- Author:
- Chris Adcock
- Subject:
- Algebra
- Material Type:
- Lesson Plan
- Level:
- Middle School
- Grade:
- 7
- Provider:
- Pearson
- Tags:

- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Interactive, Text/HTML

# Linear Measurements

## Overview

Students first create a diagram that represents the distance a ship drops in each of a series of locks. Students create their diagrams based on a video of an actual ship traveling through the locks. Students need to use contextual clues in order to determine the relative drops in each of the locks.

# Key Concepts

Students are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills.

Students will:

- Try a variety of strategies to approaching different types of problems.
- Devise a problem-solving plan and implement their plan systematically.
- Become aware that problems can be solved in more than one way.
- See the value of approaching problems in a systematic manner.
- Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.
- Make connections between previous learning and real-world problems.
- Create efficacy and confidence in solving challenging problems in a real-world setting.

# Goals and Learning Objectives

- Read and interpret maps, graphs, and diagrams.
- Solve problems that involve linear measurement.
- Estimate length.
- Critique a diagram.

# Niagara Falls

# Lesson Guide

Tell students that the waterway through the Great Lakes is called the St. Lawrence Seaway. This waterway is used to ship goods from one location on the Great Lakes to another. Have students imagine that they are the captain of a ship carrying containers full of goods, traveling along the waterway through the Great Lakes. Ask them to imagine what it must be like to suddenly encounter Niagara Falls! Have students watch the Niagara Falls video.

Ask students:

- Would you want to risk your life, the life of your crew, your ship, and the containers by going over the falls?

After some discussion, explain that for many years, ships simply avoided Niagara Falls altogether. Goods were loaded in vehicles on one side of the falls, transported to the other side, and then loaded on another ship. But this solution was costly and time-consuming. Thus, in 1824, the decision was made to build a canal system with locks that would enable ships to bypass Niagara Falls. This canal is called the Welland Canal.

## Opening

# Niagara Falls

Watch the Niagara Falls video and discuss the following with your classmates.

- What would you do if you were traveling down the river and you encountered Niagara Falls?
- What would happen to your ship if you went over Niagara Falls?

VIDEO: Niagara Falls

# Lake Erie to Lake Ontario

# Lesson Guide

Have students look at the map of the Welland Canal and locate Lake Ontario, Lake Erie, Niagara Falls, and the Niagara River.

Have partners discuss the question:

How do you think ships can navigate the change in elevation at Niagara Falls?

## Opening

# Lake Erie to Lake Ontario

Enlarge the map and locate the following:

- Lake Ontario
- Lake Erie
- Niagara Falls
- The Niagara River

Ships need to get from Lake Ontario to Lake Erie.

Discuss the following with your classmates.

- How do you think ships can navigate the change in elevation at Niagara Falls?

# The Welland Canal

# Lesson Guide

Tell students that the Welland Canal contains eight locks. These locks help ships travel from one water level to another.

Have students identify the Welland Canal on the map. Ask students:

- How do you think locks work?
- How do you think locks help solve the problem of going from Lake Erie to Lake Ontario?

Just have students brainstorm ideas about how locks work—students will learn more about locks later.

## Opening

# The Welland Canal

The Welland Canal was built to help ships navigate the change in elevation at Niagara Falls.

The canal contains mechanisms called locks that raise or lower ships, allowing them to travel between the two lakes to bypass Niagara Falls.

- Where is the Welland Canal located?
- How do you think the locks work?

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will graphically represent a ship's journey through the Welland Canal.

## Opening

# Math Mission

Graphically represent a ship’s journey through the Welland Canal.

# Explore Locks

# Lesson Guide

Have students independently explore the Lock Simulation interactive to determine how locks work. During this time, monitor students for understanding, but refrain from asking guiding questions or giving hints.

Next, allow students time to work with their partners to solve the problems. Have partners describe how a lock works from analyzing the Lock Simulation interactive.

During this time, circulate around the classroom asking guiding questions and noting strategies you would like students to share during the class discussion.

