Just found this site that explains mental strategies in detail with examples for the kids to try themselves.
Here is just an extract of these strategies. The adding 8 is a new one for me.
Adding Ten
Adding ten means jumping up ten (think of a hundred’s chart). The ones digit stays the same but the ten’s digit increases by one. Students must understand this. Using a hundreds board to teach this works well to build understanding. Have students actually count up the ten and write down the result. Then affirm with them the pattern and explain why it works every time.
Example: 5 + 10 = 15
10 + 7 = 17
For older students you can relate this to higher numbers:
Example 23 + 10 = 33
48 + 10 = 58
Adding 9
Adding 9 makes sense if students understand adding ten. It sounds more difficult than it actually is.
Remind students of the jump of ten – 5 + 10 = 15. A student would say (in their head) “5 plus 10 = fifteen”
The five and fifteen are naming the same number of ones.
With the nines – a student must count down one in the ones.
A student would say “5 + 9 = fourteen”.
It sounds difficult but once they catch on it is really simple.
Work with lots of examples until the idea is understood:
5 + 10 = fifteen 5 + 9 = fourteen 7 + 10 = 17 7 + 9 = sixteen
Adding 8
This works exactly the same only a child must think 2 less. Using the examples above students would say; 5 + 10 = 15 so 5 +8 = 13, 7 + 10 = 17 so 7 + 8 = 15 (2 less)
- Printable Resources:(in PDF Format)
Double Numbers
To add double numbers there are a couple of strategies that might help students.
When you add a double you are counting by that number once.
For example: 4 + 4 = think of 4,8 … counting by fours
Practice skip counting by each number in turn:
2-4
3-6
4-8 etc. This gets harder with the higher numbers but skip counting is an important skill for students to have.
Doubles occur everywhere in life.
For example: an egg carton is 6 + 6
two hands are 5 + 5
16 pack of crayons has 8 + 8
two weeks 7 + 7 =
Do a variety of activities with double numbers and have students determine and explain which strategies help them remember. Each student should look at each fact and relate to a visual image or counting by strategy that works for them.
Near Doubles
To use the near doubles strategy a student first has to master the doubles. Then, if the double is known, they use that and count up or down one to find the near double.
Example: 4 + 4 = 8 5 + 4 = 9 (count up one)
Or: 4 + 4 = 8 so 4 + 3 = 7 (count down one)
- Printable Resources:(in PDF Format)
link: http://olc.spsd.sk.ca/de/math1-3/p-mentalmath.html