# Lesson 4

Points and Lines All Around

## Warm-up: Which One Doesn’t Belong: Four-sided Shapes (10 minutes)

### Narrative

This warm-up prompts students to carefully analyze and compare quadrilaterals and their sides. When students make comparisons, they have a reason to use geometric language precisely (MP6). The activity also enables the teacher to hear the terminology students know and how they talk about characteristics of two-dimensional figures. The knowledge and ideas that students show here may also be insightful to teachers in the next lesson, when students learn about angles.

### Launch

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• 2–3 minutes: partner discussion
• Record responses.

### Student Facing

Which one doesn’t belong?

### Activity Synthesis

• “How might we know if the sides of a figure are parallel?” (We could extend the lines or measure to see if the two sides are always the same distance apart.)
• “All four quadrilaterals have at least one pair of parallel sides. Do all quadrilaterals have at least one pair of parallel sides?” (No) “Can you draw one with no pairs of parallel sides?”

## Activity 1: Spot Lines and Line Segments (15 minutes)

### Narrative

In this activity, students practice identifying line segments and both intersecting and parallel lines. First, students find these figures on a map and then in the alphabet. In both contexts, they encounter marks that may appear to be segments, but are not actually perfectly straight, or pairs of lines that appear to be parallel, but are not exactly so. Students have an opportunity to attend to precision when analyzing the given images (MP6).

When analyzing some letters in the alphabet, students may say that J and O have lines or segments that turn. Remind students that we had defined a line as being straight, so a line segment is also straight. In the letter J, the segment can be distinguished from the curve.

MLR8 Discussion Supports. Synthesis: To support the transfer of new vocabulary to long-term memory, invite students to chorally repeat the ending statements in unison 1–2 times: All intersecting lines cross each other, some intersecting lines form square corners, and all parallel lines never touch.

### Required Materials

Materials to Gather

### Required Preparation

• Gather Collect and Display charts from previous lessons.
• Each student will need access to their personal word walls created in previous lessons.

### Launch

• Groups of 2
• Display the map of Staten Island, NY.
• Display the chart of phrases collected during Collect and Display in a previous lesson.
• “Use your personal word walls or this chart of words and phrases to describe what you notice about this map of Staten Island, New York.”
• “What do you notice about the streets on the map?” (Some are short and some are long. Some end and some cross others.)

### Activity

• 5 minutes: quiet think time
• 3–4 minutes: partner work time
• Monitor for students who:
• notice that some marks on the map are not straight (even if they might appear to be) and are therefore neither lines nor segments
• recognize that some pairs of lines or segments might appear to be parallel but are not

### Student Facing

1. Here is a map of a neighborhood in Staten Island, New York.

On the map, find and label the following items:

• 4 line segments of different lengths
• 3 pairs of parallel lines
• 2 pairs of lines that are not parallel

(Consider using different colors for the different types of lines.)

2. In the words WHALE and JOY,

which letter has:

1. No parallel segments? _________________________

2. Exactly one pair of parallel segments? _________________________

3. More than one pair of parallel segments? _________________________

4. Only one segment? _________________________

If you have time: Which does the uppercase alphabet use more: parallel segments or intersecting segments?

### Student Response

Students may describe letters as having parallel segments (or as having no intersecting segments) because the segments do not cross. Ask students to explain and show what they mean. If students show segments that meet, but do not cross, consider asking,

• “What do you think it means for segments to be parallel?”
• “If you draw the lines that these segments are on, would the lines ever cross?”

