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