This unit builds on the number concepts that were the focus of Unit 2. By regularly incorporating counting and comparing into daily math activities, students will now be approaching counting to 100 by one and tens. Counting should include beginning at a number other than one. Students will be writing numbers to 20 and keeping track of counting a set of objects to 20. In Unit 2 students decomposed numbers to five. By now they are well on the way to decomposing numbers to ten. Students will revisit this task early in first grade as a review and as preparation for a first grade focus on place value. In kindergarten the place value focus is on reasoning about the teen numbers, from 11-19. Students work with the numbers as a group of ten ones and some leftovers. While students should have several experiences building teen numbers and, in doing so, seeing a group of ten and some more, they do not need to be able to recognize ten ones as one unit of ten. This concept, known as unitizing, considering ten ones as a unit in itself, is a concept that is addressed early in first grade. Students will be ready for that if they develop a firm foundation and understanding of teen numbers in kindergarten. Working with teen numbers is particularly challenging for kindergartners because, in English, the language of teen numbers does not follow a logical naming system as it does in some other languages.
Throughout this unit, students should continue to work with quick images to develop mental images of number patterns (subitizing). Gradually, with much exposure, students move from quickly describing the visual pattern they see to seeing these patterns as two addends and a total. If they have a visual memory of patterns to five, they benefit from working with larger numbers. For example, if students have done work with ten-frames, using five as an anchor number, and solved many word problems with numbers to five, they should be ready to take a quick look at a slide and quickly see that 5 and 3 more are 8. They may not be able to say “8”, but if they see five and three more, you can work on strategizing how to find the total. While engaging students in these types of explorations of number, ask yourself questions such as the following to assess their understanding. Which students will need to count from one and count all? Are there students who can count on from 5? Counting on involves a higher level of thinking than counting all. Fingers are very useful tools for this kind of work. Students should also have access to a personal ten-frame. By the end of the year, students are expected to “fluently add and subtract within 5,” having internalized acting out the operations of adding to and taking from.
In this unit students continue to solve addition and subtraction word problems. The types of problems the Standards identify for solving in kindergarten are addition and subtraction problems where the result is unknown and problems where both addends are unknown (but the result is known). For an example of both addends unknown, see the grape problem in the Unit 2 Highlight Lesson where students looked for all the number pairs for 5. Students act out the problem situations with objects, their fingers, drawings, and verbal explanations. They use ten-frames, linking cubes, a number grid, a number line, and other objects as tools to represent the number relationships in the story situation. They may write expressions and equations to represent their problem, but this is not a kindergarten expectation. Whatever strategy and tools students use, they should be supported in explaining their reasoning to others. Related to that is teaching students to listen to each other and to consider the reasoning of what they hear.
