##
* *Reflection: Developing a Conceptual Understanding
Spinning with Base 10 Decimals - Section 2: Concept Development

This lesson had me on my toes all day and has left me with a bit of a sore throat. Whenever a whole class works with plastic base ten blocks, there is an added level of noise in the classroom that I have to stay on top of. I had to make sure I had signals and cues for students to use in order to keep the blocks quiet during the direct instruction component of this lesson.

That being said, this is an excellent way for students to build conceptual understanding of what decimals are and begin to make sense of how decimals are used. I had many students admit that they had seen decimals in the past and after today's activity, those same students also admitted that they now have a much better understanding about what a decimal is. The use of concrete manipulatives to aid in decimal understanding is critical and crucial for my students before we move on to higher level thinking skills involving decimals. This lesson allowed my students the time to do just that.

While some students easily grasped the concept and wanted to abandon the model relatively quickly, others relied heavily on it. I need to make sure that the students who abandoned the model, are not just seeing a number pattern in the way they recorded the tenths and hundredths, but that they truly do have a solid understanding about what decimals are.

You can hear more thoughts about this lesson in my reflection video below.

*Modeling and Spinning = Understanding*

*Developing a Conceptual Understanding: Modeling and Spinning = Understanding*

# Spinning with Base 10 Decimals

Lesson 2 of 5

## Objective: SWBAT represent decimal fractions using the base ten model

#### Warm Up

*7 min*

Students will start today's lesson with a fluency assessment. This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.

This is an assessment I have my students do each week and then graph their results. It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions. (It also happens to be the quietest time in my math classroom all week!!)

This is what my classroom looks like as students work on this assessment.

This is sample of a student's graph. You can also click here to hear my thoughts about this graph below.

Click hereto see an example of a typical fourth grade fluency decrease since students are completing the fourth grade fluency set that incorporates division, multiplication, addition, subtraction, and adding and subtracting fractions with like denominators. (At this point, students have not had many fraction lessons, thus very very students are able to complete the fraction problems)

*I do not start my students with the fourth grade skills, but at this point in the year, all students are using the fourth grade set.. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards. By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics. I want to make clear that this assessment ONLY measures basic math computation. It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year. Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.*

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#### Concept Development

*45 min*

In this lesson, I use place value blocks or base ten models and direct instruction. I show students examples of base-ten blocks and lead a review discussion of what they have already seen these blocks referred to as (hundreds, tens, and ones).

I review the concept of each larger piece representing a group of 10 of the smaller piece to its right (1 flat = 10 rods, 1 rod = 10 cubes, etc.).

I then guide students to develop a “new” way to look at these base-ten blocks; they are now representations of parts of a whole. The flat becomes the one(s), the rods become tenths, and the units become hundredths.

I then tell students that today they will be learning about **decimals **and **how **to use them. I tell students that** decimals are just another way of recording fractions**.

I start by asking, “Who likes to play basketball?” I then explain that they will be using basketball to learn about fractions.

I ask for a student volunteer. I tell the student to stand on a tapeline placed 8 feet away from a trash can. The student takes 10 shots at the trashcan basket. Next, I ask students to explain how the shots made are recorded as a fraction. (Anna made 3 of the 10 shots, so she made 3/10 of the shots) I lead a brief discussion about scoring averages relating the concepts to Anna throwing the basketball. Many of my boy students are familiar with sports scores, batting averages, and scoring averages, but lack understanding of what that means. (I do not spend time talking about math averages during this discussion, but the idea of what 0.3 could mean in terms of sports.)

Next, I distribute base ten blocks to students. I ask students to cover their flat with longs or sticks, as I do the same with the document camera. I ask, “How many longs does it take to completely cover the flat?” (10) “If a flat has the value of one whole, then what will the value of each long be?” (1/10)

Next, I write 0.1 on the overhead and explain that this is the decimal form of the fraction 1/10. Then I write 0.3 and direct students to use their base ten blocks to show three tenths.

Then I display a base ten unit with the document camera and ask, “How many units would be needed to cover 1 flat.” (100) I ask,“If a flat has the value of one whole, what will the value of each unit be?” (1/100) Then I write 0.01 on the board and explain that this is the decimal form of the fraction 1/100

Next, I write a decimal like 0.14. I challenge students to use their blocks to show 14 hundredths. I make sure to establish that there are two ways to do this- with 1 long and 4 units or with 14 units. Students use their blocks to make a few more examples with decimals to the hundredths.

For the rest of the lesson students will play a game I call **Spin On Decimals. **Click here for a spinner template - spinners

Students play with their learning partners. They take turns spinning the 0-9 spinner. The first spin tells how many longs the partner must take, and the second spin tells how many units to take. Students record the value of the longs as a number of tenths and the value of the units as hundredths and then write the decimal created. Each student models the decimal as they play.

As students play the game, I circulate around the room to clear up misunderstandings and points of confusion. This activity is difficult for students as they wrestle with the idea of a hundred flat now being used as a tool to show one whole. This takes some getting used to, but is extremely helpful in building students conceptual understanding about what a decimal is.

Listen in as this student explains the decimal he is building and then even goes a step further and tells how many hundredths away from one whole the decimal is. (note: I have not previously taught this student how to do this, but he can easily see how many hundredths away the number is by using the model)

In this video you can hear and see just how difficult this concept can be for students. This student is trying to grasp the concept that a flat now has a value of one whole and the sticks have a value of one tenth.

#### Resources

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- UNIT 1: Getting to Know You- First Days of School
- UNIT 2: Multiplication with Whole Numbers
- UNIT 3: Place Value
- UNIT 4: Understanding Division and Remainders
- UNIT 5: Operations with Fractions
- UNIT 6: Fraction Equivalents and Ordering Fractions
- UNIT 7: Division with Whole Numbers
- UNIT 8: Place value
- UNIT 9: Geometry
- UNIT 10: Measurment
- UNIT 11: Fractions and Decimals