Warm-up: Which One Doesn’t Belong: Area and Arrays (10 minutes)
The purpose of this warm-up is to elicit strategies for quantifying the number of objects arranged in rows and columns and the language used to describe such arrangements. It gives students a reason to use language precisely (MP6). During the synthesis, ask students to explain the meaning of any terminology they use, such as row, column, array, group, line, grid, and rectangle.
- 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
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Which one doesn’t belong?
- “Why doesn’t B belong?” (It doesn’t have 20 dots.)
- “How did you determine the total number for each image?” (In D, I counted every dot. In C I counted by 5 since each row had 5 dots. In A, I counted by 5 since each row had 5 squares. In B, I just added 20 and 4 for the extra column.)
Activity 1: What Did I Create? (20 minutes)
The purpose of this activity is for students to create and describe rectangles of a certain area. Students work in groups of 2. One partner creates a rectangle and describes it, and the other partner creates a matching rectangle based on the description. Then students compare how their rectangles are the same and different. Students should describe their rectangle to their partner without revealing the total number of squares they used, so that the focus is on understanding the rectangular structure. In the synthesis, students share language that helped them understand the rectangle their partner built. When students revise their language to be more precise in the descriptions of their rectangle, they attend to precision (MP6).
Supports accessibility for: Social-Emotional Functioning
Materials to Gather
- Each group of 2 needs one folder.
- Groups of 2
- Ask students to place an object between them that obstructs their view, such as a folder.
- “The goal of this activity is to get both partners in a group to draw the same rectangle without looking at each other’s drawing. If you are partner A, draw a rectangle and describe it to your partner. You can’t tell them how many squares you used to draw your rectangle.”
- “If you are partner B, draw the rectangle that you think your partner is describing and then compare the drawings.”
- “After you finish describing and drawing the first rectangle, switch roles and repeat.”
- 10–12 minutes: partner work
Can you and your partner draw the same rectangle without looking at each other's drawing?
- Partner A: Draw a rectangle on one of the grids provided. Describe it to your partner without telling them the total number of squares.
- Partner B: Draw the rectangle your partner describes to you.
- Place your two rectangles next to each other. Discuss: What is the same? What is different?
- Switch roles and repeat.
- “What language did your partner use that was most helpful for you to draw the same rectangle they drew?” (The number of squares in each row or column and the number of rows or columns.)
Activity 2: Find the Area (15 minutes)
The purpose of this activity is for students to find the area of rectangles by counting squares. Larger rectangles provide more opportunities for students to practice counting strategies using the structure of the rectangles to group the individual squares (MP7). Rectangles in this activity lend themselves to show groups of twos, fives, or tens in rows or columns. Students may also see other ways to create equal groups within rectangles. For example, the second rectangle with an area of 30 square units can be seen as 3 groups of ten. If students finish quickly, encourage them to confirm the area by counting another way. Emphasize that each area is in square units.
Advances: Listening, Speaking
- Groups of 2
- “Find the area of each rectangle. Be ready to explain your reasoning.”
- 5–7 minutes: independent work time
- Monitor for counting strategies such as:
- Counting the squares in a row or a column and then skip-counting by that number for subsequent rows or columns.
- Grouping by twos, fives, tens, or other numbers.
- “Now share your strategies with your partner.”
- 2–3 minutes: partner discussion
Find the area of each rectangle and include the units. Explain or show your reasoning.
Advancing Student Thinking
If students miscount the square units in the rectangles, consider asking:
- “Tell me how you counted the squares.”
- “How could you keep track of your count as you count the squares?”
- Invite 3–4 previously selected students to share how they found the area of one of the rectangles. Try to highlight a variety of strategies.
- Consider asking, “Did your strategy change from rectangle to rectangle?”
“In the last few lessons, we learned about area. We learned that area is the amount of space covered by a shape. Then we learned that we could find the area of two-dimensional shapes by counting how many squares cover the shape.”
Display a 3 by 2 array of dots next to a 3 by 2 gridded rectangular area.
“We also revisited arrays today during our warm-up. Here is an array next to a rectangular area. How is area different from an array?” (Area is space covered by a shape, and an array is a collection of objects.)
“How do you see equal groups in these representations?” (You can see equal groups in the rows and columns. In the rectangle, you can see squares, but in the array, you count the objects.)
“Take five minutes to respond to one or more of these prompts: Describe area in your own words. How can we measure area? What lingering questions do you have about area?” (Area is the amount of space that a shape covers. We can count squares to find the area of a shape in square units. How do you find the area of a triangle?)
Cool-down: What’s the Area? (5 minutes)
Student Section Summary
In this section, we learned that area is the amount of space covered by a shape.
We saw that we can count squares to measure area. When we tile a shape, we need to make sure that the squares are covering the whole shape without gaps or overlaps.