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Grade 2
Mental Math Strategies
SCO A2:
Count in a variety of ways.
N.B. The document states that number sense and
number concepts are the foundation required to
understand more advanced math concepts. As children
prepare for mental computation, the ability to
recognize patterns in the base-ten system is an
1. Skip
Counting:
important
skill.
Children should be encouraged to count by 2’s, 3’s, 4’s, 5’s, 10’s,
25’s, and 100’s.
See Mental Math in the Primary Grades: lesson #19 & 20 for skip
counting
2. Counting Backwards and forwards:
Students need to be able to move on the number line with the
greatest ability.
See Mental Math in the Primary Grades: lessons #10 & 11.
3. Counting from various starting points.
Students need more practice with this strategy because most of
them always need to start at number 1 when they count.
To be able to count-on in addition situations,
students must be confident starting from various
numbers.
Revised April 2004
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SCO B5:
Develop and apply strategies to learn addition & subtraction
facts.
1. Relating Doubles:
Students often pick up on doubles facts early. They may use this
knowledge to find other facts.
For example: If they know 4 + 4 = 8 and need to find 4 + 5, they
may think (4 + 4) + more, so 8 + 1 = 9.
Also see Mental Math in the Primary Grades: lesson #3 on
teaching doubles.
2. Relating Facts:
Children should be encouraged to use their knowledge of one fact
to find another.
For example: If students know that 2 + 3 = 5, to find 3 + 3 they
could think that 3 + 3 is one more than 3 + 2 so it must be 6.
3. Add and compensate:
In addition situations, what ever you add to one addend to make a
nice number, you have to subtract from the other addend. You can
at first have the students do it in 2 steps and when they understand
the process and why it works, they can do both steps at the same
time.
Example: 8 + 7 = (8 +2) + 7 = 10 + 7 = 17 then take away the
extra 2 that was added 17 – 2 = 15.
If you work both steps at the same time,
8 + 7 = (8 + 2) + (7 – 2) = 10 + 5 = 15
Revised April 2004
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4. Relating to 10: (nice numbers) or Bridging to 10
Always make one addend a 10 and add the extra.
For example: If the sum is 8 + 9, taking 1 from the 8 and adding it
to the 9 will give you 10. The 1 taken from the 8 leaves 7, so the
equation can now be seen as 8 + 9 = 7 + 10 = 17.
Also see Mental Math in the Primary Grades: lesson #6, adding to
make 10.
5. Bridging to 10 in subtraction situations
With a subtraction situation where the minuend (first number) is
greater than 10, you subtract the amount exceeding 10 first to make
a nice number and then subtract the extra.
Example: 14 – 6 = (14 – 4) – 2 = 10 – 2 = 8
Once the students are comfortable doing this process, you can
teach them the short cut: When the ones digit in the minuend is
less than the second term, subtract the difference from 10.
Example: 15 – 9 = (9 – 5) is 4, so 10 – 4 = 6
6. Differences of 2:
This strategy can also build on the work with doubles.
For example, 6 + 8. If you take one from 8 (leaving 7) and adding
it to the 6 (making 7) you arrive at 6 + 8 = 7 + 7 = 14.
After having some experience with this, teach the short cut: when
you add two number which have a difference of two, double the
number that comes between these two numbers.
Example: 5 + 7 = double 6 = 12
7. Think addition for subtraction situations:
If students are taught to use the addition facts they know to learn
the subtraction facts they don’t know, they have to learn only one
set of basic facts.
Example: 12 – 7 = think … 7 + ? = 12
Also see Mental Math in the Primary Grades: lesson #15
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8. Subtract Ten:
To find 17 – 9, you think in terms of 17 - 10 (nice number) = 7
Then add 1 to the answer to balance for the 1 you added to 9 in the
original equation to get 10 you subtracted.
9. Add to each side of the equation: (Balancing strategy)
To find 17 – 9 add one to each addend to make 18 –10 = 8
(It makes an easier question to deal with). This strategy does not
work with addition.
10. Addition Table Patterns:
These patterns may be used to help students determine an unknown
sum or difference. *** This strategy relates to C3: Identify and use
patterns in an addition table.
SCO B6:
Recall addition facts involving 2 addends, each less than 10,
and the related subtraction facts.
N.B. The strategies implemented to meet
outcomes B5 can be used to help students
become more proficient in outcome B6. The
document reminds us that fact learning is a
mental exercise with an oral and/or visual
prompt so the focus should be oral, rather than
paper and pencil.
SCO B7:
Demonstrate an understanding of basic principles of addition.
Students need to understand that adding 1 to a number changes the
units, whereas adding 10 changes only the tens digit.
Also see Mental Math in the Primary Grades: lesson #28, 29
adding multiples of ten.
Revised April 2004
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SCO B11:
Estimate the sum or difference of two 2-digit numbers.
Estimation is usually a mental process.
At this level, it is easier if they start with manips. The number line
is good as they can move by tens and ones.
1. Rounding to 10:
For example: 46 + 35 may be thought of as 50 + 35 or 50 + 30,
when estimating.
2. Front-end Method:
This method combined with the associative principle will allow an
accurate answer.
For example: 44 + 33 may be seen as 40 + 30 first and then 4 + 3.
After the students understand the process of the front-end method,
with practice the students can add the tens first and then the ones
without saying the plus in between.
Example: 40 …70…74…77
3. Combinations:
More accurate estimates may be made when these 2 strategies are
combined.
For example: 38 + 27 may be thought of as 40 + 27 for an
estimation of 67.
Revised April 2004