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U n t er r i ch t spl a n
Sub t rac t 2 -Dig it Numb e rs Us ing
Ung ro up ing , Int ro d uc t io n t o
St and ard Sub t rac t io n Al g o rit hm
Altersgruppe: 2nd Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.21, 2.7 a,
2.7 b
Virginia - Mathematics Standards of Learning (2016): 2.6.a, 2.6.b
Fairfax County Public Schools Program of Studies: 2.21.a.1,
2.21.a.2, 2.21.a.3 , 2.7 .a.1, 2.7 .b.1
Online-Ressourcen: M ake C hange
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
Mat h
Worksheet
Pract ice
5
12
12
10
6
4
min
min
min
min
min
min
M at h Obj e c t i v e s
E x pe r i e nc e ungroup ten.
P r ac t i c e subtract 2-digit numbers.
L e ar n to subtract using ungroup.
De v e l o p a better understanding of place value.
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Closing
2
Ope ni ng | 5 min
Bring to class 10 big cards, each labeled with the number ”10”, and 30 small
cards, each labeled with the number “1”. Show students the cards.
S ay : I have big cards each of which represents the number 10 and
small cards, each of which represent the number 1.
Group together 2 big cards and 4 small cards, and show the cards to
students.
A sk : What number does this group of cards represent?
2 big cards represent the number 20 and 4 small cards represent
the number 4, so together they represent the number 24.
Hold in one hand 2 big cards and in the other hand 20 small cards, and show
them to students.
A sk : In my right hand I hold 2 big cards of 10, and in my left hand I
hold 20 small cards of 1. In which hand is the number represented
bigger?
The number represented in both hands is the same, 2 cards of 10
represent the number 20, and 20 cards of 1 represent the number
20 as well. Therefore, we can represent the number 20 in 2
different ways.
A sk : How can we represent the number 37?
Because we have only 30 cards of 1, we can represent the number
37 in 3 different ways:
3 cards of 10 and 7 cards of 1.
2 cards of 10 and 17 cards of 1.
1 card of 10 and 27 cards of 1.
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Demonstrate these 3 methods, using the cards, to illustrate the explanation.
S ay : When we represent a number, we will want to use a method
which allows us to utilize the smallest number of cards. That’s why,
when we represent the number 37, we prefer to so by using option 1,
because this way is easier and simpler to count.
During the explanation, show that the number of cards in option 1 is the
smallest among all options.
T e ac he r pr e se nt s M at h game : M ake C hange - S ubt r ac t 2Di gi t N umbe r s | 12 min
Using Preset mode, and a projector, present Matific ’s episode M a k e
C h a n g e - S u b t r a c t 2 - Dig it N u m b e r s to the class.
This episode practices the subtraction of 2-digit numbers by mimicking the
subtraction algorithm. The minuend is represented by coins in units of 10 and
1. You can perform the operation by moving to the side a value of coins
indicated by the subtrahend. For regrouping, you can exchange ten coins for
1 single coin of 10, or ten coins of 10 with a single coin of 100, using a
change machine.
E x a m p le :
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S ay : Each chip has a value of 1 or 10, so 10 chips of 1 (the red chip)
equals 1 chip of 10 (the yellow chip).
Demonstrate how the chips can be moved around and arranged in groups.
Rearrange the chips by moving all the red chips to the right side of the table.
A sk : What number represents the yellow chips at the left side of
the table?
At the left side of the table there are 2 yellow chips, each
represents the number 10, so together they represent the number
20.
A sk : What number represents the red chips at the right side of the
table?
At the right side of the table there are 3 red chips, each
represents the number 1, so together they represent the number
3.
Group 1 yellow chip with 2 red chips.
A sk : Which number is represented with the group created?
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We have 1 ten and 2 ones, so the value is 12. The digit 1 in the
number 12 represents the 1 ten, and the digit 2 in the number 12
represents 2 ones.
S ay : Observe how to use the drawer. If we drag a 10-value chip into
the left-hand drawer and close it, the right-hand drawer will open,
containing ten 1-value chips, and vice versa. If we drag ten 1-value
chips into the right-hand drawer and close it, the left-hand drawer
will then open, containing one 10-value chip.
Demonstrate, during the explanation, how to use the drawer to convert a 10value chip into ten 1-value chips, and vice versa.
