NUMBER LINES FOR TENTHS 4.NF.6
Forming Number Lines for Decimals and Mixed Decimals
Purpose:
To connect a visual model for tenths to a decimal number line with tenths
Materials:
Decimal Squares, Blank Tenths Number Line activity sheet (attached), and pencils
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Forming a decimal number line with tenths from 0 to 1
Decimal
Squares
Blank
Tenths
Number
Lines
pencils
1. Students need decimal squares and copies of the Blank Tenths Number Line.
 What do you notice about your number line ? (It has the numbers 0, 1.0, 2.0,
and 3.0 and 10 spaces between pairs of numbers.)
 Select a red decimal square for tenths and place it
above the number line so that the shading starts
above the point for 0 and the lines of the square
line up with the lines on the number line. Then
write the decimal for the shaded amount of the
square below the matching point on the number
line. (The square for .3 is illustrated here.)
 Select a different red square, place it on the number line, and write its decimal
beneath the number line. Continue writing the decimals for the nine points between
0 and 1.0 on the number line.
 The next point on the number has the number 1.0.
Why do we write 1.0 rather than .10? (Because 1.0
is for one whole square, that is, a square that is all
shaded.) To see why .10 is not correct for this point
on the number line, look at a green hundredths
square with 10 parts shaded. The decimal for this
square is equal to what decimal from the red
squares? (.10 equals .1)
.10 = .1
paperclips
 Use your number line to measure the length of a paperclip or a piece of chalk. Place
the end of the paperclip or chalk at the 0 point and determine the number on the line
for the point closest to the end of the paperclip. (In this example the length of the
paperclip is about halfway between the marks for .4 and .5, so it is customary to
round up to the greater number and say the paperclip has a length of .5 unit.)
Activity 2 Extending the decimal line with tenths beyond 1.0
 We will extend the numbers on your number line so you can measure greater lengths.
Decimal
Squares
Blank Tenths
Number Lines
pencils
 Select any red square for tenths and place it
above your number line so that the left edge is
above the point for 1.0 and write the mixed
decimal below the line that matches the end of
the shading on the bar. For example, if you
select the square for .4, then 1.4 should be
written below the line. The number 1.4 is called
a mixed decimal because it is a mixture of the
whole number 1 and the decimal .4
 If we use the red square with 9 out of 10 parts shaded, what is the mixed
decimal that should be written between 1.0 and 2.0? (1.9)
 Why are the points on the number line between 1.0 and 2.0 labeled with mixed
decimals whose whole number part is 1? (Because they represent lengths that are
1 plus a decimal from a tenths decimal square.)
 Continue to write the mixed decimals for the marks on the line between 1.0 and 2.0.
 Why is the number 2.0 written on the number line? (It represents 2 whole squares
and zero tenths.)
 Use your number line to measure the length of a pencil or pen to the nearest mark
on the line. (Discuss a few examples. This pencil has a length of 1.6 units.)

Continue writing the mixed decimals for the marks between 2.0 and 3.0. This is the
beginning of a number line. Number lines can be extended indefinitely to the right
for positive numbers and to the left of 0 for negative numbers.
 Use your number line to measure the height of a standard sheet of paper. (The
height is 2.8 units and the width is 2.2 units. Note: The number lines can be cut out
along the dashed lines and students can write their names on back. Students will
need these numbers lines in one of the two activity sheets below.
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 4.NF.6 #1 and #2
decimalsquares.com Decimal Darts (Typing mixed decimals to aim darts at balloons)