These fact cards are designed to help students attain mastery of the second level of their division facts. Division Level 2 consists of dividing by 4, 6, 7, 8, and 9. **Students must have mastery of their multiplication level 1 and level 2 facts before starting division level 2 fact practice.** Students must also have mastery of the division level 1 before starting division level 2.

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, table-based strategy 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.
- No more rote memorization without understanding the multiplication patterns!

The student can use the multiplication fact that he or she has mastered. Additional prior knowledge comes from modeling division concepts with concrete objects. He or she can imagine splitting 42 blocks into groups of 7. This example shows the concept of pulling out equal groups of rather than dividing into 7 equal groups. Either concept can be used, but only one picture solution is shown on the card.

If the student can’t answer, “What times 7 is 42?”, then he or she should ask a different question. “How many groups of 7 blocks can I get out of 42 blocks?” The student should estimate. He or she can start with 5 groups of 7, a fact in the middle of the table. “5 groups of 7 is 35. 6 groups of 7 is 42 (7 more than 35). 7 groups of 7 is 49. 6 × 7 = 42.”

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