The above has been taken from "Helping your child learn math A Parent's Guide". 2004, Manitoba Education, Citizenship and Youth.
Basic Fact Information
Trevor Caulkins, a math teacher in Victoria and a respected presenter, believes there is a smart order for learning the addition facts to 20 and beyond. If your child is having difficulty with the basic facts, please help reinforce these mental math strategies, so your child does not have to count on their figures or rely on a ruler.
1. Learn the doubles 1+1, 2+2, 3+3,4+4, 5+5, 6+6, 7+7, 8+8, 9+9 and 10+10
2. Learn the names for 10 (bring out the power of ten cards to practise, then play the above power of 10 games) 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1,10+0
3. Recognize that all the plus 0's = the same number example 7+0=7
4. Realize that +1 is just like counting up one example 7+1=8
5. Now learn the doubles plus one: 4+5=___
In my head I can think - I know 4+4 is 8, + 1 more is 9 , (4+4+1) OR
Doubles minus one: 4+5=___
In my head I can think - I know 5+5 is 10, so 1 less must be 9, (5+5-1)
*Children can recognize the doubles plus or minus 1 because the pair of numbers looks like they're just counting up or down one. The answer is just 1 more or 1 less than the double, because 1 has been added to an addend or 1 has been subtracted.
6. Now learn the doubles pus two: 4+6 =___
In my head I can think, I know my doubles and how to count by twos, so 4+4 is 8, +2 more is 10, because 6 is two more than 4 (4+4+2) OR
Doubles minus two: 4+6 = ____
In my head I can think, I know my doubles and how to count by twos, so 6+6 is 12, minus 2 is 10, because 6-4=2 (6+6-2)
7. Now there are only a few odd ones left to memorize:
Names for 7: 2+5, 5+2
Names for 8: 3+5, 5+3
Names for 9: 2+7, 7+2, 3+6, 6+3
As we move to the bigger numbers:
8. Now adding 10 to a number is easier when children see the pattern 10+7=17, 10 + 6=16
9. Adding 11 is a similar thing once children see the pattern 11+1=12
10. Make a 10. In other words this can be called the "thieving 9 or 8". 9 and 8 like to make themselves into a 10 so it takes 1 or 2 from the other number. Example for a "thieving 9": 9+7=___
In my head I think the 9 takes 1 from the 7, the 9 becomes 10 and the 7 drops down to a 6, since 10+6=16. This same strategy works for 9+2, 2+9, 9+3, 3+9, 9+4, 4+9, 9+5, 5+9, 9+6, 6+9, 9+7, 7+9, 9+8, 8+9.
Example for a "thieving 8": 6+8= ___
Start with 8. Take 2 from the 6. Then the 8 becomes 10 and the 6 drops down to 4, since 10+4=14. This same strategy works for 8+2, 2+8, 8+3, 3+8, 8+4, 4+8, 8+5, 5+8, 8+6, 6+8, 8+7, 7+8.
11. Now there are only a few beyond 10, which need to be memorized:
Names for 11: 3+8, four and seven are eleven ( it rhymes), seven and four are eleven, 8+3
Names for 12: 4+8, 5+7, 7+5, 8+4
Names for 13: 5+8, 8+5
Names for 14: 8+6, 6+8
Names for 15: 2+13, 3+12 (really doubles plus 1)
Names for 16: 3+13 (doubles), 4+12 (which is similar to counting on by 2s from 4)
Finally you can always Think Addition to Subtraction
For example:13-5= __ If addition is easier for me than subtraction I can think, 5+?= 13 hmmm it is 8.
So, 13 minus 5 equals 8.
If you would like to understand more about teaching your child strategies when adding and subtracting, as well as making math meaningful, please check out the Power of Ten web site.
Power of Ten Visualization
Information for the Math Corner comes from Math to the Max, the Nelson and Math Makes Sense math programs, Jump Math, Kim Sutton, Trevor Calkins, Box Cars and One-Eyed Jacks, and Carole Saundry-Fullerton's blog.
1. Learn the doubles 1+1, 2+2, 3+3,4+4, 5+5, 6+6, 7+7, 8+8, 9+9 and 10+10
2. Learn the names for 10 (bring out the power of ten cards to practise, then play the above power of 10 games) 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1,10+0
3. Recognize that all the plus 0's = the same number example 7+0=7
4. Realize that +1 is just like counting up one example 7+1=8
5. Now learn the doubles plus one: 4+5=___
In my head I can think - I know 4+4 is 8, + 1 more is 9 , (4+4+1) OR
Doubles minus one: 4+5=___
In my head I can think - I know 5+5 is 10, so 1 less must be 9, (5+5-1)
*Children can recognize the doubles plus or minus 1 because the pair of numbers looks like they're just counting up or down one. The answer is just 1 more or 1 less than the double, because 1 has been added to an addend or 1 has been subtracted.
6. Now learn the doubles pus two: 4+6 =___
In my head I can think, I know my doubles and how to count by twos, so 4+4 is 8, +2 more is 10, because 6 is two more than 4 (4+4+2) OR
Doubles minus two: 4+6 = ____
In my head I can think, I know my doubles and how to count by twos, so 6+6 is 12, minus 2 is 10, because 6-4=2 (6+6-2)
7. Now there are only a few odd ones left to memorize:
Names for 7: 2+5, 5+2
Names for 8: 3+5, 5+3
Names for 9: 2+7, 7+2, 3+6, 6+3
As we move to the bigger numbers:
8. Now adding 10 to a number is easier when children see the pattern 10+7=17, 10 + 6=16
9. Adding 11 is a similar thing once children see the pattern 11+1=12
10. Make a 10. In other words this can be called the "thieving 9 or 8". 9 and 8 like to make themselves into a 10 so it takes 1 or 2 from the other number. Example for a "thieving 9": 9+7=___
In my head I think the 9 takes 1 from the 7, the 9 becomes 10 and the 7 drops down to a 6, since 10+6=16. This same strategy works for 9+2, 2+9, 9+3, 3+9, 9+4, 4+9, 9+5, 5+9, 9+6, 6+9, 9+7, 7+9, 9+8, 8+9.
Example for a "thieving 8": 6+8= ___
Start with 8. Take 2 from the 6. Then the 8 becomes 10 and the 6 drops down to 4, since 10+4=14. This same strategy works for 8+2, 2+8, 8+3, 3+8, 8+4, 4+8, 8+5, 5+8, 8+6, 6+8, 8+7, 7+8.
11. Now there are only a few beyond 10, which need to be memorized:
Names for 11: 3+8, four and seven are eleven ( it rhymes), seven and four are eleven, 8+3
Names for 12: 4+8, 5+7, 7+5, 8+4
Names for 13: 5+8, 8+5
Names for 14: 8+6, 6+8
Names for 15: 2+13, 3+12 (really doubles plus 1)
Names for 16: 3+13 (doubles), 4+12 (which is similar to counting on by 2s from 4)
Finally you can always Think Addition to Subtraction
For example:13-5= __ If addition is easier for me than subtraction I can think, 5+?= 13 hmmm it is 8.
So, 13 minus 5 equals 8.
If you would like to understand more about teaching your child strategies when adding and subtracting, as well as making math meaningful, please check out the Power of Ten web site.
Power of Ten Visualization
Information for the Math Corner comes from Math to the Max, the Nelson and Math Makes Sense math programs, Jump Math, Kim Sutton, Trevor Calkins, Box Cars and One-Eyed Jacks, and Carole Saundry-Fullerton's blog.