Grade 2, Module 11
Core Focus
• Using place value to subtract three-digit numbers
• Exploring and relating multiplication (equal groups) and division (sharing and
repeated subtraction)
Subtraction
• Students have learned and practiced many different mental strategies
for subtraction with both one- and two-digit numbers. Extending the use of these
strategies to three-digit numbers is a natural progression.
• Students may “count back” (e.g. see 334 - 30 and think 334 - 10 - 10 - 10)
or use “place value” (e.g. see 479 - 223 and think 479 - 200 - 20 - 3, or subtract
the hundreds, tens, and ones separately: 400 - 200 and 70 - 20 and 9 - 3 = 256).
Using Place Value to Subtract Two-Digit Numbers
from Three-Digit Numbers
11.2
Hernando scored 285 points in a math game.
He beat his old record by 32 points.
Ideas for Home
• Ask your child to count back
by tens or hundreds from any
two-digit or three-digit number.
Challenge them to count past
100. E.g. starting at 136 and
counting back by tens is “136,
126, 116, 106, 96, 86.”
How could you figure out Hernando’s old record?
251 252 253 254 255 256 257 258 259 260
261 262 263 264 265 266 267 268 269 270
281 282 283 284 285 286 287 288 289 290
I could start with
285 and subtract the
tens, then the ones.
291 292 293 294 295 296 297 298 299 300
285 Ð 30 is 255
255 Ð 2 is 253
271
272 273 274 275 276 277 278 279 280
Jose crossed out blocks to help figure out the difference.
How many hundreds are left over? How many tens? How many ones?
In this
lesson, students examine strategies to
subtract two-digit
numbers from three-digit numbers.
1. Use the chart above to help you figure out each difference.
Step Up
Then write the differences.
© ORIGO Education.
− 12 =
− 21 =
c. 284 −are
23 =
• Number boards, base-10a. 278
blocks,
andb. 292
number
lines
used as aids to make
d. 297 − 32students
=
e. 289
− 14 =
f. 299 − strategies
35 =
the thinking visible and help
connect
their
to the sizes of the
numbers involved.
250
ORIGO Stepping Stones 2 • 11.2
121214
Using a Place-Value Strategy to Subtract
Three-Digit Numbers
11.5
Imagine you had $349 in savings. Which of these items could you buy?
$235
$136
$ 4 80
How could you figure out how much money you would have left over?
Hayden chose the drums. He figured out $349 – $136 like this.
6
200
213 219
30
249
349
300
+100
235
Glossary
A number board looks
similar to a hundred chart (0
to 100), but shows numbers
greater than 100 and/or a
section of numbers between
0 and 100.
100
400
Paige chose the guitar. She figured out $349 – $235 like this.
200
• 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 five
cards and use the digits to
form a subtraction problem
(a two-digit number from a
three-digit number) that is
easy to solve. Discuss the
strategies you use.
+10
300
+4
335 345 349
91
92
93
94
96
97
98
101
102
103
104 105 106
95
107
108 109
99
100
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
400
Which strategy would you use to figure out the difference?
What isthe
anotherunknown
way you could find the
difference?
• Students consider two ways
part
of a problem can be determined.
One method is to start256with the total and count back the part that is known.
The second method is to start with the known part and count on to the total.
© ORIGO Education.
© ORIGO Education.
Why do you think they used different strategies for each problem?
In this
lesson, students explore two different placeImagine you wanted to buy the keyboard.
value
strategies
to subtract
three-digit numbers.
How much
more money would
you need?
ORIGO Stepping Stones 2 • 11.5
121214
1
Grade 2, Module 11
• Subtraction problems in this module involve numbers that do not require regrouping
(regrouping 1 ten as 10 ones, or 1 hundred as 10 tens).
Using a Place-Value Strategy to Solve
Subtraction Problems
11.6
$389
$114
Isabella has $275 in the bank.
Which camera could she buy?
How could you figure out the amount of money that she will have left?
Sumi subtracted on a number line to figure out $275 – $114.
4
10
100
161 165 175
100
275
200
300
Jerome subtracted the digits in each place.
Multiplication
H
T
O
H
T
O
2
7
5
1
1
4
• Earlier in Grade 2, the multiplication concept of equal-sized groups or rows was
2 hundreds subtract 1 hundred is 1 hundred.
7 tens subtract
1 ten is 6
tens.
related to “repeated addition.”
At this
stage,
students should be ready to see, use,
5 ones subtract 4 ones is 1 one.
and understand the word “multiplication” and the multiplication symbol (x).
The difference between 275 and 114 is 161.
Which method do you prefer? Why?
11.7
Introducing the Multiplication Symbol (×)
© ORIGO Education.
Use Jerome’s method to figure out $389 – $275.
Look at this picture of fruit.
How could you describe the
number of bananas?
258
ORIGO Stepping Stones 2 • 11.6
121214
bananas
apples
How many rows of apples are there? How many apples in each row?
How could you figure out the total number of apples?
3 + 3 + 3 + 3 is the same as 4 rows of 3.
What is a short way to write “rows of”?
Where have you seen the multiplication
symbol before?
The symbol for multiplication is ×.
4 rows of 3 is the same as 4 × 3.
Step Up
1. Write the missing numbers.
In this
lesson,
students relate the “rows of” language
a. multiplication symbol. b.
to the
Division
2 rows of 3 melons is
3 rows of 5 onions is
Ideas for Home
• Roll two standard dice for your
child. Tell them one number
is the number of rows and the
other number is the number
in each row. Using pennies or
beans, have your child create
the matching array. Ask them
to describe the array using
language like “3 rows of 4 is
12” and to write the matching
equation (3 x 4 = 12).
• Have your child act out
different sharing or grouping
stories. E.g. say, “If six people
are equally sharing these
24 crayons, how many
crayons will each person
get?” or “I need eight buttons
for each shirt and I have 24
buttons. How many shirts can
I put buttons on?”
Glossary
An array shows equal
groups that are arranged
in equal rows.
2 × 3through
=
×5=
• Two division models are introduced
stories.3 The
“sharing” model is very
c.
d.
familiar to students. They know the total and they know the number of groups. As
they “fair share” the total, students find the number in each group.
2 rows of 4 pears is
3 rows of 4 oranges is
© ORIGO Education.
2 × 4 = a known total,3 ×and
4=
• The “grouping” model also starts with
the number in each group
is known. Students figure
out
how
many
equal
groups
of
that
size can be made
260
from the total. This model may also be called “repeated subtraction.”
ORIGO Stepping Stones 2 • 11.7
3 rows of 4 oranges is
3×4=
121214
• Relating multiplication and division situations (e.g. 4 groups of 2 is 8, so 8 shared by
4 is 2) aids understanding and development of both concepts.
11.10
Relating Multiplication and Division (Sharing)
What does this sharing mat show?
Imagine the pieces of gold are moved together
into the large space below.
How many pieces are there in total?
© ORIGO Education.
What numbers could you write in this sentence
to describe the groups?
groups of
is
Imagine the pieces of gold are shared equally
into the small boxes below.
How many pieces are in each share?
What numbers could you write in this sentence
to describe the sharing?
shared by
Step Up
is
1. Imagine the gold pieces are moved into the space below.
Complete the sentences.
2