## Unit 7- Number Relationships

This unit bundles student expectations that address relationships and patterns in numbers including the sum of a multiple of 10 and a one-digit number, reciting numbers, skip counting, and numbers that are 10 more and 10 less than a given number. According to the Texas Education Agency, mathematical process standards including application, 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 Kindergarten, students recited numbers by tens up to 100. In Grade 1 Unit 06, students explored place value in order to understand numbers up to 99.

During this unit, students continue delving deeply into the place value system. Various representations (e.g., linking cubes, straw bundles, base-10 blocks, place value disks,

hundreds charts, and open number lines) are used to discover numerical patterns in the number system. Students use place value patterns to determine the sum up to 99 of a

multiple of 10 and a one digit number, as well as determining a number that is 10 more or 10 less than a given number. Students continue to develop the understanding of

cardinal numbers, meaning numbers that name the quantity of objects in a set, and hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases, as they recite numbers up to 99 forward and backward by ones and tens in addition to skip counting by 2s, 5s, and 10s.

## 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.