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