“More learning time in Kindergarten should be devoted to number than to other topics.”
That statement is from the introduction to the Kindergarten Common Core State Standards for Mathematics. In other words, all standards are not created equal. There are two distinct types of skills related to numeracy—those related to counting and cardinality (CCSM K.CC) and those related to operations and algebraic thinking (CCSM K.OA).
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Counting and cardinality refers to knowing and writing number names and the counting sequence. It’s also understanding one-to-one correspondence. In other words, knowing the 5 represents 5 objects. Finally, comparing numbers is included in counting and cardinality.
Operations and algebraic thinking, on the other hand, requires that students understand that numbers are made up of smaller numbers—that smaller numbers can be composed to make larger numbers and larger numbers can be decomposed into smaller numbers. For example, the number 5 can be made with 0 and 5, 1 and 4, or 2 and 3. This aspect of number is the foundation for understanding basic addition and subtraction facts, which are required to perform multi-digit computations.
The entire Kindergarten year should be filled with activities and routines devoted to developing fluency with combinations for the numbers to ten, regardless if that is the current “unit”. Dot cards, number bracelets, and rekenreks are all excellent daily activities.
Activities that develop an understanding of number combinations are the same regardless of the target number. You can use the same activity to learn combinations for 5 as you can for 6, 7, 8, 9, and 10. For that reason, you want to build your arsenal of composing/decomposing activities or the kids will quickly tire of them. A terrific resource for quick and easy activities for composing and decomposing numbers is Building Number Sense, by Catherine Jones Kuhns. The book is literally nothing but activities for learning combinations for the numbers to ten. It’s a bonus that they all require very little prep or materials.
One of the activities in the book is Cube Trains. Students use linking cubes to make cube trains showing all the combinations for the target number. I thought it would be helpful to create some little mats for the kiddos to use.
The sheets for the numbers 3 through 6 are sized so students can actually create their cube trains and put them in the spaces. After they build the cube trains, they can color the recording sheet with two different colors. Linking cubes won’t fit on the sheets for the numbers 7 through 10, but I would suggest that students still build the trains.