Second
Grade
Math
Resources
Created by Deedee Hendrix
Hundreds Chart
-10
+10
-1
+1
Combinations of 10
Students should know all combinations up to 10 fluently. They should be
able to tell you the answer to these combinations in 3 seconds or less.
10 + 0 = 10
9 + 1 = 10
8 + 2 = 10
7 + 3 = 10
6 + 4 = 10
5 + 5 = 10
0
1
2
3
4
+
+
+
+
+
10 = 10
9 = 10
8 = 10
7 = 10
6 = 10
It’s important for them to know the commutative property. This will help
them understand it doesn’t matter what order you add the numbers, the
answer will still be the same.
Breaking Numbers Apart and
Decomposing Numbers
Students should be able to break apart numbers to make friendly numbers
in order to add or subtract. We would prefer they not add on their
fingers. This will help them develop strategies that will be used with larger
numbers as the year progresses. By the end of the year, they must be
able to add 3 digit numbers up to 1,000.
8 + 4 = 12
2 2
Students could break the four into a 2 and 2. Then they could add
8+2=10 and 10+2=12.
Doubles
Students should know all doubles. They should be able to tell you the
answer to these doubles in 3 seconds or less.
1
2
3
4
5
6
+
+
+
+
+
+
1
2
3
4
5
6
=
=
=
=
=
=
2
4
6
8
10
12
7 + 7 = 14
8 + 8 = 16
9 + 9 = 18
10 + 10 = 20
It’s important for them to know the doubles. This will help them to solve
problems. For example if they can’t figure out what the answer to 8+9 is
mentally, they can use the double 8+8 and one more to find the answer.
Skip Counting by 5’s , 10’s, 100’s
Students should be able skip count by 5s, 10s, and 100s within 1,000.
Examples:
Skip count to 80 counting by 10’s starting with the number 30.
30, _____, _____, _____, _____, _____
Skip count to 125 counting by 5’s starting with the number 100.
100, _____, _____, _____, _____, _____
Adding Simple Number Strings
There are many ways to solve a problem. We are encouraging the
students to look for combinations of tens and doubles. Here is an
example problem focusing on looking for combinations of ten.
7 + 5 + 3=____
10 + 5=15
So instead of the students counting on their fingers and adding 7+5+3,
we are encouraging them to pick out the numbers that will make 10. So
they would pull out 7+3=10, then add 5 to get a total of 15.
Here is an example of adding simple number strings while pulling out the
double facts.
8 + 4 + 8=____
16+4=20
So instead of the students counting on their fingers and adding 8+4+8,
we would encourage them to pull out the double. They know that the
double 8+8=16, then add to get a total of 20.
Money
Quarter= 25 cents
Dime= 10 cents
Nickel= 5 cents
Penny= 1cent
Second grade is the first time
money is introduced to students in
our state standards. Please work
with your child to be able to
identify the coins and their value.
Students should be able to make
an amount of money in more than
one way. For example 27 cents:
One way could be one quarter
and two pennies; another way could
be 2 dimes, one nickel and 2
pennies. Encourage them to use
the least amount of coins possible.
In other words, we don’t want them
to use 27 pennies.
Working with Numbers
Students will have to be able to write, read and record numbers in many
different ways. Here is an example of standard form, expanded form,
word form, base ten blocks (representation as a picture).
Standard Form: 74
Expanded Form: 70+4=74
Word Form: Seventy-Four
Base Ten Blocks:
Base Ten Blocks
Students will use base ten blocks or place value blocks to draw models to
help solve problems.
Ones Block-this
block represents 1.
Tens Block-this
block represents 10.
Example: Students might show the
number 32 using base ten blocks
like this.
Hundreds Block-this
block represents 100.
Example: Students might show the
number 125 using base ten
blocks like this.
It is IMPORTANT that they remember that the 3 in the number 32
represents 30, NOT 3!!! It is 3 groups of ten which is 30.
Adding Two-Digit Numbers
Without Re-grouping
There are many different ways you could solve this problem .
32 + 24 =____
They could draw place value blocks and add.
