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U n t er r i ch t spl a n
Sub t rac t ing 2 -d ig it Numb e rs By
Gro up ing and Ung ro up ing
Altersgruppe: 2nd Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.21, 2.6b, 2.8
Virginia - Mathematics Standards of Learning (2016): 2.5 .a, 2.6.a,
2.6.b, 2.6.c
Fairfax County Public Schools Program of Studies: 2.21.a.1,
2.21.a.3 , 2.6.b.3 , 2.8.a.3
Online-Ressourcen: B o unc e Do w n
Class
discussion
Mat h
Worksheet
Pract ice
10
8
10
4
min
min
min
min
Opening
T eacher
present s
St udent s
pract ice
7
10
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e grouping items into tens and ungrouping groups
of ten.
P r ac t i c e subtracting 2-digit numbers.
L e ar n to subtract with conversion.
De v e l o p basic understanding of place value.
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Ope ni ng | 7 min
Start by reviewing with students expanded notation of 2-digit numbers.
Write on the board: 53 = 50 + 3
S ay : We can decompose any 2-digit number into its tens
component and ones component. The number 53 is composed of 5
tens and 3 ones.
Have students decompose each number to its tens and ones components,
by writing them in expanded notation in their notebooks.
1. 18 =
2. 92 =
3. 76 =
4. 40 =
When students are done working, review the solutions.
1. 18 = 10 + 8 - 18 is composed of 1 ten and 8 ones.
2. 92 = 90 + 2 - 92 is composed of 9 tens and 2 ones.
3. 76 = 70 + 6 - 76 is composed of 7 tens and 6 ones.
4. 40 = 40 + 0 - 40 is composed of 4 tens and without ones.
S ay : Today we’re going to use expanded notation to help subtract
2-digit numbers.
T e ac he r pr e se nt s M at h game : B o unc e Do w n - S ubt r ac t 2Di gi t N umbe r s | 10 min
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Using the Preset mode, and a projector, present Matific ’s episode B o u n c e
Do w n - S u b t r a c t 2 - Dig it N u m b e r s to the class.
This episode practices finding the difference between 2-digit numbers,
highlighting the decimal representation of numbers. Two types of bouncing
balls are shown. You will have to find how many more there are of one type,
compared to the other. Which can be accomplished by dispatching the balls
into jars containing ten balls each.
E x a m p le :
S ay : Please read the instructions at the bottom of the screen.
Students can read the instructions.
S ay : We have to find how many more yellow balls there are than
purple balls. So we have to find how many balls there are in the left
dispenser and how many balls are in the right dispenser.
A sk : How can we find out how many balls are there in the left
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dispenser?
There are two options - to count the marbles in the dispenser one
by one, or to use the jars and group the marbles into groups of
ten.
S ay : Let's group all the balls of each type into tens, and place the
jars on the shelf.
Show students how to use the jars, and fill 5 jars with 10 balls each, from the
left dispenser.
A sk : How many balls were in the left dispenser?
We filled 5 jars, each jar with 10 balls, so altogether there were
50 balls in the left dispenser.
Fill 2 jars with balls from the right dispenser.
A sk : How many balls were in the right dispenser?
We filled 2 jars, each jar with 10 balls, so altogether there were
20 balls in the right dispenser.
E x a m p le :
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A sk : How many more jars of yellow balls are there than jars of
purple balls?
There are 3 more jars of yellow balls than jars of purple balls (5 3 = 2).
A sk : How many more balls were in the left dispenser than balls in
the right dispenser?
In the left dispenser we had 5 jars of 10 balls, which is 50 balls. In
the right dispenser we had 2 jars of 10 balls, which is 20 balls. The
difference is 3 jars, which equals 30 balls.
Show students the next question.
E x a m p le :
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S ay : Please read the instructions at the bottom of the screen.
Students can read the instructions.
S ay : In order to find the difference between the number of balls in
the left and right dispensers, first we have to find the number of
balls in each dispenser. We can use the jars again.
Fill 4 jars from the left dispenser and one jar from the right one. Show
students that the fifth jar from the left dispenser is not full so it doesn't
automatically seal and can not be placed on the shelf.
E x a m p le :
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A sk : How many balls were in the right dispenser?
We fill 1 jar with 10 balls, so altogether there were 10 balls in the
right dispenser.
A sk : How many balls were in the left dispenser?
We fill 4 jars with 10 balls (which is 40 balls) and 7 more balls are
left, so altogether there were 47 balls in the left dispenser.
A sk : How many more balls were in the left dispenser than there
were balls in the right dispenser?
The difference between the jars, with balls, from the left
dispenser and right dispenser is 3 jars and 7 additional balls. Each
jar is filled with 10 balls so the difference is 30 balls plus 7 balls
- i.e. 37 balls.
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S t ude nt s pr ac t i c e M at h game : B o unc e Do w n - S ubt r ac t 2Di gi t N umbe r s | 10 min
Have students play B o u n c e Do w n - 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.
C l ass di sc ussi o n | 8 min
Discuss any problems students faced while working individually.
Ask the class for responses as to how they dealt with issues their
classmates brought up.
S ay : Using balls in order to solve subtraction problems is an
excellent method, but now we will try to solve subtraction
problems without using balls.
Write on the board: 82 - 37 =
S ay : In order to solve this problem we use expanded notation.
Write on the board each number in its expanded notation:
82 = 80 + 2
37 = 30 + 7
S ay : The number 82 is composed of 8 tens and 2 ones. The number
37 is composed of 3 tens and 7 ones. Now let’s subtract ones from
ones and tens from tens.
A sk : How many are 2 ones minus 7 ones?
We have a problem because there is no answer to this question,
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reflecting positive numbers. We will have to ungroup one set of
ten. We take one ten from the 8 tens and ungroup it into 10 ones
(you can show on the board how the number 82 turns into 70 + 10
+ 2, and explain that this is just a different notation and the value
of the number doesn't change). Together we now have 12 ones.
Therefore, 12 ones minus 7 ones equals 5 ones.
A sk : What is the value of 7 tens (the number left after the
ungrouping) minus 3 tens?
4 tens.
A sk : What is the difference of 82 - 37 ?
We are left with 4 tens and 5 ones, i.e. 45.
Write on the board: 82 - 37 = 45.
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M at h W o r kshe e t P r ac t i c e : P r o pe r t i e s Of S ubt r ac t i o n E q ui v al e nt E q uat i o n Up T o 100 | 10 min
Have the students work on the following worksheets:
1. Pr o p e r t ie s Of 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 Up T o 1 0 0
2. S u b t r a c t in g T e n s - M in u e n d u p t o 1 0 0
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
4. 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
5. S u b t r a c t in g T e n s - W h o le T e n s S u b t r a c t io n
6. S u b t r a c t in g w it h Un k n o w n s - T e n s u p 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 S u b t r a h e n d u p t o
1 00
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 M in u e n d u p t o 1 0 0
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
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
episode’s method of subtracting 27 from 53.
When students are done writing, review their responses. Write on
the board and discuss any questions students may have:
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