### Activity Synthesis

• Select students to share their responses to the first question. Display their work (using a document camera or projection), or display the map and ask them to show their lines on it.
• To elicit the use of precise vocabulary and encourage more participation, consider asking:
• “Were there any pairs of lines that you had assumed to be parallel at first but then realized that they are not? How did you find out?”
• “Can someone else show a different pair of parallel lines? A different pair of lines that are not parallel?”
• “Do two segments have to be the same length to be parallel? For example, the top horizontal segment in E and the middle horizontal segment have different lengths. Are they parallel?” (Yes. The segments are part of lines that are parallel. The length of the segments does not determine if they are parallel.)
• “How might we finish these statements?”
• “All intersecting lines _____.” (cross each other)
• “Some intersecting lines _____.” (form square corners, make an “X” shape)
• “All parallel lines _____.” (never cross)

## Activity 2: Draw and Design with Lines (20 minutes)

### Narrative

In this activity, students look for parallel and intersecting lines in their environment and record them in a drawing. Students notice that parallel and intersecting segments can be found in logos and symbols and use these figures to design their own logo. When students recognize mathematical features of objects in their classroom and design a logo with intersecting and parallel line segments they model with mathematics (MP4).

If time permits, ask students to display their drawings and logos and do a gallery walk.

Action and Expression: Develop Expression and Communication. Offer students an alternative to drawing on paper, such as using pipe cleaners to create a representation of lines in the classroom or using painter’s tape to physically mark lines around the classroom.
Supports accessibility for: Visual-Spatial Processing, Fine Motor Skills

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “For this activity, look around the classroom, find parts that have certain geometric parts we've been studying, and draw a sketch of them.”

### Activity

• 5–7 minutes: independent work time on the first question
• 2–3 minutes: partners trade sketches and verify that the required lines are shown
• Monitor for students who:
• represent the thickness of objects (of a frame or a countertop, for example) with two parallel lines
• represent objects abstractly, showing only essential shapes and lines
• attend to precision by using tools like rulers or straightedges
• choose to draw freehand
• For students who draw freehand, consider asking:
• “How can you be sure that what you are sketching are lines or segments and not curves?”
• “How do you know if you are drawing parallel segments?”
• 5 minutes: independent work time on the second question

### Student Facing

1. Draw a sketch of a part of our classroom and be sure to include:

1. at least 3 pairs of parallel line segments
2. intersecting line segments that make square corners
3. intersecting line segments that don’t make square corners

Trade sketches with a partner and find the specified lines in each other’s sketches.

2. Here are some symbols and logos that you may recognize. All of them have intersecting and parallel line segments.

Design a logo with at least 8 parallel segments and 8 intersecting line segments.

Use a ruler for any straight parts of your logo.

### Activity Synthesis

• “Where did you find parallel lines in our classroom?” (windows, doors, floor tiles, cubbies, desks)
• “Where did you find lines that make square corners?” (windows, doors, floor tiles, cubbies, desks)
• “Where did you find lines or segments that do not make square corners when they intersect?” (design on the doors, slant on the ceiling or floor, railings of stairs, braces or brackets of desks or chairs, hands on the clock)
• If time is limited, ask partners to trade their logo designs, look for the required lines in each other’s work, and share feedback.
• If more time is available, ask students to display their designs and visit others’ work in a gallery walk. As they look at each design, students should look for parallel and intersecting lines and line segments.

## Lesson Synthesis

### Lesson Synthesis

“Today we saw various examples of parallel and intersecting lines and line segments.”

Display:

“Where do you see parallel lines in the images?” (The left and right sides of the ladder. The outside pieces of the drawing of the track.)

“What’s the difference between the lines you see in the photos of the track and the drawing of the track?” (The horizontal lines look parallel in both. The vertical lines of the track do not look parallel in the photo, but do look parallel in the drawing.)

“Why do you think there’s a difference?” (Maybe some things in the real-world look parallel, but are not really parallel. I think it depends on how you look at it. If we looked at the track from above, maybe the lines would look parallel. When you draw things, you might make some lines parallel to make it look nicer or simpler.)

“When you were creating your sketch or logo today, how did you make sure that the segments that need to be parallel are actually parallel?” (I measured the distance between them, I used a ruler or another rectangular object as a guide.)

“Take 1–2 minutes to add any new words from today’s lesson to your word wall. Share your new entries with a neighbor and add any new ideas you learn from your conversation.”