These fact cards are designed to help students attain mastery of the second level of their multiplication facts. Multiplication Level 2 consists of the 4, 6, 7, 8, and 9 times tables. Students must have mastery of their addition and subtraction facts through 20 before starting multiplication level 2 fact practice. Students must also have mastery of multiplication level 1 before starting multiplication 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!

Before learning the 8x table in a picture, the student should model the 8x table in rows or columns of equal groups of 8 with concrete objects such as counting tiles or blocks.

The student should see the pattern of equal groups in the rows or columns. In this example, the groups of 8 are shown in the columns. The student should learn how to read a table from left to right, adding groups of 8, or right to left, subtracting groups of 8.

“Do you know 5 groups of 8? If 5 groups of 8 is 40, then how much is 6 groups of 8? Add 8 to 40 to get 48.” The student should know 5 X 8 because it was mastered in level 1 multiplication. This strategy, shown in the picture above, is called **using the nearest fact**.

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