##
* *Reflection: Rigor
The Next Decade - Section 2: Active Engagement

This work is easy for students. They are able to find the nearest 10 or 100, but rarely do they know "why" they do that. Asking the children to work through the complexity of this task by explaining their reasoning other than just simply rounding, gives them experience in realizing how rounding a number helps, but can also add complexity. For example, if we round to the tens, rather than the 100's, our actual answer and estimate may be closer, but if we say we have about $90.00, we might only have $86.00 and not enough to cover a $90.00 bill!

This kind of rigorous thinking is imperative to the success of really understanding mathematical concepts. Acquiring procedures and simply solving algorithms tend not to stick, unless it works for one of those rare children for whom it make sense.

*Why ask Why?*

*Rigor: Why Ask Why?*

# The Next Decade

Lesson 8 of 10

## Objective: Students will be able to apply their rounding knowledge by using a number line or a number grid.

## Big Idea: Students need to understand what a rounded number represents, and how that representation may be for several numbers. As the students solve various situations in this lesson, they come to know that a rounded number represents 9 different values.

*45 minutes*

#### Mini Lesson

*10 min*

To begin this lesson, I inform the students that by the end of the session, they should be able to explain why people round. I ask them to tell me what they already "know" about the reasoning behind rounding.

This clip accurately displays the majority of my class's ideas.

As you move through the lesson, be sure to use terms such as the 20's decade, or the 70's decade. work with students to explain the position of numbers. For example, 17 falls between the 10 and 20 decades (or 10's). This will help students communicate their movement, and in time their rounding skills.

Now, armed with the prior knowledge, I tell the students that we will play a "hopping game" on the number line I have tapped onto our carpet. We number the intervals from 0 to 100, by 10's. Then, we discuss the terms "decade" and "century". I give examples of decade changes (people talking about music from the 50's or 70's). I have the students share any examples they may have heard of. Then we discuss the term "century" in the same way.

For the game, I will have volunteers come up and stand on 0, which is our start number. I have students roll two dice and create a number with it. I then ask the volunteer to hop to the decade that is closest to their their number, and then to explain why their "landing place" is correct. (The idea is that they would go to the closest "island" to their number.)

We do this several times, with several volunteers. The number line on the floor gives a wonderful visual for the entire class and allows the students to use some movement. Their jumps are shorter to the closer decade, or 10. They can "feel" this movement when making decisions.

The number grid is especially helpful, as they can count, like a game board, the number of jumps to each decade.

This student was told by the class that if he was at 45, he would need to jump to 50. He was at 100 from a jump from 97.

Next, I ask questions to elicit thinking about what the actual numbers could "possibly be" before they are rounded. For example, the rounded number 70 could actually be any number between 65 and 74.

To visualize this, we "hop" to these places on the line and and use comparison to discover that these numbers (65 through 74) are "closer" to the decade 70.

The use of a number line, or number grid, is imperative here. The students need to see the decade they are closest to in order to understand rounding as a concept. It is also important to discuss with them what two decades each number is between. Count how many hops forward, or backward.

If your students are ready, you can easily convert the tens on the tape into the hundreds digits.

*expand content*

#### Active Engagement

*25 min*

To give students independent practice, I use a set of situations found on the Georgia Department of Education website. The document is called "Island Hop Scavenger Hunt". I gave the students a 100's chart to help them visualize the distance between numbers and the bookmarking decades. The students were give stories and asked to defend what numbers could be the number prior to rounding. I chose to use a number grid, rather than a number line, because I wanted students to see all intervals from 0-100.

As the children work, I circulate and discuss with them their thinking, listening for them to accurately explain their solutions. Many times, the "why" is tricky for the students, as in this clip. During the discussion afterwards, I work with this child on the definition of "nearest" or "closest".

This student is able to explain to me that the distance on a number line dictates the rounding of a number.

#### Resources

*expand content*

#### Closing

*10 min*

To deepen understanding, students share their work and explain how they solved the situations they were assigned. Then, I ask the same question from the beginning of the lesson, "Why do we round?".

I got the answer I was hoping for!

*expand content*

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- UNIT 1: Developing Mathematical Practices
- UNIT 2: Understanding Multiplication
- UNIT 3: Using Multiplication to Find Area
- UNIT 4: Understanding Division
- UNIT 5: Introduction To Fractions
- UNIT 6: Unit Fractions
- UNIT 7: Fractions: More Than A Whole
- UNIT 8: Comparing Fractions
- UNIT 9: Place Value
- UNIT 10: Fluency to Automoticity
- UNIT 11: Going Batty Over Measurement and Geometry
- UNIT 12: Review Activities

- LESSON 1: Mental Math with Place Value
- LESSON 2: Place Value and the Number Line
- LESSON 3: Exploring Place Value Strategies While Journaling
- LESSON 4: Adding 3 Digits to 3 Digits Using Expanded Form
- LESSON 5: Journaling About Place Value
- LESSON 6: Regrouping Using Riddles
- LESSON 7: Rounding to Check Accuracy
- LESSON 8: The Next Decade
- LESSON 9: Two Digit Subtraction With Rounding
- LESSON 10: Multiple Step Story Problems