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U n t er r i ch t spl a n
Ad d ing 2 -Dig it Numb e rs b y
R e g ro up ing − Int ro d uc t io n To
St and ard Ad d it io n Al g o rit hm
Altersgruppe: 2nd Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.21, 2.6a,
2.6b, 3 .4
Virginia - Mathematics Standards of Learning (2016): 2.6.a, 2.6.b,
3 .3 .a
Fairfax County Public Schools Program of Studies: 2.21.a.1,
2.21.a.2, 2.6.a.1, 2.6.b.1, 2.6.b.2, 2.6.b.3 , 2.6.b.4 , 3 .4 .a.3 ,
3 .4 .a.5 , 3 .4 .a.7
Online-Ressourcen: M ake C hange
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
Mat h
Worksheet
Pract ice
5
10
10
10
10
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 regrouping.
P r ac t i c e adding 2-digit numbers.
L e ar n to add with regrouping.
De v e l o p basic understanding of place value.
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Closing
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Ope ni ng | 5 min
Bring to class ten large cards and twenty small cards. On each large card
write the number 10 and on each small card write the number 1. Show
students the cards.
S ay : I’m holding large cards, each one of them represents the
number 10, and small cards, each one of them represents the number
1.
Make a group of two large cards and six small cards and show them to the
class.
A sk : What number does this group of cards represent?
Two large cards represent the number 20, and six small cards
represent the number 6, together the cards represent the number
26.
In one hand hold two large cards and in the other hold twenty small cards.
A sk : In one hand I grouped two cards of 10, and in the other I
grouped twenty cards of one. In which hand is the represented
number bigger?
Although I have more of the 1 cards , the numbers represented in
both hands are equal. Two cards of 10 represent the number 20
and twenty cards of 1 also represent the number 20. Illustrating
we can represent the number 20 in more than one way.
Write on the board:
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A sk : How can we represent the number 45?
In our case there are only 20 cards of 1, so we have two options
to represent the number 45. First option - 4 cards of 10 and 5
cards of 1. Second option - 3 cards of 10 and 15 cards of 1.
Demonstrate the two options using the cards, while explaining.
A sk : If we had unlimited cards of 1 and 10, what would be the other
options for representing the number 45?
If we had unlimited cards we could represent 45 in three other
forms:
45 cards of 1.
1 card of 10 and 35 cards of 1.
2 cards of 10 and 25 card.
T e ac he r pr e se nt s M at h game : M ake C hange - A dd 2- Di gi t
N umbe r s | 10 min
Using Preset mode, and a projector, present Matific ’s episode M a k e
C h a n g e - A d d 2 - Dig it N u m b e r s to the class.
This episode practices addition of 2-digit numbers by mimicking the longaddition algorithm. Each addend is represented by chips of 10 and 1 units.
Using the change machine you can exchange ten chips of 1 for a single chip
of 10, or ten chips of 10 by a single chip of 100, and vice versa.
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E x a m p le :
S ay : Each chip has a value of 1 or 10, so a ten chips of 1 (the red
chip) is equal to one chip of 10 (the yellow chip).
Demonstrate how the chips can be moved around the table and arranged into
groups. Move all the yellow chips to the left side of the table and all the red
chips to the right side of the table.
A sk : What number does the yellow group represent?
There are 5 chips of 10, so the yellow group represents the
number 50.
A sk : What number does the red group represent?
There are 12 chips of 1, so the red group represents the number
12.
Group four 10-chips and three 1-chips together.
A sk : We have four tens and three ones – what number is
represented here?
The number represented is 43.
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A sk : What group of chips can we create to represent the number
21?
In our case we can create a group of two 10- chips and one 1- chip
or one 10- chip and eleven 1- chips.
Demonstrate, using the computer, each of the proposed options to create
the number 21.
A sk : If we had unlimited chips of 1 and 10, what would be the other
options for representing the number 21?
If we had unlimited chips we could represent 21 in one other
option - by using twenty one 1-chips.
