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
TASKS The following tasks represent the level of depth, rigor, and complexity expected of all Kindergarteners. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. Task Name Standards Task Type/ Grouping Strategy Content Addressed Brief Description MGSEK.NBT.1 MGSEK.MD.3 3-Act Task Whole Group Estimating, Number relationships, Comparing sets, One to one correspondence, Categorizing Students will use their number knowledge to count forwards and backwards and count numbers higher than ten (11-20) MGSEK.CC.5a,b-7 Scaffolding Task Whole/Small Group Partner/Individual Number relationships, Comparing sets, One to one correspondence Students engage in numerous activities to count quantities of objects greater than ten. MGSEK.CC.1-4 Scaffolding Task Whole/Small Group Partner/Individual Counting, Numeral recognition, Number relationships, Recognizing number words Students engage in numerous activities to connect numerals, picture representations and words. MGSEK.NBT.1 MGSEK.CC.3,4a,5a,b Constructing Task Whole Group/Partner Number relationships Students work in a class discussion to understand the concept that a teen number is a group of ten and some more MGSEK.NBT.1 Constructing Task Whole Group/Partner Number relationships Students continue the work of the previous task with numbers 13-19. MGSEK.NBT.1 MGSEK.MD.3 Practice Task Small Group or Partner Estimating and one to one correspondence Students practice counting forwards and backwards with various amounts of objects. The Cardinal Cup (revisited 11-19) MGSEK.CC.2,4 Constructing Task Whole Group/partner Counting and number sequence Students practice counting forwards and backwards.
MGSEK.NBT.1 MGSEK.CC.4a,6 Scaffolding Task Small Group/Individual Counting, Numeral recognition, Number relationships, Recognizing number words Students practice making sets that are the same, less, and more than the quantity given. MGSEK.CC.4a,5a,b,6 Scaffolding Task Small Group/Individual Comparing sets, Number relationships Students work with one more and one less when completing the task. MGSEK.NBT.1 MGSEK.CC.4a,6 Constructing Task Whole Group/Partner Number relationship, Comparing sets Students use their knowledge of counting and cardinality to answer riddles. MGSEK.NBT.1 MGSEK.CC.3,4b,5a,b Constructing Task Partner Counting, One to one correspondence, Unitizing Students practice making ten and some more when building teen numbers. MGSEK.NBT.1 MGSEK.MD.3 Constructing Task Whole Group/Partner Counting, Unitizing Students use pennies and dimes to create a group of ten and some more. MGSEK.NBT.1 Constructing Task Whole Group/Partner Counting, One to one correspondence, Skip counting, Unitizing Students use their knowledge of building teen numbers to complete the activity using ten and some more. MGSEK.NBT.1 MGSEK.MD.3 Culminating Task Small Group/Individual Counting, One to one correspondence, Number relationships, Comparing sets Students will use all the information gained from this and the previous unit to complete the task by showing their understanding of teen numbers. Each task is suggested but not required; teachers should choose the most appropriate tasks based on the needs of their students. For more information on the tasks in this unit please refer to the unit webinar found at:
17 a group of 10 and 7 more 18 a group of 10 and 8 more 19 a group of 10 and 9 more 20 a group of 10 and 10 more CONSTRUCTING TASK: “Teen” Frame Talk-About (11-12) Approximately 1 day STANDARDS FOR MATHEMATICAL PRACTICE 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others.
Ten and Some More Name:___________________________ Bag How many groups of 10 can you make? How many singles are left over? Total in the bag Closer to 10, 15, or 20? How far away? A 10 15 20 _________ B 10 15 20 _________ C 10 15 20 _________ D 10 15 20 _________ E 10 15 20 __________