KinderPrep
All things Kindergarten Math
Unit 15- Numeracy
This unit bundles student expectations that address numeracy concepts as they are applied to operational situations involving addition and subtraction and graphing
situations.
Prior to this unit, in Units 08, 09, and 10, students developed concepts about numeracy which included counting, subitizing, number relationships, composing and
decomposing numbers, and part-whole relationships. Students developed ideas about reading, writing, and representing numbers. Other concepts about numbers were
developed including comparing and describing sets of objects. Students applied this knowledge about numbers and number relationships in addition and subtraction
situations and explored and explained different strategies for solving these problem situations. Students also applied their understanding of number and number relationships to data analysis situations involving real-object and picture graphs.
During this unit, students apply their knowledge of mathematical relationships to counting, problem solving, and graphing. Students increase their foundational
understandings of the mathematical relationships that exist within numbers. Counting is no longer simply rote. It now involves an understanding of the relationship between
the numbers in the counting sequence. Students acquire a mathematical understanding of how numbers increase by one during the forward count or decrease by one during
the backward count. Because of this understanding, students are able to count forward and backward easily without the use of objects. The understanding of this relationship
will also apply when reciting numbers by ones or tens beginning with any given number and when generating a number that is one more or one less than a given number.
Students transition to reading, writing, and representing numerals without objects or pictures. Students also transition from one-to-one correspondence to working with
number relationships. These mathematical relationships are applied when students generate and compare sets of objects or compare written numerals using comparative
language. Students use the subitizing skills of instantly recognizing quantities as they compose and decompose numbers. An understanding of cardinality and conservation
supports their work with addition and subtraction. This understanding that the last number names the set and that the arrangement of the set does not matter, allows
students to perform operations with numbers with greater accuracy. Students demonstrate an understanding that joining represents addition situations while separating represents subtraction situations. Students are able to explain the strategies used to solve problems with sums and minuends to 10. Numeracy concepts extend into
graphing. Students draw conclusions about data in both real-object and picture graphs.
After this unit, in Grade 1, students will continue to develop their understanding of numbers and number relationships. Students will be introduced to the concept of place
value and will use this knowledge when composing and decomposing larger numbers to 120. The operations of addition and subtraction will also be further developed as use
knowledge about number relationships and place value to develop addition and subtraction fact strategies.
CPA-Concrete, Pictorial, Abstract
Due to unit and state testing, we often rush students to the abstract form of understanding before they are ready. Students have to learn by doing and that means using manipulatives 50% of daily instructional time. And smart boards, apps and the book are not manipulatives...they are tools! Now, I am not saying you cannot use these great resources, I am just reminding you that a manipulative is something the kids are handling and learning from. Think of \knowledge in these stages
Using-This is the time when there is no algorithm-just the materials (counters, beans, cubes) Looks like-lots of questioning that leads to student discovery. Kids are talking and “playing”.
Modeling-In this stage, the students have the materials and the teacher is modeling the procedure while using manipulatives. The students are still not writing the procedures/algorithm. Instead they are seeing patterns and predicting.
Materials & Procedures-Here students are copying procedures you are modeling and beginning to try problems on their own. They still have materials and you are watching to see who is using them for necessity vs. comfort or out of habit.
No Materials-This is where students understand the concept and can generalize their problem solving. They may not get to this during the unit-remember mastery may not come until the end of the year. “But on a test…?”-If you have truly covered the concept concretely, students will know they can draw a picture to solve. That is why it is important to transition from concrete to pictorial throughout the unit! In one lesson I may fluctuate between concrete materials and pictorial representations. Another day I may try to go from pictorial to abstract and back to concrete in small groups.