32 + 24 =____
50+6=56
Students can add by place value. 30 + 20 = 50 and 2 + 4 = 6. Then
add 50 + 6 = 56
32 + 24 =____
36+20=56
Students can add by compensation. This strategy takes 4 away from the
24 and gives it to the 32. Then add 36+20=56
Adding Two-Digit Numbers
Without Re-grouping
There are many different ways you could solve this problem .
32 + 24 =____
30
Students could
decompose the numbers
or break the number 32
and 24 apart and add by
place value.
2 20 4
30+20=50
2+4=6
50+6=56
32 + 24 =____
+10
+10
32
42
Students could add
using a number line.
+4
52
56
32 + 24 =____
32
42
52 53 54 55 56
Students can add using a
hundreds chart.
Adding Two-Digit Numbers
Without Re-grouping
There are many different ways you could solve this problem .
32 + 24 =____
20 4
32+4=36
36+20=56
Students may choose to decompose one number. This example is
breaking apart the 24 into a 20 and 4. They could also have chosen to
break the 32 apart instead of the 24.
For example:
32 + 24 =____
30 2
24+2=26
26+30=56
Subtracting Two-Digit Numbers
Without Re-grouping
There are many different ways you could solve this problem .
34 - 22 =____
They could draw place value blocks and subtract.
34 - 22 =____
10+2=12
Students can subtract by place value. 30 - 20 = 10 and 4 - 2 = 2.
Then add 10 + 2 = 12.
34 - 22 =____
+10
22
+2
32 34
Some students may
use the strategy of
putting the number
22 in their head and
count up to 34.
Subtracting Two-Digit Numbers
Without Re-grouping
There are many different ways you could solve this problem .
34 - 22 =____
-10
-2
12 14
-10
24
34
Students may subtract using a number line.
34 - 22 =____
20 2
34-20=14
14-2=12
Students can subtract by place value. 34 - 20 = 14 and 14 - 2 = 12.
34 - 22 =____
12 13 14
24
34
Students can use
a hundreds chart
to subtract.
Adding Two-Digit Numbers
With Re-grouping
There are many different ways you could solve this problem . All of the
strategies shown on addition without re-grouping page can also be used.
43 + 29 =____
They could draw place value blocks and add.
43 + 29 =____
Students can add by place
value. 40 + 20 = 60 and
3 + 9 = 12. Then break the
12 into a 10 and a 2 to make
a friendly combination. Then
add 60+10=70 and
70+2=72.
60+12=72
10 2
60+10=70
70+2=72
43 + 29 =____
42+30=72
OR
43 + 29 =____
43+30=73
73-1=72
Students can add by compensation.
Adding Two-Digit Numbers
With Re-grouping
There are many different ways you could solve this problem .
43 + 29 =____
20 2+7
43+7=50
50+20=70
70+2=72
Students could
decompose the numbers
or break the number 29
apart and add by place
value. Students are
encouraged to make
friendly numbers.
43 + 29 =____
20 9
43+20=63
63+9=___
7 2
63+7=70
70+2=72
Students could decompose the number or break the number 29 apart
and add by place value. 43+20=63, then break the 9 into a friendly
combination of 2 + 7. Then students can add 63+7=70 and 70+2=72
Subtracting Two-Digit Numbers
With Re-grouping
There are many different ways you could solve this problem . All of the
strategies shown on subtraction without re-grouping page can also be
used.
14
43 - 29 =____
6
4
They could draw place value blocks and subtract. Students would have
to take 6 out of one stick of ten.
43 - 29 =____
40-20=20
3-9=-6 (difference of 6)
Students can subtract by
place value. 40 - 20 = 20
and 3 - 9 = -6. Then take
the difference of 6 from 20.
20-6=14.
20 – 6 = 14
43 - 29 =____
Students can subtract by
compensation.
43+6=49
49-29=20
20-6=14 (They must subtract what they added to the first number.)
Subtracting Two-Digit Numbers
With Re-grouping
There are many different ways you could solve this problem . All of the
strategies shown on subtraction without re-grouping page can also be
used.
