Grade K students are typically introduced to addition and subtraction in the spring semester. Introducing them conceptually to counting on and counting back prior to those units in school math will help prepare them for success with those units in school.
In grade one, students are often expected to master many basic facts. Extending counting on, counting back, and counting up to larger numbers will help students develop flexibility in using these strategies and prepare them for fluency with the strategies as they master these facts.
Mastery of the remaining basic facts is usually expected in grade two. Helping students make sense of using ten and using known facts will greatly increase the probability of their success. These strategies will also enable students to develop skills with mental computation and estimation with larger numbers.
The web-site lessons for each of these reasoning strategies should be used as previews to enable students to use the new thinking as they begin the addition and subtraction units in school math. By spacing instruction for the reasoning strategies and meshing them with units in school math, more students will be prepared for success and fewer students will have difficulties with math.
Expand Conceptual Understanding And Develop Number Sense
The gaps, after planning the lessons to help students make sense of reasoning strategies, should be filled by selecting lessons from counting, numbers & partitions, and explore with word problems under the heading of adding & subtracting. These lessons will expand understanding.
PreK children may need lessons on counting to address common errors or ways to use counting to solve problems. Throughout PreK and the primary grades, students can benefit from making sense of numbers and partitions. This will help them learn to put numbers together and take them apart and develop number sense. From about age five through the primary grades, students need to explore adding and subtracting through word problems. These lessons involve a variety of problem structures and include solving and creating everyday problems.
Since each of these lessons is an explore lesson, there is no need to master that content before moving on. By repeatedly experiencing different numbers and their partitions and solving problems with different structures, students gradually develop number sense and a deep understanding of addition and subtraction. A sample plan is shown below.