Grade 5, Module 7
Core Focus
•
•
•
•
Concepts and strategies for subtracting decimal fractions — tenths and hundredths
Introducing the coordinate plane and plotting ordered pairs
Recognizing relationships in numeric patterns and plotting these ordered pairs
Using the coordinate plane in solving problems
Subtracting Decimal Fractions
• Students use their ideas and skills with whole number subtraction to subtract
decimal fractions. Their strategies range from drawing jumps on a number line
to using the standard written algorithm.
• The lessons provide an excellent reminder of how everything in mathematics
is connected. Students recognize and take advantage of connections between
known strategies (whole number subtraction) and new ideas (decimal subtraction).
Subtracting Decimal Fractions (Tenths or Hundredths)
7.1
Layla is planning a hike. How much farther
is Springwood Falls than Hard Rock Valley?
Hard Rock Valley 1.2 miles
Springwood Falls is more
than double the distance.
Springwood Falls 3.9 miles
-0.2
Damon drew jumps on this number line
to figure out the exact difference.
-1
2.9
2.7
3.9
What steps did he follow? What is another way to find the difference?
In Lesson 1, students explore a variety of strategies to subtract tenths from tenths,
Layla decides to buy some supplies.
and hundredths
from
hundredths.
How would you
figure
out the difference in cost between these two items?
Janice figured it out like this.
2.45
$
• Just as with whole numbers,
students learn to subtract like quantities
from like
$7.99 − $2.45
$7.99 − $2they
= $5.99 must subtract tenths from tenths and hundredths
quantities. In other words,
$5.99 − 40¢ = $5.59
$7.99
$5.59 − 5¢ = $5.54
from hundredths.
• One strategy to ensure students are subtracting like quantities is to rewrite decimal
fractions as common
fractions
with either 10 or 100 as the denominator.
1. Draw jumps on the number line to figure out each difference.
Step Up
What steps did Janice follow? What is another way to find the difference?
a.
Using
Written Methods to Subtract Decimal Fractions
7.3 6.5 − 2.3
=
Ideas for Home
• To practice subtracting
tenths, play this game with
your child. Both players
start with the number 10.
Roll a number cube and
decide whether to subtract
the number shown as a
whole number or as a tenth.
The goal is to get as close
to zero as possible after
ten rounds. To practice
subtracting hundredths,
play the same game starting
with the number 1. Players
decide to subtract the
number shown as a tenth or
a hundredth with the same
goal of reaching zero.
Glossary
Students may use a written
method like the standard
written algorithm shown
below to make sure they are
subtracting like quantities.
How could you figure out the difference in mass
b.
between
these two dogs?
T
© ORIGO Education.
7.8 − 4.1 =
It must be about 3 kg
because 17 14 = 3.
152
ORIGO Stepping Stones 5 • 7.1
14.2 kg
© ORIGO Education.
These students figured it out like this.
Kylie
1 7. 65
− 0.20
1 7 . 45
− 1 4.00
3.45
65
100
−
20
100
=
45
100
45
100
t
6
12
h
1 7 . 2 5
5 . 6 0
1 1 . 6 5
17.65 kg
Megan
1 7. 65
− 1 4.2
3.45
7
11
8 . 1
− 0 . 8
7 . 3
Difference is 3
What are the steps in each method? Whose method do you prefer? Why?
In LessonWhat
3, students
use
variety
written methods to subtract decimal fractions.
other way could
youa
calculate
the of
difference?
How could you figure out the difference in cost between these two items?
$8.6
270815
Juan
17.65 − 14.2
17 − 14 = 3
−
O
8
5
$3.2
The numbers are a
bit ÒmessyÓ so I would
use a written method.
1
Grade 5, Module 7
• Just as with whole numbers, students may need to regroup before they can
subtract. For example, for 8.1 − 0.8, students cannot subtract 8 tenths from 1 tenth,
so they regroup exactly as they do in the standard subtraction algorithm for whole
numbers (as shown in the example on the side).
• Students compare the different methods for subtracting decimal fractions
to determine which method they prefer and explain why.
Subtracting Decimal Fractions Involving Hundredths
(Decomposing Tenths)
7.5
Kimie jumped 4.85 meters in the long jump event at school.
Logan jumped 0.97 meters less than Kimie. Mia jumped 0.29 meters less than Kimie.
How could you figure out the length of Logan’s jump?
-1
I would count back
and adjust my
answer like this.
+0.03
3.85
3.88
These three written methods were used to figure out the length of Mia’s jump.
What are the steps for each method? Complete the calculations.
4.85 − 0.29
4−0=4
4.76 − 0.20 =
−
7
4
8
5
0
2
9
• Students begin by learning about the coordinate plane — a rectangular grid on
which they graph ordered pairs (x, y) of numbers. Graphing the ordered pair (3, 2),
for example, students begin in the bottom left corner (the origin) and move three
160
units to the right, then 2 units up, then draw a point.
• Some everyday examples
of number patterns can be
found in cooking ( 23 cup of
water to 1 cup of pancake
mix, 1 31 cups of water to 2
cups of pancake mix, and
so on) and shopping (three
items on sale for $2, six
items on sale for $4 and so
on). Look for other examples
with your child.
• As students graph points on the coordinate plane, they see patterns among pairs
of numbers and use this to solve problems.
Glossary
85
100
Difference is
−
100
=
100
Difference is
Which method do you prefer? Why?
In Lesson 5, students
subtract decimal fractions that require students to regroup
1. Paige jumped 1.80 meters short of this long-jump record.
Step Up
Record
ones for tenths.
5.5
4m
Write a number sentence to show how far Paige jumped.
Then draw jumps on the number line to show how you figured it out.
Algebra: Ordered Pairs and Patterns
=
© ORIGO Education.
−
ORIGO Stepping Stones 5 • 7.5
7.10
Generating and Graphing Ordered Pairs
from Two Numerical Patterns
This growing pattern was made with toothpicks.
1
2
3
4
Number of toothpicks
What do you notice?
What patterns do you see?
© ORIGO Education.
Complete this table to match the pattern.
Picture number
1
2
Number of squares
1
2
Number of toothpicks
4
7
3
4
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
What ordered pairs should they write to show the pattern?
The ordered pair for point Q
on the coordinate plane below
is (4,3).
0
0 1 2 3 4 5 6 7 8
Number of squares
Marking
ordered pairsidentify
on a coordinate
plane
In Lesson
10, students
relationships
between numerical patterns and graph
is called graphing or plotting.
the ordered
pairs of related numbers.
How would you graph the ordered pairs on the coordinate plane? 30
28
Step Up
1. Look at this pattern
made with toothpicks.
a. Complete the table. If necessary,
draw more pictures on scrap paper.
270815
• When shopping, compare
the prices of two similar
items by asking, “How much
more is this item than the
other?” Listen as your child
describes their strategy.
They may count back
by subtracting the parts
(whole numbers, tenths,
hundredths), or count on
to find the difference.
• Many maps of roads or
cities use ordered pairs to
name locations (often a
letter and a numeral).
Practice finding locations
by first moving horizontally
and then moving vertically.
4.85
Draw jumps on this number line to show how you could figure out the length of Mia’s jump.
4.85 − 0.09 = 4.76
Ideas for Home
Picture number
1
2
3
26
24
1
2
4
3
5
22
20
2