43 - 29 =____
20 3+6
43-20=23
23-3=20
20-6=14
Students could
decompose the numbers
or break the number 29
apart and subtract by
place value. Students are
encouraged to make
friendly numbers.
43 - 29 =____
20 3+6
43-3=40
40-6=34
34-20=14
Students could decompose the number or break the number 29 apart
and subtract by place value. Students are encouraged to make friendly
numbers.
Subtracting Two-Digit Numbers
With Re-grouping
There are many different ways you could solve this problem .
43 - 29 =____
-10
-9
14
23
-10
33
43
Students may subtract using a number line.
43 - 29 =____
29 +10 = 39
39 + 4 = 43
Then add 10+4=14.
OR
43-29 =____
29 + 1 = 30
30 +10 = 40
40 + 3 = 43
Students might add
up from the smaller
number to get to the
larger number.
These are a few of the many strategies your children use every day!
The biggest thing right now is to NOT show them the traditional
algorithm (carrying and borrowing) that we learned as a child. That is
a fourth grade standard and they will see it later in elementary, but not
now.
For example, this is the traditional algorithm. Do not show them this way.
2 11 11
321
- 156
I hope these pages will help! Let me know if you have any questions or
if you want me to show you more about how we are working these
problems. Your children are amazing, and I learn from the every day!
I know new things can seem scary but believe me your kids can do cool
things with the number sense that they have so please don’t hold them
back, but instead embrace their deep understanding of numbers! It will
make all the difference in their success in school and life
mathematically!!
Understanding Negative Numbers: In one of the problems you will see
negative numbers. 1 - 6 = -5 We have shown negative numbers in
many ways: Temperature being below zero..... Starting on the number
line on 1 and walking back six places and letting them see that we would
be at -5...owing someone money like 6 cents but I only have 1 cent
therefore I am in the hole 5 cents....
Please remember they can use many different strategies to solve a
nd
problem. The only strategy not accepted in 2 grade standards is the
traditional algorithm.
If you would like to look at our second grade standards and more explanations and
examples, here is a link to the pdf file. It is a great resource, too.
http://www.azed.gov/azccrs/files/2013/11/2flipbookedited.pdf
= 100
=10
=1
321-156 =___
5
Place Value
Model Strategy
5
Students might draw place value models to help them subtract. First they would
take 1 bundle of a hundred away from the 321. Then they would trade 1 bundle
of hundred for 10 ten sticks. They would then subtract the 50 by taking the two
sticks of ten out of the tens place and three more tens out of the bundle of
hundred that was traded for 10 ten sticks. Next they would subtract the 6 ones by
taking 5 ones out of a tens stick and 1 out of the ones place. Giving them the
answer of 165.
321-156=___
300 -100 =200
20 -50 = -30
1-6 = -5
200 -30 =170
170 -5 =165
Students might subtract by
place value: by starting
with the hundreds, then
tens, then the ones.
321-156=___
Students might
break the 2nd
number down into
100, 50, 6.
100 50 6
321-100 = 221
221-50 =171
171- 6 = 165
Think about the
hundreds chart when
subtracting the 50
from 221:
171
181
191
-50 201
211
221
321-156=___
321+ 30 + 5 = 356
356-156 = 200
200 - 30 =170
170 – 5 =165
Students might compensate
by adding or subtracting. In this problem
the student added 30 and 5 to get the
first number equal to the second number
in the tens and ones place. They must
subtract whatever they added after they
finish manipulating the numbers.
321-156 =___
-6
165
Students might use
a number line to
help them solve
problems.
-10 -10
171 181
-10
-10 -10
191 201 211 221
-100
321
321-156=___
156 + 100 = 256
256 + 5 = 261
261 + 60 = 321
Then add 100 +5 +60 =165.
OR
321-156=____
156 + 4 = 160
160 + 40 = 200
200 + 100 = 300
300 + 21 = 321
Then add 4 + 40 + 100 + 21=165.
Students might
add up from the
smaller number to
get to the larger
number.