We should use the Chinese philosophy and us 10 as a bridge because of its importance in the base-ten numeration system. Also, we could introduce the basic facts in units, such as 6+ unit, the 7+ unit, and so on. These units are categorized by the know entity (addends) instead of the unknown entity (sums). Lastly, the article reveals that we should teach different strategies that are not in textbooks but that can help children see the patterns among addition and subtraction facts (still using 10 as a bridge).

In the second article (The Road to Fluency and the License to Think), the author/teacher started out the year using a whole new method to teach basic math facts. She followed a schedule of teaching addition strategies: doubles, doubles plus one, doubles plus two, doubles minus one, doubles minus two, combinations of ten, counting up, add one to nine, make ten, adding ten, and commutative property. Following this schedule, she would follow a certain “routine” as she taught each new strategy: introduce and explore using manipulatives, create illustrations, use math journals, and assign homework including a parent information page. Finally, she would complete each day with a Mental Math session in which students would share with the class their “strategy” for solving the problem. This helped give other students strategies that they had not before considered and gave a whole “thinking math” feeling to the classroom environment. Students would even name their particular method for figuring out problems – which made things more interesting for them and created more of an investment on their part.

In the final article, many different “types” of multiplication problems were discussed: repeated addition, scalar, rate, cartesian produce, and area. And the importance of helping children understand that multiplication has a variety of meanings and is not just a sequence of isolated facts. This article that the the most effective sequence of instruction for multiplication facts is:

- introduce multiplication with real problems involving repeated addition
- use hands-on materials that truly represent the problem (ie markers in the ex)
- then, substitute blocks for problem items as a next step
- then, substitute student drawings for tangible manipulatives
- then, advance to students using tally marks or other representations instead of drawing true items
- give students many thinking strategies to simplify problems such as 8 times a number can be 5 times a number added to 3 times that number or 4 times a number added to 4 times a number
- give many opportunities for practice with games, flash cards, dice, calculator, computer-based practice, concentration cards, etc.
- finally, reteach those who really struggle by beginning showing them how much thy DO KNOW …. using a known and unknown multiplication fact table so that they can feel proud and confident in their current abilities and not be discourage about what they need to improve upon