Examples of mathematical content[edit]
Second grade example: In the second grade there are 26 standards in four domains. The four critical areas of focus for second grade are (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. Below are the second grade standards for the domain of "operations and algebraic thinking" (Domain 2.OA). This second grade domain contains four standards, organized into three clusters:[SUP]
[32][/SUP]
Represent and solve problems involving addition and subtraction.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Teaching students to solve one and two step word problems involving addition and subtraction is standard practice. Teaching them to understand addition and subtraction as a process is very desirable but doesn't always happen using just rote learning.
Add and subtract within 20.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.Mental arithmetic is nothing new but mere rote is not good enough. Mental strategies are even more important.
Work with equal groups of objects to gain foundations for multiplication.
3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
The beginning of understanding that multiplication is about groupings. Again, rote learning of tables has some value but understanding how the tables are constructed in the first place is also important. Pairings, groupings of objects, counting by 2s, 3s, 5s etc are all strategies to build up an understanding of the multiplication process.
4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Pre algebra being introduced here. This should produce students able to deal with generalised arithmetic further down the track.