A child using a Direct Modeling strategy represents each number in the problem with concrete objects.
A child using a Counting On/Back strategy is able to hold a number in her/his mind and count on or back from that number while keeping track of the quantity that is added or subtracted using fingers, tally marks, or counters. They use aids such as number lines or hundreds charts to help keep track of their counting. Many students get “stuck” at this level, never really becoming automatic with their facts, instead relying on a variety of counting strategies or technology such as calculators or spreadsheets. That is why it is important to also work on math facts fluency as well.
In CGI, the goal at this level is to understand the action of addition, subtraction, multiplication and
division. After understanding the mathematical action, we will focus on how to record that action using math notation.
A child possessing good number sense is able to solve problems in flexible ways, often breaking numbers down and recombining them by using known facts. This child frequently visualizes the quantities and solves the problem with mental math. Using number facts to solve problems.