All things Kindergarten Math

Unit 8-Introducing and Developing Numbers 16-20 and Counting to at least 100

This unit bundles student expectations that address the foundational skills for developing an understanding of numbers 0 – 20, counting forward and backward 1 – 20,

cardinality, subitizing, conservation of set, comparing numbers and sets of objects using comparative language, and generating numbers or set of objects less than or greater

than a given amount. This unit also includes the student expectation that addresses reciting numbers up to at least 100 by ones beginning with any number and by tens

beginning with any multiple of 10. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this unit, in Unit 06, students continued to investigate the foundational skills for understanding and using numbers from 0 to 15 and recited numbers up to 90 by ones

beginning with any given number.

During this unit, students are introduced to the numbers 16 – 20. They use sets of objects up to 20 to further develop an understanding of the concepts of cardinality, meaning that the last number said when counting a set of objects names the number of objects, hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases, and conservation of set, meaning if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change. Students apply cardinality, hierarchical inclusion, and conservation of set as they continue to explore the true meaning of numbers. Students count forward and backward to 20 with and without objects, as well as read, write, and represent the numbers. Students also compose and decompose numbers up to 10 using objects and

pictures which parallels the development of subitizing, meaning instantly recognizing the number being represented by a small quantity of objects in random and organized

arrangements. Students apply all of these skills as they consider magnitude, or relative size, to compare sets of objects up to 20 and generate a set of objects and pictures

that is more than, less than, or equal to a given number. Students use comparative language to describe the comparison of numbers represented using objects, pictures, or

numerals. When given a number up to 20, students are expected to generate a number that is one more than or one less than a given number. Along with the investigation of

number and quantity, students are expected to recite numbers up to at least 100 by ones beginning with any number. Students also extend reciting numbers to include reciting numbers by tens up to at least 100 beginning with any multiple of 10 (e.g., 10, 20, 30, 40, etc.). Practice with rote reciting of numbers and learning the correct sequence of numbers aids in developing the foundation for meaningful counting strategies.

After this unit, in Unit 15, students will revisit foundations of numbers from 0 – 20 and reciting numbers up to 100 by ones and tens along with contextual sums and minuends to


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

  1. 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”.

  2. 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.

  3. 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.

  4. 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.

Love this idea for comparing numbers and a brain break!

Shake it Off Kindergarten Lesson
The teacher writes 2 numbers on the board. She has told them to Shake off either the greater than or less than number. Then repeats this! Great to get them moving and shaking!
Fun songs with UMIGO - That Makes10 (ADDITION)
Climbing Up This Mountain (Counting by 10s up to 100)
COUNTING SUPER HERO! (Counting by 1s to 100 for kids)
The friends of 10