These fact cards are designed to help students attain mastery of their subtraction facts through 10. Students must have mastery (automatic recall) of their math facts so that they can focus on the harder problem solving processes.

A student has **automatic recall** of a fact when he or she has practiced the fact enough with effective strategies to be able to produce a correct answer immediately. The student knows the fact **automatically** when he or she no longer needs a strategy to figure it out; he or she no longer has to pause and think.

### How are these cards different from “flash” cards?

- Self-teaching, strategy-based solutions on the back, not just the answers!
- Based on the Jerome Bruner instructional approach of teaching math in overlapping stages of Concrete (real objects) to Pictorial (drawing) to Abstract (symbols) for conceptual understanding.
- Two or three step problem solving strategies are used to improve visualization, working memory and sequential processing skills. No more rote memorization without understanding the process!
- Pictorial solutions are used to visualize the process of breaking the problem into easier steps. No more guessing!
- Multiple strategies are modeled so that the student learns the easiest, fastest strategies for a given problem type. A student will often use fingers because there are too many steps in his or her strategy. No more fingers!

Since 7 and 10 are close together on the number line, it does not make sense to count down 7 times from 10. That is too many steps!

“Can you count on from 7? To find the difference between 7 and 10, count on three times from the number 7: 8, 9,10. How is 10 different from 7? 10 is 3 more than 7. 3 away from 10 on the number line.” This strategy, demonstrated with a number bond missing part picture, is called counting on.

By using this two-step mental process, students not only master math facts but improve working memory and sequential processing skills.

A student should progress through the fact card arithmetic levels in the sequence below. He or she must have mastery of prior levels before progressing to the next level.

- Number Relationship Cards
- Addition through 10 Cards
- Subtraction through 10 Cards
- Addition through 20 Cards
- Subtraction through 20 Cards
- Multiplication Level 1 Cards
- Division Level 1 Cards
- Multiplication Level 2 Cards
- Division Level 2 Cards