##
* *Reflection: Developing a Conceptual Understanding
Skating on a Number Line - Section 2: Teacher Demonstration

When creating this activity for students, I wanted to make sure each slide was created with great intentions:

1. I wanted to expose students to the tape diagram (also called bar diagram) prior to teaching students how to use this model on their own.

2. Instead of creating a skating word problem, I simply placed a girl skating next to one "part," a boy skating next to another "part," and a boy and girl skating together next to the "whole." I was hoping students would be able to focus more on modeling the processes of adding/subtracting.

3. I modeled a variety of addition and subtraction scenarios, including Part-Part Whole (unknown part or whole) and Comparison (unknown part or unknown difference).

4. Finally, I developed a staircase of complexity by beginning with easier tasks (addition, smaller numbers) and building up to more difficult tasks (subtraction, larger numbers, inclusion of zero).

*Developing a Conceptual Understanding: Reflection*

# Skating on a Number Line

Lesson 6 of 16

## Objective: SWBAT use an open number line to solve multi-digit addition and subtraction problems.

#### Opening

*5 min*

To begin today's lesson, I decided it would be fun to show this roller skating commercial for Evian water to students. I explained: *Fourth graders, today we are going to solve some roller skating problems! I thought we should watch a roller skating video to help us feel inspired! *Many students giggled all the way through the video. Others excitedly said, "Oh yeah! I've seen this before!"

**Rationale**

I knew roller skating would be a fun context for adding. Later on, students will be solving word problems involving roller skating. This commercial will help spark interest.

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#### Teacher Demonstration

*30 min*

**Reasoning for Teaching Multiple Strategies**

During this Addition and Subtraction Unit, I truly wanted to focus on Math Practice 2: Reason abstractly and quantitatively. I knew that if students learned multiple strategies of adding and subtracting numbers, I wouldn’t only be providing them with multiple pathways to learning, but I would also be encouraging students to engage in “quantitative reasoning” by “making sense of quantities and their relationships in problem situations.” By teaching students how to use a variety of strategies, such as using number lines, bar diagrams, decomposing, compensating, transformation, and subtracting from nines, I hoped students would begin to see numbers as units and quantities that can be computed with flexibility.

**Number Line Rationale**

Even though the 4th grade standards don't specifically address the use of a number line, the number line model allows students to see the addition and subtraction processes. In addition, working with a number line with whole numbers is a foundational skill that will help with identifying fractions on number lines later on.

**Vocabulary**

I began this lesson by reviewing key vocabulary from past lessons. We reviewed the meanings of Open Number Line, Point, Starting Point & Ending Point, Landmark Numbers, and Nearest 10. By teaching math vocabulary, students will have the tools to truly practice MP 3 (Constructing Viable Arguments).

**Presentation & Goal**

In order to continue teaching students how to take jumps left and right on an open number to model the addition and subtraction process, I created a Google Presentation using Google Drive Documents called Skating on a Number Line prior to the lesson. Here are specific directions explaining How to Create a Google Presentation for Student Practice. Next, I was able to share this presentation with students using their student Google email accounts.

Students then copied the shared presentation and saved it in their math folders under the Google Drive. Once all students were successful at copying the presentation and making it their own, we discussed the first slide together, which was the Goal of the lesson: *I can add and subtract multi-digit numbers using a number line model.*

**Group Practice**

We then moved on to the first problem in the Group Practice section: Adding on an Open Number Line. I explained: *Let's say that our school had a roller skating contest. The girls skated a total of 10 miles. The boys skated a total of 8 miles. How many miles did they skate altogether? *I modeled how to begin with the starting point of 10 miles and add on 8 miles by taking jumps to the right. Students completed their number lines on this slide in their presentation right along side of me. I recreated this video at home without sound to demonstrate How to Add on the Number Line.

I then modeled how to solve a subtraction problem, Subtracting on an Open Number Line. I explained: *Let's say that the boys skated 58 miles and altogether, the boys and girls skated 347 miles. How many miles did the girls skate? What operation will we use to find the answer? *The students immediately knew we needed to subtract! Again, I modeled as the students completed their own number lines. This time, we started on the right side of the number line at 347 and took jumps to the left as we subtracted 58 (decomposed). Students caught on quickly! This video demonstrates How to Subtract on the Number Line (Again, recreated without sound).

##### Resources (14)

#### Resources

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#### Partner Practice

*65 min*

At this time, I knew students were ready to try using the open number line in a partner setting so we moved on to the Partner Practice section of the presentation, assigned partners, and began working collaboratively!

**Choosing Partners**

Assigning partners is always quick and easy as I already have students strategically placed in groups of 4-5 students throughout the room (based on abilities, behavior, communication skills, etc.). I simply divided these larger groups into smaller groups of 2-3 students. During partner work, sometimes students choose to work alone, but they frequently check answers with each other.

**Right to Work!**

Most students understood what to do and got to work right away. Others needed a little more guided practice (in the areas of technology and math). I took this time to roam about the room and provide extra support.

To begin with, I checked to make sure some students understood the guided practice. This student explains Subtracting 289 - 58 = ? perfectly. She also explains how she likes using the computer. This shows how technology can truly increase student engagement.

At first, many students chose to Subtract Inefficiently. I did question this student a bit to encourage him to find a more efficient strategy, however, I also wanted him to successfully develop a deep understanding of the open number line model.

This video shows two students working together to solve a comparison problem (one part is 17 more than the other part): Finding a Missing Part. I really try to encourage students to learn from one another instead of relying on me to point out mistakes.

I loved listening to this student explain how he used Adding to Subtract 52-10 =?. This was the trickier way of solving this problem and a limited number of students gave this strategy a try!

Here, two students explain how they are Using Mental Math First. It made me proud to see them truly using their reasoning skills.

Some students weren't able to complete their projects. However, students were able to successfully practice both addition and subtraction using an open number at their own pace. Here's a Student Example.

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- UNIT 1: Measuring Mass and Weight
- UNIT 2: Measuring Capacity
- UNIT 3: Rounding Numbers
- UNIT 4: Place Value
- UNIT 5: Adding & Subtracting Large Numbers
- UNIT 6: Factors & Multiples
- UNIT 7: Multi-Digit Division
- UNIT 8: Geometry
- UNIT 9: Decimals
- UNIT 10: Fractions
- UNIT 11: Multiplication: Single-Digit x Multi-Digit
- UNIT 12: Multiplication: Double-Digit x Double-Digit
- UNIT 13: Multiplication Kick Off
- UNIT 14: Area & Perimeter

- LESSON 1: Rounding to Check Addition
- LESSON 2: Finding Compatible Numbers to Check Subtraction
- LESSON 3: Checking the Reasonableness of Addition
- LESSON 4: Checking the Reasonableness of Subtraction
- LESSON 5: Using an Open Number Line
- LESSON 6: Skating on a Number Line
- LESSON 7: Flying on a Number Line
- LESSON 8: Animal Weights & Bar Diagrams
- LESSON 9: Decomposing to Compare Daily Salaries
- LESSON 10: Decomposing to Compare Monthly & Annual Salaries
- LESSON 11: Compensating to Compute Smaller Numbers
- LESSON 12: Compensating to Compute Larger Numbers
- LESSON 13: Transforming to Compute Smaller Numbers
- LESSON 14: Transforming to Compute Larger Numbers
- LESSON 15: Subtracting from Nines
- LESSON 16: Verifying Answers