Download Problem 3.1 Extending the Number Line

September 30, 2015
Problem 3.1
Extending the Number Line
Integers and Mixed Numbers
Focus Question:
How can the number line help you think about fractions
greater than 1 and less than 0?
Vocabulary
rational numbers - zero, whole numbers, fractions, and
their opposites
September 30, 2015
What happens on the other side of zero?
Let's make a number line...
1) Using your ruler, draw a line that is 10 inches long.
2) Starting at the left end of your line, put a tally mark every 1 inch.
You should have 11 marks when you're done.
3) Find the very center tally and label it zero.
3) Label the whole numbers to the right of zero.
4) Where would you place -5, -4, and - 5 ?
2
September 30, 2015
Where have you encountered fractions greater than 1?
A fraction whose numerator is greater than or equal to the
denominator is called an improper fraction.
A number written with both a whole number part and a
fraction part is called a mixed number.
September 30, 2015
How would you write 2 1 as a fraction?
2
1
2
0
?
1
2
2 names?
p. 63
-5
-4
-3
-2
-1
0
1
2
3
4
5
1) Do you agree with Betty?
2) Do you agree with Judi?
3) What should you label the mark between -2 and -3?
4) What is halfway between that mark and -2?
QP
September 30, 2015
-5
-4
-3
-2
-1
0
1
2
3
4
5
Two numbers whose sum is zero and are located on opposite
sides of zero on a number line are called opposites.
QP
12 3
4
How many thirds does it take to make a whole?
How would you write 37 as a mixed number?
3
QP
September 30, 2015
-2
-1
0
1
2
3
Which of the fractions can be written as mixed numbers? Explain.
-2
-1
0
1
2
3
Which of these numbers can be written as improper fractions? Explain.
September 30, 2015
-2
-1
0
1
2
What do you notice about 2 and -2 on the number line?
The distance a number is from zero is called absolute value.
QP
September 30, 2015
Summarize
If I want to put -2 2 on the number line, is it to the left or right of -2?
3
Is -2 2 closer to -2 or closer to -3? How do you know?
3
Exit Slip
JoAnn noticed that the distance between 3 and -3 on the
number line is 6 units. She tries out other pairs of
opposites and concludes that the distance between
N and -N is always twice the absolute value of N.
Is she right? Why does this work?