Derek: Derek has a much more sophisticated understanding of numbers after the instruction. He recognizes how numbers relate to one another and how you can use these relationships to make addition easier. For example, Derek is asked what is 5 +4. Derek realizes that 4 is one away from 5. Derek then adds 5 plus 5 to get 10, but then takes away the 1 that he added in to get the correct answer of 9. Derek uses the same process for the subtraction and word problems.
Elizabeth: Elizabeth also uses the relationships between numbers to understand addition facts now. When given the problem of 7+6, Elizabeth uses her knowledge of 7+7=14 to get to the correct answer of 13 because it is 6 is one less than 7. Elizabeth counts the cows when she they are shown to her. Elizabeth uses number relationships again to solve the problem about how many cows were hiding.
Jim: After instruction, Jim now understands how he comes to an answer. Jim understands that he can break apart numbers to make addition easier. Jim understands that you count down in subtraction. Jim also uses his understanding of how numbers relate in subtraction. Jim uses more strategies in his problem solving after the instruction.
Lauren: Lauren also uses the relationships between numbers to solve problems. She uses what she already knows and related this knowledge to the problems she was given. Lauren also breaks down numbers to make addition and subtraction easier.
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