They are assumed to move along the same path if there are individual differences it is just that some children move along the path more slowly-hence, some need more time, or remediation. Each lesson, each day, is geared to a different objective, a different "it." All children are expected to understand the same "it," in the same way, at the end of the lesson. In a framework like this, learning is understood to move along a line. ocusing only on the structure of mathematics leads to a more traditional way of teaching-one in which the teacher pushes the children toward procedures or mathematical concepts because these are the goals. analyzed the structure of mathematics and delineated teaching and learning objectives along a line.
We should keep in mind that these concepts of number sense do not describe a linear progression of understanding. Watch the following videos, if kindergartners can see the images and identify the teen number that is represented, then they have met the conditions of the Common Core Standard. Although the language of the standard includes the terms "ten ones and one, two, three, four, five, six, seven, eight, or nine one" this vocabulary is there for the teacher, the standard itself specifically requires "understanding" from the student.
Nowhere in the standard is it required for the teacher to use place value language (as Walle and Lovin discourage) but to make representations of the teen numbers using objects and drawings. According to the standard, children should compose and decompose a number in the teens into a group of tens and some ones. Let's dissect this standard to figure out exactly what it is and what it is not asking you to evaluate. The following standard requires unitizing:Ĭ.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8) understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. In kindergarten, the goal is not to formalize unitizing, but to begin to help students see numbers in groupings. The inappropriateness of discussing "one ten and six ones" (what's a one?) does not mean that a set of ten should not figure prominently in the discussion of the teen numbers" (Walle and Lovin 2006). Some would say that it is not appropriate for grade 1 at all. The concept of a single ten is just too strange for a kindergarten or an early first grade child to grasp. That is, prior to a much more complete development of place-value concepts (appropriate for second grade and beyond), children should not be asked to explain the 1 in 16 as representing "one ten".
However, the numbers between 10 and 20 are not an appropriate place to discuss place-value concepts. When children see a set of six with a set of ten, they should know without counting that the total is 16. Grouping numbers into tens is especially significant, because "A set of ten should play a major role in children's initial understanding of numbers between 10 and 20. It is an ability they use to see that there is simultaneously 1 chair with 4 legs, to count by 2's with understanding, to hold one number in their head when counting on, or to begin grouping numbers into tens. Unitizing is a child's ability to see numbers in groups. Compensation strategies can be used in the following Common Core standards:Ĭ.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Ĭ.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Ĭ.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).Ĭ.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.Ĭ.OA.A.5 Fluently add and subtract within 5.
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