Students will investigate and construct understanding of the angle relationships that exist between parallel lines and transversal lines.

Students will explore angle relationships that exist between parallel lines and transversal lines to decide which shelves are parallel.

Big ideas that will be uncovered include:

• Any set of two or more lines that never meet are considered to be parallel;
• The distance between each pair of parallel lines never changes; and,
• Any transversal line intersecting two or more lines that are parallel will produce angle relationships that can be used to find missing angle measures.

Show students the video of 4 shelves being hung on a wall. Some shelves look parallel to one another and some do not.

Ask students to engage in a notice and wonder protocol. ANYTHING and EVERYTHING that comes to mind is fair game.

Write down all of the student noticing and wondering. For example:

• I noticed four shelves.
• It looks like some shelves are slanted.
• I wonder if the books would slide off some of the other shelves?
• I wonder if the shelves are level?
• And many others…

Take time to acknowledge the noticing and wondering your students have engaged in and try to answer any that you can address right away.

Then, pose the following question:

Which shelves are parallel?  

Make an estimate.

Have students estimate which shelves appear to be parallel. A discussion about what makes two lines parallel might be useful and/or necessary.

Record those estimates on the black/whiteboard or on chart paper.

Show an image of each of the shelves paired with the blue (level) shelf.

Ask students:

The blue shelf is level.

What is needed if we are to prove which shelves are parallel to the blue shelf and which are not?

Students may say:

1. Use a level.
2. Measure the height from the ground along different points on each shelf.
3. Put the books on the shelf and see if they slide off.
4. Measure the angles the shelves make compared to each other.

Now that students have shared some of the ways they might go about determining which shelves are parallel to the blue shelf, we can ask them:

What is needed if we are to prove which shelves are parallel to the blue shelf and which are not? 

Essentially we want to have students think critically about what information would help them make their argument.

At this point, show students this image and ask them:

How this might this image be helpful?

Lead students in a discussion on why measuring angles may be a more efficient and accurate way to determine if the shelves are parallel compared to some of the responses students may have shared previously in the discussion (i.e.: measuring from the ground to two different points on the shelf or putting books on the shelf to see if they slide off).

A big idea we want students to walk away with is that a transversal line provides an opportunity to easily compare whether two or more lines are parallel.

If we withhold the angle measurements on this image then the class can have a conversation around this question:

What is the least amount of angle measurements needed to determine if the shelves are parallel?

For example:

In each diagram if one angle is revealed, is that enough information to determine if the shelves are parallel?

Why or why not?

Show students this image (or pass out this image on a page):

Optional: Use this image instead.

Allow students to use the given information to determine which shelves are parallel to the blue shelf.

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After consolidating learning using student generated solution strategies and by extending their thinking intentionally, we can share which shelves are parallel.

Show a video that clearly indicates that one shelf is parallel, while the other two shelves are not.

Revisit the student answers. Have students discuss their thinking and what they would change if they did the task again. Return to the questions you recorded from the Spark portion of the lesson, and answer any questions that have not been answered.

If you wish to pursue an extension of this activity, you could ask students these consolidation prompts.

Consolidation Prompt #1:

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Consolidation Prompt #2:

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