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 overgeneralize that answers to addition are always greater. Doubles Many times students will use doubles as an anchor when adding and subtracting.
Task Name Standards Task Type/ Grouping Strategy Content Addressed Brief Description MGSEK.OA.1-5 3-Act Task Whole Group Addition and subtraction through word problems Students make different combinations to build the same quantity MGSEK.OA.1-5 Constructing Task Individual, Whole and Small Group Addition and subtraction through word problems Students use addition and subtraction while solving a story problem. MGSEK.OA.1-5 Practice Task Individual or small Group Number relationships to 10 Students play a card game to build combinations to 10. MGSEK.OA.1-5 Scaffolding Task Individual, Whole or Small Group Modeling number combinations through problem solving Students build different combinations for the same sum. MGSEK.OA.1-5 Practice Task Partners Number combinations to 5 and 10 and development of 8 SMPs Students use number combinations of 5 and 10 to play a game. MGSEK.OA.1-5 Scaffolding Task Individual, Whole or Small Group Number combinations to 5 through problem solving Students build number combinations to five through story problems MGSEK.OA.1-5 Constructing Task Individual, Whole and Small Group Number relationships to 10 Students show different combinations to 10 MGSEK.OA.1-5 Constructing Task Individual, Whole and Small Group Making generalizations in number relationships to 10 Students come up with different combinations to build 10
MGSEK.OA.1-5 Practice Task Individual, Whole or Small Group Modeling number combinations to 10 through problem solving Students model different ways to make combinations up to 10. MGSEK.OA.1-5 FAL Modeling number combinations to 10 through problem solving Students complete this activity to show their knowledge of modeling combinations up to 10. MGSEK.OA.1-5 Constructing Task Individual, Whole and Small Group Development with the understanding of equality and number relationships to 10 Students manipulate the different quantities to make the number sentence true. MGSEK.OA.1-5 Practice Task Individual, Whole or Small Group Number combinations to 5 through problem solving Students build number combinations to 5. MGSEK.OA.1-5 Constructing Task Individual, Whole and Small Group Making generalizations in number relationships to 10 Students look for patterns to solve word problems through 10. MGSEK.OA.1-5 Culminating Task Individual, Whole and Small Group Number combinations to 10 through problem solving Students use the knowledge gained to find patterns and build different number combinations to 10. 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 these tasks in this unit please refer to the unit webinar found at
As students identify how many boxes there are, be sure that they can explain their strategy of solving the problem (Example: counting up, subtracting from 10, etc…) (SMP1-8) Part II In pairs, have one student use the part-whole mat and create a situation that is shielded from the partner’s view with the folder (example: 2 boxes in the car and 8 boxes in the trailer). The player then verbally shares part of the mat with the partner and the partner must identify the other part. (Example: One student says “I have 2 boxes in the car, how many boxes are in the trailer? The other student then determines how many boxes are in the trailer). If the responding player identifies the correct amount of boxes, the roles change.(SMP1-8) Part III Give each student a piece of blank white paper and have them create a picture or situation that can be used as a part-whole mat. Have them create 3 questions to go along with their picture. They can use any accessible manipulative in the classroom in conjunction with their mat. After they have created the mat and 3 word problems, they partner with another student and share each other’s mat. Each student must try and solve their partner’s word problems using the mat. (Some mats can be laminated and saved as a center for ongoing practice).(SMP1-8) TEACHER REFLECTION QUESTIONS Did students discover patterns during their work? What strategies did students use to solve their problems? FORMATIVE ASSESSMENT QUESTIONS Are there more ways to decompose the number 10? Why did you decide to do it this way? Are you sure that you have found them all? Why do you think so? Did you develop a strategy to find your answers? Did you identify any patterns or rules? DIFFERENTIATION Extension Instead of using 10 counting objects as boxes, the students can explore number relationships to 20 by increasing the number of manipulatives. Intervention Allow students to work with numbers less than 5 so that they can practice using efficient strategies to solve the problems. Counting strategies are efficient at this stage, but will become inefficient and distracting as numbers become greater. As students begin to understand the relationships among numbers, they will begin learning number facts at a recall level (Carpenter et al. 1999).
Equally Balancing Numbers Draw the missing shape(s) in side “B” to make both sides equal Justify with numerals Add the shape that is missing from side “B” Add the 5 shapes to side B. 4 shapes are equal Side “B” has NO triangles Side “B” is missing 2 shapes