Simply because a student is capable of quickly recalling facts, this may not show a true understanding of number relationships. Instead students should be able to communicate and demonstrate more efficient strategies based on their understanding. This looks different at each grade level because the skills build on each other. Fluency is the ability to creatively express their math thinking using the structure of mathematics and the meanings of its representations.

**Kindergarten**

- Adding and subtracting numbers within 1 to 5.
- Using objects and drawings to compose and decompose number from 11 to 19 into tens and ones.

**First Grade**

- Adding and subtracting numbers within 10.

**Second Grade**

- Fluently add and subtract within 20 using
**mental strategies**. **Know from memory**all sums of two one-digit numbers. (1+6=7)- Fluently add and subtract within 100
**using strategies.**(No algorithm needs to be taught)

**Third Grade**

- Fluently multiply and divide within 100
**using strategies** - Fluently add or subtract within 1000
**using strategies and algorithms**(algorithm is introduced but not mastered)

**Fourth Grade**

- Fluently add and subtract multi-digit whole numbers
**using a standard algorithm.** - Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors,
**using strategies.** - Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (No standard algorithm)

**Fifth Grade**

- Fluently multiply multi-digit whole numbers
**using a standard algorithm.** - Find whole-number quotients of whole -numbers with up to four-digit dividends and two-digit divisors,
**using strategies**. - Add, subtract, multiply and divide decimals to the hundredths place
**using strategies.**