ELL: Before assigning an investigation to students, you may want to model the investigation to ensure that all students understand the task. Make sure all students know the meaning of the command words for the animation. Discuss how upstream, downstream, valve, gate, and light will control the animation. Let students investigate the best way to move the ships down the canal.

# Possible Answers

- Explanations will vary.
- Observations will vary.
- Possible answer: Valves are used to let water in or out of the lock until the water is the same level as the side the ship is traveling toward. The gates will open and close when the water is at the same level on each side of the gate. Once the gate is open, the light function will move the ship through the in and out of the lock.

## Work Time

# Explore Locks

Use the Lock Simulation interactive to find out how locks will raise or lower ships.

- Explore the Lock Simulation interactive.
- Experiment with closing and opening the valves, raising and lowering the gates, and turning the lights on and off. When you find the right combination, the ship will move upstream or downstream through the lock.
- Once you have gotten the ship to travel through the lock, explain how a lock works.

INTERACTIVE: Lock Simulation

# Explore the Welland Canal

# Lesson Guide

Have partners watch the Welland Canal video of the ship traveling through the Welland Canal and create their diagrams.

As students work through the problem, identify students who:

- Use different strategies to make sense of the video and the distance the ship drops at each lock.
- Create different types of diagrams and graphic representations to show the journey through the Welland Canal.

SWD: Students with visual-spatial vulnerabilities may struggle to recognize the relationships between the number of locks and the length of the Welland Canal. Some students may need support determining the elevation drop between locks. Direct instruction and explanation of this concept may be necessary.

# Mathematical Practices

**Mathematical Practice 1: Make sense of problems and persevere in solving them.**

- Students must make sense of the video and persevere in finding a method for calculating the distance the ship drops at each of the locks.

**Mathematical Practice 2: Reason abstractly and quantitatively.**

- Students must reason abstractly when measuring indirectly to find the distance the ship drops at each lock.

**Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.**

Students must construct a viable argument for why their answer and methods are reasonable to show the journey through the Welland Canals. They have the opportunity to critique the diagrams of other groups as well as their strategies during the class discussion.

**Mathematical Practice 4: Model with mathematics.**

- Students create a diagram to model the ship's journey though the Welland Canals.

**Mathematical Practice 5: Use appropriate tools strategically.**

- Students use appropriate tools and strategies to measure each distance the ship drops and to complete their diagrams.

**Mathematical Practice 6: Attend to precision.**

- Students' diagrams exhibit a variety of precision regarding the distance the ship drops at each lock as well as the distance the ship travels between locks. Some diagrams may only take into account the distance of the drop at each lock and not the distance between each of the locks.

**Mathematical Practice 7: Look for and make use of structure.**

- Students make use of the problem-solving structure while creating their diagrams and finding solutions to these problems.

# Interventions

**Student has difficulty getting started.**

- Describe the task to your partner in your own words.
- What happens to the ship at each lock in the Lock Simulation interactive? What has to occur before the ship can travel through the lock? Why?
- How can you estimate the distance the ship drops at each lock? What things in the video can help you estimate the distance?
- How can you estimate the length between each lock?
- What was your journey through the Welland Canal like?

**Student has an answer, but it is incorrect.**

- What contextual items did you use in the video to show the distance the ship drops at each lock?
- What decisions do you need to make in order to create your diagram?
- What does your diagram need in order for others to understand your thinking?
- Is your diagram a reasonable representation of what you saw in the video? Why or why not?

**Student has an answer but is having difficulty articulating his or her thinking.**

- How did you estimate the distance the ship drops at each lock?
- How did you estimate the distance from lock to lock?
- How did you decide what type of diagram would best illustrate the journey through the Welland Canal?
- How did you represent the distance the ship drops at each lock?

**Student has a correct answer and is waiting on others to finish**.

- What types of questions can you answer by looking at your diagram?
- How does your diagram describe the journey through the Welland Canal?
- Can you make another diagram to display this journey?

# Possible Answers

- Diagrams will vary. The overall length of the canal is about 27 miles. Seven of the locks

have an average drop of 46.43 feet; the eighth lock has an average drop of 1 to 4 feet. (Answer based upon Welland Canal dropping 326 feet and the 8th lock dropping by 1 foot) - Explanations will vary.

