Grade 5, Module 5
Core Focus
• Comparing, ordering, rounding and adding decimal fractions
• Describing polygons by their angles
• Identifying parallelograms and exploring categories of quadrilaterals and triangles
Decimal Fractions
• Students compare and order decimal fractions with up to three decimal places
(tenths, hundredths, and thousandths).
• Thinking about where the decimal fractions would be on a number line helps when
comparing, as does imagining a picture (a square divided into tenths and hundredths).
• Students use place value to compare like quantities. Comparing 0.6 and 0.583 as
thousandths (i.e. 0.600 and 0.583) helps students see that 0.6 is greater than 0.583.
Rounding Thousandths
5.3
On this number line, the distance between each whole number is one whole.
Where would you show this decimal fraction on the number line?
0
1.391
1
2
What is the nearest whole number? How do you know?
Mark the same decimal fraction on this number line. Be as accurate as possible.
0
1
2
What is the nearest tenth? How do you know?
1.391 is very close to 1.4.
The number line below shows thousandths. What numbers are between 1.39 and 1.40?
1.38
1.39
1.40
What hundredth is nearest to 1.391? How did you decide?
In this lesson, students round decimal fractions with three decimal
1. Draw an arrow to show the approximate position of each number
Up nearest
placesStep
to the
or number.
hundredth.
on the whole
number line.number,
Then write the tenth,
nearest whole
a. 0.257
b. 0.401
c. 0.730
d. 1.010
e. 1.620
© ORIGO Education.
• Students extend their skills to adding decimal fractions building on what they
already know about adding like quantities to like quantities, no matter what sort
of numbers are being added.
0
1
2
108
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ORIGO Stepping Stones 5 • 5.3
5.6
Adding Decimal Fractions (with Regrouping)
These students threw a shot put twice and added the distances.
1st Throw
2nd Throw
Andre
3.5 m
3.7 m
Lilly
3.09 m
3.45 m
Jacob
4.2 m
3.92 m
Total
m
m
m
Ideas for Home
• Create a set of cards
showing the digits 0–9,
shuffle the cards and place
them face down. Take turns
with your child to draw three
cards and use the digits in
order of selection to write a
decimal fraction in the form
0.___ ___ ___. Compare the
two decimal fractions to see
which is greater. Be sure to
ask how they know.
• Using the same digit cards,
take five cards and create
a decimal fraction addition
sentence that is as close
to 10 as possible (over or
under). E.g. with the digits
1, 2, 5, 6, and 9, an addition
sentence could be
9.6 + 0.521 = 11.21. Take turns
with your child to see who
can get the closest.
• Shopping for food or ordering
in a restaurant is a natural
time to practice addition with
decimal fractions. Ask your
child to mentally add the
price of two items. Ask which
strategy they used.
How could you figure out the total distance of Andre’s throws?
How could you figure out the total distance of Lilly’s throws?
© ORIGO Education.
Carlos figured out the total
like this.
3+3=6
0.0 + 0.4 = 0.4
0.09 + 0.05 = 0.1 4
6.54
3.09 + 3.45
3
9
100
+ 3 45 = 6 54
100
100
Mary figured out 3.10 + 3.44.
She knew it would give the same total.
What steps does each person follow? Which strategy do you prefer? Why?
Use the strategy you like best to figure out the total length of Jacob’s throws.
In this lesson,
students
place value to add tenths to tenths,
Who threw the
greatest total use
distance?
hundredths to hundredths, and tenths to hundredths.
Step Up
060815
Amber figured it out like this.
3.09 + 3.45
1. Figure out each total. Show your thinking.
a.
b.
3.6 + 4.8 =
c.
2.65 + 3.18 =
5.71 + 2.63 =
1
Grade 5, Module 5
• The written procedure for adding decimal fractions “lining up the decimal places”
ensures students are adding like quantities (tenths with tenths, hundredths with
hundredths, etc.).
Using a Written Method to Add Two Decimal Fractions
5.7
These two packages were weighed in kilograms.
Estimate the mass of the two packages together.
5.7
6.8 kg
g
2k
Ideas for Home
• Help your child identify
parallelograms in your home,
neighborhood, or town. Some
examples might include floor
tiles, business logos, stripes
in a parking lot, or patterns of
windows on a building.
How could you figure out the exact mass of the two packages?
These numbers are too messy to add in
my head. I need to write them down.
Glossary
A numeral expander
names the value of each
digit in a decimal fraction
(tenths, hundredths,
thousandths).
Cody used the standard addition algorithm to figure out the total. What steps did he follow?
T
O
t
1
6
+
1
h
8
5
7
2
2
5
2
0
In this
lesson,
students
add
with different numbers
1. Calculate the
total decimal
mass of each fractions
pair of packages.
Step
Up
of places.
a.
b.
8.34 kg
Geometry
3.25 kg
4
3
9
c.
12
14.08 kg
kg
.47
6.
5
kg
12.81 kg
Students think about the
place value of each digit in a
decimal fraction.
© ORIGO Education.
• Students extend theirT skills
with
and
triangles
and quadrilaterals
O
t
h identifying
T
O
t
h naming
T
O
t
h
1
1
8
3
4
1
2
4
7
2
8
according to a shape’s angles, length of sides, and other important properties (such
3
2
5
4
0
8
6
5
+
+ 1
+
as parallel sides).
• Students explore relationships among different types of quadrilaterals, such
116
as parallelograms
(two pairs of parallel sides), rectangles (parallelograms with right
angles), rhombuses (parallelograms with all sides the same length), and squares
(a special type of rectangle with all sides the same length).
3.76 + 2.15
is the same as
ORIGO Stepping Stones 5 • 5.7
180215
>
parallelogram
>>
>
Identifying Parallelograms
Think about the quadrilaterals you know.
>
Right angles can be
shown using this symbol.
>>
What do you know about the angles of rectangles?
What do you know about the sides of rhombuses?
>>
5.10
A four-sided polygon is
called a quadrilateral.
>>
• A “family tree” is used to illustrate how the various quadrilaterals are related to
each other because many of the categories overlap. E.g. a rectangle is also both a
quadrilateral and a parallelogram.
___ ones ___ tenths ___ hundredths
rhombus
>
A square is a type of rectangle and also a type of rhombus. Why?
>>
Parallelograms are quadrilaterals that have two pairs of parallel sides.
What are all the ways of describing each shape below?
What do you think the arrows mean?
>>
>>
>>
>>
>>
>
>>
>
>
>
© ORIGO Education.
>
>
>>
>
>
Step Up
rectangle
>
>
square
Cut out the shapes from the support page.
In this lesson, students examine a defining feature of parallelograms.
a. Paste the parallelograms in the space below.
2
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