Number Sense Trajectory It All Together –Putting Subitizing Comparison Counting One-to-One Cardinality Hierarchical Inclusion Number Being able to Being able to Rote procedure of Correspondence how many things Understands numbers are Conservation visually compare counting. The Students can are in a set. When nested inside of each other The total number of recognize a quantities by meaning attached connect one counting a set of and that the number grows objects remains the quantity of 5 identifying to counting is number with one objects, the last word by one each count. 9 is same when they are or less. which has more developed through object and then in the counting inside 10 or 10 is the same rearranged spatially. Trajectory and which has one-to-one count them with sequence names the as 9 + 1. 5 is 4&1 OR 3&2. less. correspondence. understanding. quantity for that set. Each concept builds on the previous idea and students should explore and construct concepts in such a sequence Spatial Relationship One and Two-More or Less Understanding Anchors Part-Part-Whole Patterned Set Recognition Students need to understand the relationship of number as it Students need to see the Relationship Students can to recognize relates to +/- one or two. Here students should begin to see that 5 relationship between Students begin to sets of objects in patterned is 1 more than 4 and that it is also 2 less than 7. numbers and how they conceptualize a arrangements and tell how many relate to 5s and 10s. 3 is number as being Number without counting. 2 away from 5 and 7 made up from two Relationships away from 10. or more parts. Addition and Subtraction Strategies One/Two More/Less Make a Ten Near Doubles These facts are a direct Use a quantity from one the doubles application of the One/Two addend to give to another anchor and More/ Less than relationships to make a ten then add the combining it with 1 remainder.9 + 7 = 10 + 6 and 2 more/less. Facts with Zero Doubles Need to be introduced so that Many times students will students don’t overgeneralize use doubles as an anchor that answers to addition are when adding and always bigger. subtracting.
Number Sense Trajectory –Putting It All Together Trajectory Subitizing Being able to visually recognize a quantity of 5 or less. Comparison Being able to compare quantities by identifying which has more and which has less. Counting Rote procedure of counting. The meaning attached to counting is developed through one-to-one correspondence. One-to-One Correspondence Students can connect one number with one object and then count them with understanding. Cardinality how many things are in a set. When counting a set of objects, the last word in the counting sequence names the quantity for that set. Hierarchical Inclusion Understands numbers are nested inside of each other and that the number grows by one each count. 9 is inside 10 or 10 is the same as 9 + 1. Number Conservation The total number of objects remains the same when they are rearranged spatially. 5 is 4&1 OR 3&2. Each concept builds on the previous idea and students should explore and construct concepts in such a sequence Number Relationships Spatial Relationship Patterned Set Recognition Students can to recognize sets of objects in patterned arrangements and tell how many without counting. One and Two-More or Less Students need to understand the relationship of number as it relates to +/- one or two. Here students should begin to see that 5 is 1 more than 4 and that it is also 2 less than 7. Understanding Anchors Students need to see the relationship between numbers and how they relate to 5s and 10s. 3 is 2 away from 5 and 7 away from 10. Part-Part-Whole Relationship Students begin to conceptualize a number as being made up from two or more parts. Addition and Subtraction Strategies One/Two More/Less These facts are a direct application of the One/Two More/ Less than relationships Make a Ten Use a quantity from one addend to give to another to make a ten then add the remainder.9 + 7 = 10 + 6 Near Doubles the doubles anchor and combining it with 1 and 2 more/less. Facts with Zero Need to be introduced so that students don’t overgeneralize that answers to addition are always bigger. Doubles Many times students will use doubles as an anchor when adding and subtracting.
CCGPS_Math_K_Unit5Framework.docx