Grade 4 Lesson 14: Number Lines and Mixed Numbers
Purpose:
To form the beginning of a number line with fractions
Materials:
Fraction Bars, Transparent bars, Transparent Number Line (Transparency Kit),
Master "Fraction Number Line", pencils, markers
TEACHER MODELING/STUDENT COMMUNICATION
Fraction
Bars and
pencils
Masters
Fraction
Number Line
Transp
Number
Line
Transp
bars
Activity 1 Forming a number line from 0 to 1 with fractions
1. Each group will need a deck of bars and each student will need a pencil and a Master
"Fraction Number Line".
 What do you notice about your number line? (It has the numbers 0, 1, and 2. It
has 12 spaces between 0 and 1 and 12 spaces between 1 and 2.)
 Which color of your bars is divided into 12 equal parts? (orange bars)
 You can think of this line between 0 and 1 as a very skinny bar with 12 equal
parts. Instead of shading the parts, we will write fractions beneath the marks on
the line.
To illustrate this, place your transparent Fraction Number Line on the overhead and,
above this, place a transparent orange bar with 2 shaded parts.
 What fraction should we write below the line for this bar and where should it be
written? (2/12 should be placed beneath the mark at the end of the shaded part of
the bar.)
 Write this fraction on your number line.
 Select a different orange bar that is not a zero bar or a whole bar and place it on
your line between 0 and 1. Write the fraction on your line at the end of the
shaded part of your bar. Ask a volunteer to describe the bar they selected. Place
a transparent copy of their bar on the overhead and write its fraction on the line.
Ask students to write all the fractions for the remaining marks between 0 and 1 on their
number line. Then place the transparent orange whole bar below the line and between 0
and 1 and ask:
 Why is the number 1 written for the whole bar? (Because the fraction for a
whole bar equals one.) Leave this whole bar below the number line for the next
activity.
same
materials
Activity 2 Extending the line to the length of two whole bars
Place the transparent orange 2/12 bar between 1 and 2 (see next page) and ask:
 What number should be written below the 2/12 bar? (1
2
) Write this number
12
on the transparent line and ask students to write it on their lines.
 The "1" in this number is for the 1 whole bar and 2/12 is for the shaded
amount of the next bar. We call this number "1 and 2/12".
 This type of number is a mixture of two types of numbers: the whole number
1 and the fraction 2/12. It is called a "mixed number." We can also write 1
and 2/12 as the sum 1 + 2/12.
 Select a different orange bar that is not a zero bar or a whole bar, place it on
your line between 1 and 2 and write the mixed number for the bar. Ask a few
students to describe their bar and give its mixed number. As they do, point to
the marks on the transparent line.
 To avoid crowding on your number line between 1 and 2, we will just write
the mixed numbers: 1 and 2/12; 1 and 4/12; 1 and 6/12; 1 and 8/12; and 1 and
10/12. Point to these marks on the transparent number line and write these
mixed numbers.
 Why is the number 2 written on the number line? (It is at the end of the
second bar and represents a length of 2 whole bars.)
markers
Fraction
Bars
completed
Fraction
Number
Lines
Fraction
Playing
Cards
Game: Number Lines Race
The Fraction Number Lines and markers will be needed to play a racing game.
 Place one marker above the zero point on your number line.
 The bars should be spread out face down.
 Each player in turn takes a bar and the shaded amount tells how far this player's
marker can be moved.
 The first player to reach the number "2" or go beyond is the winner.
Discuss this game and any questions. Ask each student to write their names on the
back of their Fraction Number Line and collect these for use in Lesson 16, Activity
sheet #16A, and Lessons 20 and 22.
Option: Use the deck of Fraction Playing Cards for the Number Line Race.
INDEPENDENT PRACTICE and ASSESSMENT
Activity Sheet #14A Writing fractions and mixed numbers for points on number lines
Activity Sheet #14B Writing fractions and mixed numbers for points on number lines
fractionbars.com Set 2 Fraction Darts (Using mixed numbers to aim darts at balloons)
Grade 4 Activity Sheet #14A
Name:
The first number line below is the number
line you formed in class using the twelfths
bars, but it has some missing numbers.
1. Write the missing fractions and mixed numbers on the line in the markers.
2. This number line was made using the twelfths bars, but it has the fractions for
halves and thirds that equal the fractions for twelfths. Write the missing numerators in
the markers.
3. This number line was made using the twelfths bars, but it has the fractions for
halves and fourths that equal the fractions for twelfths. Write the missing numerators
in the markers.
4. Here is part of the twelfths number line from 2 to 4. Write the missing mixed numbers for
this line on the markers.
Grade 4 Activity Sheet #14B
Name:
For each line, write a fraction or mixed number
on the marker for the given point. Notice that the
first point beyond zero is numbered for each line.
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