Mental Math Strategies
1
Grade 2
Mental Math Strategies
SCO A2:
Count in a variety of ways.
1. Skip Counting:
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.
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
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
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.
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.
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