Mastery of Basic Facts
It is important that most students have mastery of basic facts. It is equally
important that they make sense of number combinations as they are learning
these facts. Here are some strategies to help with this understanding.
Adding Zero:
Model adding zero (with younger students) or review it with older students.
If a child understands that when you add zero you add nothing, he/she should
never get a basic fact with zero wrong. Make sure this understanding is in
place.
Adding One (Count up)
Adding one means saying the larger number, then jumping up one number, or
counting up one number. This happens every time you add one. It never
changes. Never recount the larger number, just say it and count up one.
Example: 6 + 1 = say 6 then 7
44 + 1 = say 44 then 45
Adding Two – Count up Two
Adding two means saying the larger number, then jumping up or counting up
twice. Again this is always correct and never changes.
Example: 9 + 2 = say 9 then 10 then 11
45 + 2 say 45 then 46 then 47
Commutative Property:
You also have to teach or review the commutative property. The answer will be
the same regardless of the order you add the two numbers. 9 + 2 = 2 + 9 Order
doesn’t matter.
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)
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 =
legs on an insect (4 on each side) 4 + 4
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)
Adding 5
Adding five has a strategy that is helpful but not completely effective as it
is a bit tricky. You can decide if it is helpful or not.
• To add fives look for the five in both numbers to make a ten then
count on the extra digits.
Example: 5 + 7 = (10 + 2) = 12
5 + 8 = 5 + 5 + 3 = 13
Students who can see the five in 8 should have no difficulty. Students who
can’t visualize numbers will find this hard. Most students can be taught to
do this with some extra work.