Download Subtract 3 Digit Numbers

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U n t er r i ch t spl a n
Int ro d uc t io n To The St and ard
Sub t rac t io n Al g o rit hm - Sub t rac t
3 Dig it Numb e rs
Altersgruppe: 2nd Gr ade , 3 r d Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.21, 2.7 a,
2.7 b, 2.8, 3 .4
Virginia - Mathematics Standards of Learning (2016): 2.6.a, 2.6.b,
3 .3 .a, 3 .3 .b
Fairfax County Public Schools Program of Studies: 2.21.a.1,
2.21.a.2, 2.21.a.3 , 2.7 .a.2, 2.7 .b.5 , 2.8.a.4 , 3 .4 .a.3 , 3 .4 .a.6,
3 .4 .a.7
Online-Ressourcen: M ake C hange
T eacher
present s
Mat h game
St udent s
pract ice
Mat h game
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Opening
Class
discussion
Mat h
Worksheet
Pract ice
Closing
M at h Obj e c t i v e s
E x pe r i e nc e visual models of subtracting 3 digit numbers.
P r ac t i c e subtraction of 3 digit numbers.
L e ar n to convert one hundred to ten-tens, and one-ten to tenones.
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De v e l o p understanding of the base 10 representation.
Ope ni ng | 1 min
S ay : Today we will talk about subtracting 3 digit numbers.
T e ac he r pr e se nt s M at h game : M ake C hange - S ubt r ac t :
M ul t i pl e R e gr o upi ng | 8 min
Present Matific ’s episode M a k e C h a n g e - S u b t r a c t : M u lt ip le
R e g r o u p in g to the class, using the projector.
This episode practices subtraction of 3-digit numbers by mimicking the
subtraction algorithm. The minuend is represented by coins of 100, 10 and 1
units. 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 by a single coin of 10, or ten coins of 10 by a single coin of 100, using a
change machine.
E x a m p le :
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Go over the different types of chips and explain their values. Demonstrate
how the chips can be moved around and arranged in groups. Rearrange the
chips.
First, group some chips together (for example, take 4 10-value chips and 3 1value chips).
A sk : What number do they represent? How do you know?
We have four tens, and three ones, so the number represented is
43.
A sk : How would we represent 23?
The number 23 is composed of two tens and three ones, so we
represent it by two 10-value chips and 3 1-value chips.
Demonstrate how to use the drawers to convert a large-value chip
into 10 smaller-value chips: drag a 100-value (or 10-value) chip into
the left-hand drawer, and close it. The right-hand drawer will then
open, containing ten 10-value (or 1-value) chips.
Demonstrate how to use the drawers to convert a 10 small-value
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chips into 1 larger-value chip: drag chips into the slots of the righthand drawer. Demonstrate how the drawer only closes if all slots
are filled, and if all the chips are of the same value (all 1's or all
10's). Once the drawer is full, closing it opens the left-hand drawer
that now contains a new chip - a 10-value chip if 1's were placed,
and a 100-value chip if 10's were placed.
Group 12, 1-value chips, together and count them together.
A sk : Is there a simpler way to represent the same number using the
chips?
Hint at representation in base 10. For example, if there are 12, 1value chips, then a more convenient way to represent them is a
single 10-value chip and two 1-value chips.
Use the drawers to convert 10 1-value chips into 1 10-value chip, and
demonstrate how you represent the number 12 in a different way.
A sk : Does the number represented by the chips differ in any way?
No. The number 12 can be represented by 12 1-value chips, or 1
10-value chip and 2 1-value chip.
A sk : How would we subtract 5 from the 12 chips?
First we must convert the 10-value chip into 10 1-chips, making it
possible to remove 5 1-value chips from the group. Then, we
remove 5 1-value chips, and leaving 7 1-value chips.
S ay : Read the instructions at the bottom of the screen.
A sk : What is the connection between the subtraction equation and
the chips that are placed on the table?
The number represented on the table is the number to be
subtracted from (516).
A sk : How would we subtract 178 from 516?
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We need to have, on the table, one 100-value chip (or more),
seven 10-value chips (or more) and eight 1-value chips (or more).
Then, we will take aside one 100-value chip, seven 10-value chips
and eight 1-value chips, and the number that is represented by the
chips remaining represents the answer.
E x a m p le :
A sk : So what is the answer to 516 - 178 ? How do you know?
After we moved aside one 100-value chip, seven 10-value chips
and eight 1-value chips (which altogether represents the number
178), we are left with three 100-value chips, three 10-value chips
and eight 1-value chips on the left side of the table. So the
answer is 338.
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S t ude nt s pr ac t i c e M at h game : M ake C hange - S ubt r ac t :
M ul t i pl e R e gr o upi ng | 20 min
Have students play M a k e C h a n g e - S u b t r a c t : M u lt ip le R e g r o u p in g
and M a k e C h a n g e - S u b t r a c t 3 - 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 | 6 min
Use packs of Monopoly money. Invite two students (Tom and Liz) to
participate. Tom will act as the first number, and Liz will act as the drawer.
Hand Tom 7 1-dollar bills, 8 10-dollar bills, and 3 100-dollar bills. Hand Liz the
rest of the pack.
A sk : How much money does Tom have?
Tom has 387 dollars.
Ask Tom to put 263 dollars on the table.
A sk : What is the most efficient way to do so?
The most efficient way is using 2 100-dollar bills, 6 10-dollar bills
and 3 1-dollar bills.
S ay : We want to take away 94 dollars from the 263 dollars that are
on the table. The bills that Liz is holding can be used as the drawers
in the episode.
Ask Liz to take one 10-dollar bill from the table and replace it with ten 1-dollar
bills.
A sk : Has the total number of dollars on the tablechanged?
No, it hasn't.
Together with the class, take away 94 dollars from the table. Emphasize that
the number of dollars left on the table is the difference between 263 and 94.
S ay : On the table we are left with 1 100-dollar bill, 6 10-dollar bills,
and 9 1-dollar bills. How much is that?
169.
Repeat the game for two or three more rounds, with different students.
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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 h R e gr o upi ng Up t o 1, 000 | 7 min
Have students work on the following worksheets:
1. 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 0 .
2. S u b t r a c t io n S t r a t e g ie s - Up T o 1 0 0 0 - L e v e l 1 .
3. 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 0 .
4. 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
1 000.
5. 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 0 .
6. 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 0 .
7. S u b t r a c t io n S t r a t e g ie s - Up T o 1 0 0 0 - L e v e l 2 .
Advanced students can continue to work on the following worksheets:
1. 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 0 .
2. Pr o p e r t ie s o f S u b t r a c t io n - E q u iv a le n t E q u a t io n u p t o
1 000.
3. S u b t r a c t io n S t r a t e g ie s - Up T o 1 0 0 0 - L e v e l 3 .
Circulate among them answering questions.
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C l o si ng | 3 min
Write on the board the equation: 428 - 153 = ? and ask the students to
complete the equation in their notebooks.
After they finish, share the answers.
S ay : We subtract 3 ones from the 8 ones, leaving 5 ones. Then, we
want to subtract 5 tens from 2 tens, but we can't so we take one
hundred and convert it to 10 tens so we now have 12 tens (instead
of 2 tens). Now subtract 5 tens from the 12 tens, leaving 7 tens. We
subtract 1 hundred from 3 hundreds (1 hundred we converted
already) and left with 2 hundreds. So the answer is 275.
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