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.
