Tile Rectangles
10 min
Narrative
The purpose of this Warm-up is to draw students' attention to different ways of covering a plane figure with squares and reinforce the idea that tiling involves covering a region without gaps or overlaps. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about characteristics of the items in comparison to one another. During the discussion, ask students to explain the meaning of any terms they use, such as "rows," "columns," "area," "gaps," "overlap," and "tiling."
Launch
- Groups of 2
- Display the image.
- “Pick 3 rectangles that go together. Be ready to share why they go together.”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
Which 3 go together?
Solution Steps (4)
- 1Examine each rectangle to see how tiles are arranged→A: checkered pattern, B: partially tiled, C: fully tiled, D: tiles with gaps/overlaps
- 2Identify which rectangles have proper tiling (no gaps, no overlaps)→A and C have squares touching along sides without gaps or overlaps
- 3Identify which rectangles have gaps or overlaps→B has gaps (incomplete), D has both gaps and overlaps
- 4Group 3 rectangles based on shared characteristic→A, B, C go together - squares aligned without overlapping
Sample Response
Sample responses:
A, B, and C go together because:- They show squares lined up touching other squares along their sides without overlapping.
- They have places where you can see white squares or white space inside the rectangle.
- They are mostly covered with shaded (blue) or white squares.
- The shaded (blue) squares touch or overlap on their sides.
Activity Synthesis (Teacher Notes)
- “How could you use the squares to find the area of each rectangle?” (In Rectangle C, I could just count the tiles. In Rectangle B, I could finish tiling the rectangle and then count the tiles. In Rectangle D I could straighten out the tiles so they cover all of the rectangle. In Rectangle A, I could count the blue tiles and double the number since in each row there are the same number of white tiles as there are blue tiles.
Standards
- 3.MD.6·Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
- 3.MD.C.6·Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
15 min
20 min
Knowledge Components
All skills for this lesson
Tile Rectangles
10 min
Narrative
The purpose of this Warm-up is to draw students' attention to different ways of covering a plane figure with squares and reinforce the idea that tiling involves covering a region without gaps or overlaps. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about characteristics of the items in comparison to one another. During the discussion, ask students to explain the meaning of any terms they use, such as "rows," "columns," "area," "gaps," "overlap," and "tiling."
Launch
- Groups of 2
- Display the image.
- “Pick 3 rectangles that go together. Be ready to share why they go together.”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
Which 3 go together?
Solution Steps (4)
- 1Examine each rectangle to see how tiles are arranged→A: checkered pattern, B: partially tiled, C: fully tiled, D: tiles with gaps/overlaps
- 2Identify which rectangles have proper tiling (no gaps, no overlaps)→A and C have squares touching along sides without gaps or overlaps
- 3Identify which rectangles have gaps or overlaps→B has gaps (incomplete), D has both gaps and overlaps
- 4Group 3 rectangles based on shared characteristic→A, B, C go together - squares aligned without overlapping
Sample Response
Sample responses:
A, B, and C go together because:- They show squares lined up touching other squares along their sides without overlapping.
- They have places where you can see white squares or white space inside the rectangle.
- They are mostly covered with shaded (blue) or white squares.
- The shaded (blue) squares touch or overlap on their sides.
Activity Synthesis (Teacher Notes)
- “How could you use the squares to find the area of each rectangle?” (In Rectangle C, I could just count the tiles. In Rectangle B, I could finish tiling the rectangle and then count the tiles. In Rectangle D I could straighten out the tiles so they cover all of the rectangle. In Rectangle A, I could count the blue tiles and double the number since in each row there are the same number of white tiles as there are blue tiles.
Standards
- 3.MD.6·Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
- 3.MD.C.6·Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).