S ay : Pay attention that the drawer only closes if all slots are filled
with chips of the same value.
A sk : How can we represent the number 14?
We can represent the number 14 in two ways:
Group 1 chip of 10 and 4 chips of 1.
Group 14 chips of 1.
Demonstrate these 2 ways of representing 14, using the chips.
A sk : Does the number represented change between these two
methods?
The number stays the same (14), only its presentation mode has
changed.
S ay : When we represent a number, we prefer to use the lowest
number of chips as possible. For example, if we represent the
number 14 we will want to use one 10-chip and four 1-chips, rather
than using 14 1-chips, because this method is more convenient.
A sk : What is the connection between the chips that are placed on
the table, and the subtraction equation on the bottom of the
screen?
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The number represented on the table is the number to be
subtracted from (the minuend). In order to complete the equation
we can use the drawer.
A sk : How do we subtract 5 from the 23 chips?
Hint at understanding that one 10-value chip must first be
converted to 10 1-chips, making it possible to remove 5, 1-value
chips, from the group.
Convert one yellow chip into 10 red chips. Group together the 13 red chips
and the 1 yellow chip at the center of the table. Now move aside 5, 1-value
chips.
A sk : How many chips are left in the center of the table?
8 red chips and 1 yellow chip.
A sk : What number do these chips represent?
18.
Write on the board the equation representing the situation: 23 - 5 = 18
S ay : Notice that when we subtract a number (subtrahend), whose
number of ones is greater than the number of ones in the number to
be subtracted from (minuend), we will have to convert 1 ten into 10
ones.
S t ude nt s pr ac t i c e M at h game : M ake C hange - S ubt r ac t 2Di gi t N umbe r s | 12 min
Have students play M a k e C h a n g e - S u b t r a c t 2 - Dig it N u m b e r s on
their personal devices.
Circulate among them answering questions.
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C l ass di sc ussi o n | 10 min
Discuss any challenges students faced while working individually.
Ask the class for responses relating how they dealt with common issues
their classmates proposed.
Use the cards you brought to class.
Invite two students to participate a short game. Hand the first student 15
cards of 1, and 5 cards of 10, and the other student 15 cards of 1, and 3
cards of 10.
Ask the first student to put on the table cards that represents the number 23.
A sk : What is the most efficient way to do so?
2 10-value cards and 3 1-value cards, we could also use 1 10-value
card, and 13 1-value cards, or 23 1-value cards, but these two
ways are less efficient.
S ay : Now we want to take away 8 from the table. Point out that the
second student can utilize the drawers, as illustrated in the episode
just played.
Ask the second student to exchange one 10-value card on the table with ten
1-value cards.
A sk : Has the total number represented on the table changed?
It hasn’t, because 10 ones equals the same as 1 ten. On the table
now, there are 1 10-value card- and 13 1-value cards, which
represents the number 23.
Together with the class, take away 8, 1-value cards, from the table.
S ay : The number represented on the table is the difference
between 23 and 8.
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A sk : There is one ten and 5 ones on the table – how much is that?
The number represented on the table is 15.
Write on the board the equation that represent the situation: 23 - 8 = 15
Repeat the game for two or three more rounds, with different students.
M at h W o r kshe e t P r ac t i c e : S ubt r ac t i ng w i t ho ut
R e gr o upi ng - Up t o 100 | 6 min
Have the students work on the following worksheets:
1. S u b t r a c t in g w it h o u t R e g r o u p in g - Up t o 1 0 0
2. S u b t r a c t in g w it h R e g r o u p in g - Up t o 1 0 0
Advanced students can proceed to the next worksheets:
1. S u b t r a c t in g w it h Un k n o w n s - Un k n o w n M in u e n d u p t o 1 0 0
2. S u b t r a c t in g w it h Un k n o w n s - Un k n o w n S u b t r a h e n d u p t o
1 00
3. S u b t r a c t in g w it h Un k n o w n s - Up t o 1 0 0
4. S u b t r a c t io n - 2 S u b t r a h e n d s u p t o 1 0 0
Circulate, answering questions as necessary.
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C l o si ng | 4 min
Ask each student to write down the steps they would take, using the
episodes method of subtracting, for subtracting 18 from 32.
When students are done writing, review their responses. Write on
the board and discuss any questions students may have:
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