This is a travesty to number sense and computation skills. I encourage all teachers to continue teaching students to skip count by every number from 2 to It is a simple task as students are familiar with skip counting and usually have had success with it and have self-confidence that they can do it. When it comes to number sense, skip counting helps students notice numerical patterns. The more patterns they see in numbers the more generalizations they can make about how numbers work. This will be invaluable to students as they move on to computation.
Drawing the jumps on a number line and repeating the numbers orally is an easy activity students can do independently. I use laminated number lines that students can use repeatedly with dry erase markers. Coloring in the pattern on a hundreds chart will also help them see when the patterns repeat and how often. Again, laminated charts and dry erase markers are great. What do they notice? How does it help them? Encourage them to come up with an observation that no one has stated yet.
This particular solution strategy is not necessarily indicative of a higher stage of thinking e. Implications for Teaching. This suggests that many children in the sixth grade are still predominately additive thinkers and thus not poised for handling multiplicative thinking and relative thinking that is necessary for fractional and proportional thinking.
It is thus important for teachers to provide continued opportunities for children to develop multiplicative thinking as early as possible. We have discussed the importance of skip counting to help children develop composite units, however, this level of development does not guarantee that a child has developed multiplicative thinking it does not imply that they have developed iterable units of 1. Many children like the one in Figure 1d are able to use their skip counting to solve multiplication tasks, but cannot work with units as countable objects and thus must depend on their additive strategies to solve such multiplicative tasks.
Without further development, children will have trouble developing more sophisticated ways of thinking that require higher levels of units coordination Ulrich, This understanding is necessary for multiplicative thinking, and thus many children reach middle school still working with their additive understandings. In addition to encouraging the continued use of skip counting, helping children develop notions of composite units can be aided through the intentional use of well-chosen mathematical manipulatives.
For example, when students are working with tasks that ultimately involve multiples e. Consider a task similar to the Cupcake Task in which there are 15 cupcakes to be put into boxes of 3 cupcakes. Figure 2 shows four models of a solution to this task using different types of manipulatives. Children with an INS may use single objects to represent 15 cupcakes and then make groups of three cupcakes see Figure 2a. For INS children, providing interlocking cubes Figure 2b could make it possible for them to build their own figurative composites, a first step in developing composite units.
In addition, making available unpartitioned rods that represent 3 Figure 2d may help promote the notion of an iterable unit of one and a multiplicative unit relationship. Subtle changes in the manipulatives provided to children for solving tasks can afford or constrain their growth in understanding. For example, only having rods like those in Figure 2d for a child with only an INS may actually constrain their development. However, for children with a TNS these rods could afford them the opportunity to develop the notion of an iterable unit of 1, thus helping them construct an ENS.
Again, subtle changes in the use of manipulatives can provide opportunities for children to combine their skip counting and notions of composite units to make important growth in the construction of their number sequences. Figure 2. Different models representing different types of unit structures for a Cupcake Task with 15 cupcakes.
Children who reach middle school without having made this transition are at a stark disadvantage because most of the middle school mathematics curriculum presumes multiplicative thinking. In this article we highlighted the characteristics of the different stages of number sequences that children move through as they construct their notions of composite and iterable units on their way to developing multiplicative thinking.
At the same time, it is important for teachers to recognize that the proficient use of skip counting does not necessarily imply that children have developed multiplicative thinking. By being aware of the characteristic ways of thinking associated with each of the different number sequences teachers are better able to provide appropriate scaffolding to move children through the stages. Olive, J. The Mathematics Educator , 11 1 , Steffe, L.
New York, NY: Springer. Construction of arithmetical meanings and strategies. Ulrich, C. Stages in constructing and coordinating units additively and multiplicatively Part 1. For the Learning of Mathematics, 35 3 , 2—7. Stages in constructing and coordinating units additively and multiplicatively Part 2. We stand in a circle and skip count up and down. I decided what direction and what we will be counting by, as well as starting and end points ex. When we hit the end point, the next three kids in the circle are Bing, Bang and Bong.
Bong has to sit down. You also sit down if you take longer than 3 seconds to respond, or if you are incorrect in your number. Last person standing wins a prize. We play the game BUZZ using a hundreds chart.
My kids LOVE it. Afterwards we look for patterns within the numbers. This has helped us improve our multiplication dramatically! Thank you for sharing these great ideas.
I have attached the link to "count By Tens and Then Count On" to my white board presentations for identifying the number that is represented by groups of tens and ones. Thanks for sharing your awesome ideas and for participating in our collaborative linky. Thanks for this collection of great ideas, Greg! I'm a big fan of Harry Kindergarten's math videos, too! Your email address will not be published. This site uses Akismet to reduce spam. Learn how your comment data is processed.
Skip counting is the method of counting forwards by a number that is not 1. TO skip count, you would add the same number each time to the previous number. However, skip counting is the foundation to learn other math concepts covered in higher grades, including:. We have created worksheets for students in kindergarten to grade 3 to practice skip counting at increasingly harder levels.
For late kindergarten use, these worksheets help students practice skip counting by 2 and Students fill in the missing numbers for skip counting by 2, 5 and Using number charts , students count by 3, 4, 5 and
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