For the last couple of days I have been teaching addition strategies for adding 2 digit numbers with something could be called success. These guys have a hard time remembering the steps--which makes moving on to regrouping tough but yet they have a couple of strategies that have helped them. The basic strategies they have built on to help them work to find the answers. I would love, love if they would memorize the basic facts but getting a correct answer with another strategy is all that matters at the end of the day. Even if its not the most efficient. It has to be efficient and effective for them--not me the teacher.

Though mastering the basic facts is one strategy its not the end all be all. 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

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)

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.

Manipulatives
Math manipulatives are an important bridge to help students connect the concrete to the abstract in mathematical learning. Math manipulatives allow students to see, touch, and move real representations of conceptual ideas. Numbers on a page are brought to life when students can model with representations. Concepts such as decomposition, place value, and fractions benefit from the visual and kinesthetic aspects of manipulatives. Challenging and multi-step problem-solving activities can be made more manageable when students are able to use tools like manipulatives to compute and represent various parts of the problem. Practice in choosing appropriate manipulatives deepens student expertise with identifying the correct tools for solving a problem.

Explaining and critiquing mathematical reasoning are important skills in understanding mathematics. Manipulatives help students discuss and demonstrate their methods for solving problems. This type of collaborative communication builds precision in language as well as procedure. When students can demonstrate the how and why of a math concept, they build connections and prepare for more advanced skills. Manipulatives also provide students a tool for testing their theories and the theories of others. And, manipulatives can assist English language learners, who are still building their vocabularies, demonstrate understanding of math concepts.

Manipulatives are great for concrete, visual learners who need to see the problem to solve them. Unifix cubes moved my math group from having no clue on how to add two digit numbers to having a working strategy that they can use with confidence. For showing their work they just draw what they created. This list is full of great ways to help students to solve addition problems. I hope your students find one or two that help them solve addition problems efficiently and effectively. Have a great week!