Grade 4, Module 11
Core Focus
• Introducing decimal fractions and reviewing common fractions involving tenths
and hundredths
• Introducing decimals with tenths and hundredths (by subdividing squares
and by locating on a number line)
• Writing, comparing, and ordering decimals
• Exploring kilograms/grams, liters/milliliters, and solving word problems involving
these metric measures
Fractions
• Decimal fractions are fractions with denominators of 10, 100, 1000, etc. Decimals
are used in many real-world applications and are often easier to compute than
common fractions. Students connect their understanding of common fractions
to begin learning about decimal fractions using area models.
11.2
Introducing Decimal Fractions
Look at this picture.
Each square is one whole.
What amount is shaded?
What are the different ways you can write
this number without using words?
When fractions have a denominator that is a power of 10
they can easily be written in a place-value chart. Powers
of 10 include numbers such as 10, 100, 1,000 and so on.
A number such as 2
4
10
can be written like this.
Ones
tenths
2
4
The dot between them is called a decimal point. The decimal
point is a mark that identifies the ones place.
A decimal fraction is a
fraction that is written with
no denominator visible. The
position of a digit after the
decimal point tells us what
the invisible denominator is.
Sometimes packets of
food use a decimal point
for weights like 3.5 lb.
Look at the expanders below.
In this
lesson, students are formally introduced to the idea
How would you say the number that each expander shows?
of the decimal point, which is used to separate the whole
A decimal fraction is a
numbers in the ones place from the tenths.
2 4
fraction that is written with
2
4
3.38
no denominator visible. The
position of a digit after the
decimal point tells what the
invisible denominator is.
© ORIGO Education.
• Already familiar withHow
the
decimal
point
when
working with money, students see that
do these
numbers relate
to mixed
numbers
and common fractions?
decimal numbers are actually fractions. The position of a digit after the decimal point
Why do you
need to show the decimal
point fraction is (10, 100, 1000, etc.). E.g. 1.4 (read
tells what the (unwritten)
denominator
of the
2 4
when the expander is completely closed?
4
“one and four tenths”) is the same as 1 10 .
250
ORIGO Stepping Stones 4 • 11.2
7
10
© ORIGO Education.
0
4
1
1 10
A common fraction is
a fraction expressed
by a numerator and a
denominator, not decimally.
9
2 10
1
• Notice decimals in shopping
circulars and in the news.
Analyze the actual meaning
of the numerals and practice
saying them as a decimal
fraction. E.g. a toy priced
$8.99 is “8 ones and 99
hundredths” or “8 ones plus
9 tenths plus 9 hundredths”
or “8 + 0.9 + .09”.
Glossary
Where have you seen numbers written with a decimal point?
I«ve seen a decimal
point used for
prices like $3.99.
Ideas for Home
2 10
2
4
5
3
• Numeral expanders extend to decimal ideas. Students focus on numbers in their
fraction form, their decimal form, their location on the number line (see above),
4
and how they appear on an expander. Here is how 2 10 is represented.
2
4
2
4
2
4
1
Grade 4, Module 11
• Area models and the numeral expander also help students explore and read decimals
46
involving hundredths. This area model shows 100
or .46, read “forty-six hundredths,”
which is the same as 0.4 + .06 ( 4 tenths plus 6 hundredths).
4
6
• To compare and order decimal fractions, students look at the value of the digits
in the greatest place value first, the same way they compare and order whole numbers.
Comparing and Ordering Hundredths
11.7
Student
Anna
Cole
Peta
Franco
Sumi
Amos
2.21
1.84
3.49
1.22
4.10
3.13
Mark the length of Peta’s throw on this number line. How did you figure out the position?
1
2
3
4
5
Was Sumi’s throw longer or shorter than Peta’s? How did you figure it out?
When I said each
number name aloud
it was really easy
to figure it out.
• If you are not familiar with
the metric system, we
encourage you to learn
about it along with your child
by practicing conversions
between kilograms and
grams, liters and millimeters,
and kilometers, meters
and millimeters. Check
conversions using an online
conversion calculator.
• A glass 2-cup measure
typically shows milliliters
(500 ml = .5 liter). Notice these
metric scales and measure
out quantities based in metric:
e.g. 1.5 liters compared to
1.7 liters.
Six students had a throwing competition using a ball made of scrunched paper.
They measured the distance of their throws in meters and fractions of a meter.
This table shows the results.
Distance (m)
Ideas for Home
I looked at the value
of the digit in the
ones place first.
Which
student threw
the greatest
How doline
you know?
In this
lesson,
students
usedistance?
a number
and place-value
Mark and label all the throws on the number line.
understanding to compare and order decimals fractions to the
hundredths
Five students had a throwing competition. They played three rounds.
Step Up place.
• Notice the serving size
listed on a 2-liter soda
bottle (typically 240 ml or
.24, “24 hundredths” of a
liter), estimate using decimal
fractions how much is left after
some has been poured out.
Use this data to help you answer the questions on page 261.
Measurement
Student
Blake
Lela
Kayla
Carter
Luis
Round 1 (m)
3.45
4.06
3.38
3.21
4.30
© ORIGO Education.
• Because the metric system
is a 3.87
base-10
system,
the3.86
conversions
are easier than
Round 2 (m)
4.15
3.50
4.51
Round 3 (m)
in the customary US measurement
Relationships
like
3.18 system.
4.27
3.42
2.97
4.04 1,000 grams =
1 kilogram or 1,000 milliliters = 1 liter are more convenient than 16 ounces = 1 pound
260
or 32 fluid ounces = 1 quart.
ORIGO Stepping Stones 4 • 11.7
• The metric system is ideal for applying concepts of decimal fractions. Because
1
decimals can be used to express fractions of a kilogram, 1 kg can be written
10
as 1.1 kg, and this is also the same as 1 kg + 100 g.
Exploring the Relationship Between Kilograms and Grams
11.8
Look at this balance picture. Each small box has the same mass.
How could you figure out the mass
of each one?
kg
11 kg
Glossary
A kilogram (kg) measures
mass and is the same as
1,000 grams (g).
A kilometer (km) measures
distance and is the same as
1,000 meters (m).
I know that 1,000 grams is
the same mass as 1 kilogram.
Look at this scale.
How could you write the mass shown?
© ORIGO Education.
• On a trip in the car or on the
bus, give your child 2 decimal
fractions (5.6 and 5.9) to
decide which is greater and
tell why.
A liter (L) measures capacity
and is the same as 1,000
milliliters (mL).
1 would write 121 kg or 1.5 kg.
How could you write the same mass in grams?
Complete
these students
statements. explore the relationship between
In this
lesson,
kilograms
and
grams.
1
1
1
2
kg is the same as
g
10
kg is the same as
What are some other kilogram masses that you can say in grams?
Step Up
1. Read the scales carefully. Write each mass in grams.
g
2