# Implementing Think Math! - Support for Students

## First year of implementation, student

### Three things are potentially new for students: mathematical ideas, solidity of facts, and special formats used in Think Math!

Think Math!, from the very start, treats addition and subtraction as two sides of the same coin, the same idea viewed two different ways. Likewise, division appears as soon as multiplication does (2nd grade, though only as single digit by single digit arrays), and when division becomes the focus of attention, it is introduced as unmultiplication. Fractions, because they have many meanings (number, represented as position on number line, is primary, but all the usual other senses are accounted for as well), appear in many forms: rods (ratio); dots (and sets); number line (number); function machine (multiplication, process/operator). Think Math! uses its own formats, but these are genuinely also ideas that may be new to students (and teachers).

## Facts

Kids need to be totally comfortable with certain basic facts as stepping-stones for all their work. We don’t need all facts, and Think Math! doesn’t advocate random fact drills, but kids must find the following mental computations easy. This list is not complete (for one thing, it doesn’t include any multiplication), but represents the kinds of basic building blocks that students find relatively easy to acquire, even if they do not already have the skills, and that serve well enough while additional skill is built up. For a more complete list, see basic facts; for strategies for working with students, see addition and subtraction and multiplication.

• pairs that make 10 (and, equivalently, pairs of multiples of 10 to make 100)
• adding 10 (or 100) to anything
• adding multiples of 10, and adding multiples of 10 and then a single digit number to the result
• adding 8 or 12 to anything by adding 10 and then adjusting
• adding 80 to anything by adding 100 and then adjusting; and, later, using the same strategy for adding 28 or 98 to anything mentally.