S ay : Note how the two drawers on the right side work. If we put ten
1-chips into the right drawer and click on the drawer, the left drawer
will open and give us one 10-chip, and vice versa, if we put one 10chip into the left drawer, the right drawer will give us ten 1-chips.
Explain that the drawer closes only if all the holes are occupied by
chips of the same value.
Demonstrate how the drawers can be used to convert one 10-chip into ten 1value chips: drag a 10-chip into the left, and close it. The right drawer will then
open, containing ten 1-value chips. Note: when using a PC, there is no need to
drag chips into holes. Just double-click any chip, and it will jump into one of
the vacant holes.
S ay : When representing a number, we always seek to use as few
chips as possible (this will motivate students to practice grouping
and ungrouping operations) because eventually this is how we will
write our numbers, according to the decimal number system. Each
place in the decimal number system can hold one digit in the range
of 0-9. For example, if we wish to represent the number 43 we
prefer to use four 10-chips and three 1-value chips rather than to
use three 10-chips and thirteen 1-value chips (13 1-chips cannot
represent a digit in the decimal number system).
A sk : What is the connection between the addition equation written
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at the bottom of the screen and the visual scene?
Each of the addends is represented by a group of chips.
S ay : Let’s order the chips so that they will help us complete the
equation.
Convert ten 1-chips into one 10-chip. Now we have six 10-chips and two 1value chips.
E x a m p le :
A sk : What number do the chips represent?
Six 10- chips represents 60. Two 1- chips represents 2. Together
the chips represent the number 62. So 35 + 27 = 62.
S ay : In addition the order of the addends, in the exercise, does not
matter. That’s why we can add the tens and the ones separately. If
we get more than 9 ones, we should regroup ten ones into one 10
using the drawers.
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S t ude nt s pr ac t i c e M at h game : M ake C hange - A dd 2- Di gi t
N umbe r s | 10 min
Have students play M a k e C h a n g e - A d d 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 problems students faced while working individually.
Ask the class for responses regarding how they dealt with any issues their
classmates brought up.
Use the cards you brought to class (which you used on the opening). Invite
three students to play a game. Give the first two students seven 10-cards
and fifteen 1- cards together. Give the third student all the remaining cards.
Ask the first student to put, on the table, cards that represent the number 17.
A sk : What is the most efficient way of doing so?
The most efficient way is by using one 10-card and seven 1-cards.
Ask the second student to put on the table cards that represent the number
34.
A sk : What is the most efficient way of doing so?
The most efficient way is by using three 10-cards and four 1cards.
Announce that we want to calculate the total number represented by the
cards on the table. Point out that the third student can play a similar role as
the drawers in the game: ask him/her to collect ten 1-cards from the table
and replace them with a single 10-card.
A sk : Has the total number represented on the table changed?
No, it hasn’t. Ten ones equals exactly one ten.
Together, with the class, calculate the total number represented by the cards
on the table. Emphasize that this number is the sum of the two numbers the
first two students originally placed on the table.
Repeat the game for several similar rounds with different students.
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M at h W o r kshe e t P r ac t i c e : A ddi ng W i t ho ut R e gr o upi ng Up T o 100 | 10 min
Have the students work on the following worksheets:
1. A d d in g W it h o u t R e g r o u p in g - Up T o 1 0 0
2. A d d in g w it h R e g r o u p in g - Up t o 1 0 0
3. A d d in g T e n s - Up t o 1 0 0
Advanced students can proceed to the next worksheets:
1. A d d in g W it h Un k n o w n s - Up T o 1 0 0
2. R e la t in g A d d it io n A n d S u b t r a c t io n - Up T o 1 0 0 - L e v e l 1
Circulate, answering questions as necessary.
C l o si ng | 4 min
Ask each student to write down the steps they would take, using the
episode’s method of adding 68 and 15.
When the students are done writing, review their responses. Write
on the board and discuss any questions students may have:
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