## Work Time

# Explore the Welland Canal

Today you will journey through the Welland Canal—just as though you were the captain of a ship. The Welland Canal have a series of eight locks; you will travel through all eight of them.

Watch the Welland Canal video.

- Draw a diagram that represents the journey through the locks. In your diagram, show estimates of the the distances the ship dropped at each lock.
- Describe how you gathered the data you used to make your diagram accurate.

Use objects in the video, such as people or cars, to help you make estimates of the distance that the ship dropped in each lock.

VIDEO: Welland Canal

# Total Drop Distance

# Lesson Guide

Continue as in Tasks 5 and 6.

SWD: For students with disabilities, participating in a whole class discussion such as Ways of Thinking can be intimidating for a variety of reasons. However, it is important for students to work on the speaking and listening skills implicit to this portion of the lesson. Possible supports for students include:

- Give students a few minutes to discuss their ideas, the questions posed, and what they learned in the lesson with a partner or small group before sharing out in the whole class setting.
- Conferencing with individual students prior to the discussion to ascertain what they might be able to successfully contribute to the discussion. Give students time to rehearse their contribution or to write notes for themselves to refer to when they speak. This will support students with expressive language difficulties and/or students who are anxious or reluctant to participate in class discussions.

# Possible Answers

The total distance that the ship dropped is about 326 feet.

## Work Time

# Total Drop Distance

Look at your estimates of how far the ship dropped at each lock.

- Make an estimate of the total distance the ship dropped for all of the locks combined.

# Prepare a Presentation

# Preparing for Ways of Thinking

As pairs work, identify students who:

• Have different strategies for estimating the distance the ship drops at each lock.

• Have different strategies for calculating the distance from lock to lock.

• Have gotten stuck at some point in solving this problem.

• Complete the Challenge Problem.

# Challenge Problem

## Answers

- Diagrams will vary.

## Work Time

# Prepare a Presentation

- Summarize what you have learned about the Welland Canal. Use your work as evidence in your summary.

# Challenge Problem

- Display the information in your diagram in a new way. Draw a different kind of diagram to represent the eight locks of the Welland Canals.
- Think of ways to construct a diagram that shows both the distance the ship drops at each lock and the distance between the locks.

# Make Connections

# Ways of Thinking

## Mathematics

Have students share their strategies and ways of approaching the problem. Encourage classmates to critique students' work and strategies.

Ask guiding questions, for example:

- How do locks work? What happens to the ship as it travels through a lock?
- Does this video show the ship traveling from Lake Erie to Lake Ontario or Lake Ontario to Lake Erie? How do you know? What would your diagram look like if the ship was traveling the other way?
- Are your answers exact or an estimate? Why?
- What strategies did you use to find the distance the ship drops at each lock?
- How did you calculate the distance from lock to lock?
- How does your diagram show the distance the ship drops at each lock?
- How does your diagram show the distance from lock to lock?
- How did you label the vertical and horizontal axes on your graph?
- How did you persevere in finding the solution?
- How do you know that your answer is reasonable?
- What tools did you use to help you find your solution?
- What was the most challenging aspect of the problem? How did you overcome this challenge?
- Are there multiple solutions to the problem? Why or why not?

Highlight the strategies and contextual tools students used to calculate the distance the ship drops at each lock as well as the distance from lock to lock.

Point out any mathematical practices you observed during as students worked.

Have students who completed the Challenge Problem share their diagrams.

## Performance Task

# Ways of Thinking: Make Connections

- Take notes about other students’ approaches to solving the problem, and their resulting diagrams.

As your classmates present, ask questions such as:

- How did you estimate the distance the ship dropped at each lock? What “context clues” helped you find this distance?
- How did you estimate the distance between each lock?
- How does your diagram show both the distance between the locks and the distance the ship drops at each lock?
- How did you decide what type of diagram would best illustrate the journey through the Welland Canal?

# Reflect on Your Work

# Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections to learn about the processes students used to make their diagrams of the ship's journey though the Welland Canal.

## Work Time

# Reflect on Your Work

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**The process I used to make a diagram of the journey through the Welland Canal is…**