## Unit 8- Foundations of Numbers up to 120

This unit bundles student expectations that address the understanding of whole numbers up to 120, comparing numbers using place value, and ordering these numbers

using an open number line. 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 explored base-10 place value system as they explored whole numbers up to 99. Students composed and decomposed numbers

through 99 using concrete objects, pictorial models, and numerical representations. In addition, students used place value relationships and tools, such as a hundreds chart,

as they generated numbers more or less than a given number. Students compared whole numbers up to 99 using comparison symbols and were introduced to using place

value and open number lines to order whole numbers.

During this unit, students extend their understanding of the base-10 place value system to include the hundreds place as they continue exploring the foundations of whole

numbers up to 120. Students compose and decompose numbers through 120 as a sum of so many hundreds, so many tens, and so many ones using concrete objects

(e.g., proportional objects such as base-10 blocks, non-proportional objects such as place value disks, etc.), pictorial models (e.g., base-10 representations with place value

charts, place value disk representations with place value charts, etc.), and numerical representations (e.g., expanded form and standard form). Students use place value

relationships to generate numbers that are more or less than a given number using tools (e.g., a hundreds chart, calendar, base-10 blocks, etc.). Students use place value

to compare whole numbers up to 120 and represent the comparison using comparison language and comparison symbols. Students also extend using place value and open

number lines to order whole numbers up to 120.

## Unit 9- Number Relationships up to 120

This unit bundles student expectations that address using skip counting, determining numbers that are 10 more or 10 less than a given number, and reciting numbers. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, 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 07, students discovered numerical patterns in the place value system for numbers up to 99. Students recited numbers up to 99 forward and backward by ones and tens; skip counted by 2s, 5s, and 10s; and determined a number that is 10 more or 10 less than a given number up to 99.

During this unit, students continue to explore place value and numerical relationships in numbers up to 120. Students further 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. Students recite numbers up to 120 forward and backward by ones and tens; skip count by 2s, 5s, and 10s; and use place value patterns to determine a

number that is 10 more or 10 less than a given number.

## Linking Cubes, Base Ten Blocks, Place Value Disks, OH MY!

When starting to think about what manipulative to use for this unit, we need to think about what is developmentally appropriate and also take into account the specificity of the TEK.

1.2B states that students will use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones. In the specificity it says to use concrete proportional models (linking cubes, base ten, and bundles of sticks) and non-proportional models

Knowing all of this research says that developmentally 1st graders are not ready for base ten blocks so linking cubes are the best way to do place value. Van de Walle recommends groupable manipulatives prior to using traditional base-10 blocks, because they can physically be joined together and broken apart. Traditional base-10 blocks are actually a little more abstract because, for example, you can’t break the tens rod apart into ones–you have to trade it for ones.

That being said we have to also get kids ready for 2nd grade and the expectation that they will have to go from only doing numbers to 120 to 1,200. Not to mention they also have to use place value disks and are tested on those skills. So if we never expose them to base ten is that the best?

So here is what I recommend, review numbers 0-20 with linking cubes and then make the connection to base ten blocks. We will also make sure that we are taking students through the whole concrete-representational-abstract process during this unit.

## 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.

place value math song: ones, tens, hundreds
Teacher Tipster (Place Value Song)