Grade 4, Module 5
Core Focus
• Engaging in a range of related activities involving equivalent fractions (finding
common denominators; comparing fractions with related and unrelated denominators)
• Adding fractions using the area model and number line model to solve word problems
• Working with angles
Fractions
• This module provides students with strategies to make sense of equivalent fractions
using models (area, number line and arrow diagrams) rather than memorizing rules.
• Equivalent fractions are the different names for the same fractional amount.
An area model solidifies understanding of the relationships between numerators
and denominators of equivalent fractions.
5.2
Calculating Equivalent Fractions
Wesley wanted to figure out an equivalent fraction for
5
6.
He drew this picture to help.
Wesley realized that if he drew another line horizontally,
he would find an equivalent fraction.
He noticed that splitting the shape that way would double the value of the denominator.
In this lesson, 65 is renamed as 10
when a horizontal line is drawn, doubling the number
12
of pieces, but keeping the same fractional amount.
• When both the numerator and the denominator of a fraction are multiplied by the
same number, as seen in this arrow diagram, an equivalent fraction is created.
Ideas for Home
• Fold paper to prove fractions
are equivalent. Talk about
“fraction families” and how
related fractions are created
by one fold that doubles or
halves the total number of
1 1 1
pieces, e.g. 2 , 4 , 8 , etc.
1 1 1
3 , 6 , 12, etc.
• Encourage your child to
draw pictures of fractions
to make sense of addition.
A common error is to add
across the numerators
and the denominators
6
4
2
(e.g. 10 + 10 = 20 ), drawing
often prevents this error.
Glossary
The bottom number of a
fraction is the denominator,
the total number of equal
parts in the whole.
• Students compare fractions with related and unrelated denominators. When the size
of the fractions are not easy to compare, students find a common denominator
and rename the fraction.
The top number is the
numerator, the count of
equal parts considered.
6
The light gray whole is 6 . The
© ORIGO Education.
•
4
dark gray blocks cover 6 . The
light gray showing is
the whole.
2
6
or
1
3
of
Arrow diagrams show how equivalent fractions with common denominators can be created.
1
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In what different ways could two people split the leftover pie?
Complete this equation to match your thinking.
Grade 4, Module7 5
8
=
+
In what ways could three people split
the leftover pie?
4
2
6
7
== 10, with
• Students also explore addition of fractions, e.g. 10 + 10
+ the+ same
8
denominator
using
an
area
model
or
a
number
line.
Complete this equation to match.
Teena drew dots on
4
10
Ideas for Home
• On a walk, take turns to point
out right, acute and obtuse
angles in your environment
(buildings, billboards, etc.).
of this rectangle.
She then drew stripes on
2
10
of the rectangle.
What fraction of the shape did she draw on in total?
Look at all of the equations you wrote.
Measurement
When you add fractions, what part of the total
+
• Students work with=different
types ofstays
angles
to describe the amount of turn from
the same?
What
part changes?
Why?is described as a fraction
one arm of the angle to the other. The
“amount
of turn”
of a full turn around a circle.
a.
5.10
1. Each large rectangle is one whole. Write fractions to complete true
equations. Shade parts in different colors to show your thinking.
b. to Measure Angles c.
Using a Protractor
One full turn around a point can be divided
into 360 parts.
60
100
110
12
0
50
40
8
=
10
13
0
+
+
15
0
30
+
90
0
8
=
12
80
14
160
20
Each part
is called a degree and
3
=
+
1
5of a full turn.
is 360
70
10
170
ORIGO Stepping Stones 4 • 5.6
180
0
START
350
190
340
200
The symbol ° is used
for degree. One full
turn around a point
is 360°.
114
21
0
33
0
180215
20
3
23
0
0
24
0
250
0
260
270
280
290
30
31
1
2
3
• Or use a paper plate with
two paper “clock hands”
attached at the center with
a brad or tack.
4
• Students name and measure angles by their turns using a protractor: right (90
degrees), obtuse (wider than 90 degrees) or acute (narrower than 90 degrees).
5.115
When the minute hand
goes from 12 to the 3,
it has gone 41 of a
revolution (90 degrees) or
one-quarter ( 41 ) of the way
around, connect this to the
expression “quarter after”
when telling time.
0
In this lesson, students use a 360-dgree protractor to measure and draw angles.
Geometry
When the minute hand on
a clock goes all the way
around from 12 and back
to 12, this is one complete
revolution (or 360 degrees).
22
Look at the protractor on the right.
A protractor is a tool used to measure angles.
© ORIGO Education.
Step Up
• Use an old clock with
moveable hands to name the
various angles formed.
Glossary
right angle
Identifying Acute,
6 Right, and Obtuse 7Angles
A right angle is one-fourth of a full turn.
How many degrees does that equal? How do you know?
Find two right angles in the picture.
Mark them with a blue arc.
acute angle
An acute angle is an angle that is less than a right angle.
Find two acute angles in the picture.
Mark them with a red arc.
An obtuse angle is angle that is greater than a right
angle but less than a half turn.
Find two obtuse angles in the picture.
Mark them with a green arc.
•
obtuse angle
© ORIGO Education.
In this lesson, students identify angles as acute, right or obtuse, and measure with a protractor.
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