hard Night Quiet Out Short Exit Small Slow Below Bonus: ___________ ___________
Identifying Opposites on a Number Line In our Warm-Up, we showed that we are able to plot positive rational numbers on a number line. On the previous page, we compiled a list of words that are opposites of each other. Numbers also have opposites, and we can explore this by looking at the horizontal number line below. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line As we move farther right on the number line, what happens to the number values? Justify your answer. The numbers become larger positive numbers. We can see on the number line that the numbers are going up: 1, 2, 3. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line What numbers are to the left of 0 on the number line below? Negative Numbers The raised hyphen preceding the numeral is a symbol for negative. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line What do you notice about the number values as we move to the left as compared to the number values as we move to the right on the number line? The numerals are the same as we move away (farther left or farther right) from 0, but the numbers on the left are negative and the numbers on the right are positive. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Take a look at the table below. Original Number Opposite of Original Number 1 3 ? ? 2.5 ? ?
Identifying Opposites on a Number Line Take your string and tape an algebra tile to one end. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line What is the first Original Number that we see in the table? 1 Plot this Original Number on the number line. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Place the algebra tile that is attached to your string on positive 1 that is on the number line and hold it down with your finger. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Gently pull the excess string so that you have a straight line of string from 1 to 0. Place your finger on the string right at 0. Let the rest of the string lay below the number line. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Taking your finger off of the algebra tile, swing the tile around so that it passes over 0 and lands on the other side of the number line and hold the algebra tile down at its new location. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Where does the algebra tile land? 1 Plot a point here. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line What do you think the 1 represents in relation to our original number of 1? Explain your answer. It represents the opposite number of our original number because it s on the other side of the number line. Record this number in the second column. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Original Number Opposite of Original Number 1 1 3 ? ? 2.5 ? ?
Identifying Opposites on a Number Line What is the second number in the list? 3 Plot this Original Number on the number line. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Place the algebra tile that is attached to your string on positive 3 that is on the number line and hold it down with your finger. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Gently pull the excess string so that you have a straight line of string from 3 to 0. Place your finger on the string right at 0. Let the rest of the string lay below the number line. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Taking your finger off of the algebra tile, swing the tile around so that it passes over 0 and lands on the other side of the number line and hold the algebra tile down at its new location. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Where does the algebra tile land? 3 Plot a point here. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line What do you think the 3 represents in relation to our original number of 3? Explain your answer. It represents the opposite number of our original number 3, because it s on the other side of the number line. Record this number in the second column. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Original Number Opposite of Original Number 1 1 3 3 ? ? 2.5 ? ?
Identifying Opposites on a Number Line Take a moment to find the opposite of three halves. You may want to convert this value to a decimal first! 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Original Number Opposite of Original Number 1 1 3 3 ? ? ? ? 2.5 ? ?
Identifying Opposites on a Number Line What do you notice about the first set of values in the table? The opposite number is the same numeral but with a negative sign. Look at positive 1 and negative 1 and describe their relationship to zero. Both of those values are the same distance from zero, which is one unit.
Identifying Opposites on a Number Line What do you predict about the values of 3 and negative 3 and the distance of each from zero. Both values will be 3 units from zero! Explain your answer. When we are determining distance, it cannot be a negative value, so the distance from either positive or negative three to zero is the same, 3 units. Take a moment to predict what the outcomes for the rest of the table will be.
Identifying Opposites on a Number Line What is the next number in the list? 2.5 Plot this Original Number on the number line. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Place the algebra tile that is attached to your string on 2.5 that is on the number line and hold it down with your finger. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Gently pull the excess string so that you have a straight line of string from 2.5 to 0. Place your finger on the string right at 0. Let the rest of the string lay below the number line. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Taking your finger off of the algebra tile, swing the tile around so that it passes over 0 and lands on the other side of the number line and hold the algebra tile down at its new location. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Where does the algebra tile land? 2.5 Plot a point here. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line What do you think the 2.5 represents in relation to our original number of 2.5? Explain your answer. It represents the opposite number of our original number, 2.5, because it s on the other side of the number line. Record this number in the second column. 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Original Number Opposite of Original Number 1 1 3 3 ? ? ? ? 2.5 2.5 ? ?
Identifying Opposites on a Number Line Take a moment to find the opposite of negative one third. You may want to convert this value to a decimal first! 3 2 1 0 1 2 3
Identifying Opposites on a Number Line Original Number Opposite of Original Number 1 1 3 3 ? ? ? ? 2.5 2.5 ? ? ? ?
Identifying Opposites on a Number Line What do you notice about the second set of values in the table? The opposite number is the same numeral but with a positive sign. What can you conclude about opposites of negative numbers? Justify your answer. We can conclude that the opposites of negative numbers are positive versions of the negative numerals. We can see from our table that the numbers are the same but the signs are different.
Identifying Opposites on a Number Line Do you notice any patterns in the numbers in the table? Justify your answer. The opposite of the original number keeps the same value, but has the opposite sign. The word opposite is a signal word to use the negative symbol ( ) in front of a number, and it can help us to decode what the question is asking us to find.
Identifying Opposites on a Number Line What is ( 1) equal to? What is the question asking us to find? The opposite of the opposite of 1 3 2 1 0 1 2 3
