Squares and Cubes
5 min
Teacher Prep
Setup
Narrative
This activity introduces the concept of “perfect squares.” It also includes opportunities to practice using units of measurement, which offers insights about students’ knowledge from preceding lessons.
Some students may benefit from using physical tiles to reason about perfect squares. Provide access to square tiles, if available.
As students work, notice whether they use appropriate units for the questions about area.
Launch
Tell students, “Some numbers are called ‘perfect squares.’ For example, 9 is a perfect square. Nine copies of a small square can be arranged into a large square.” Display a square like this for all to see:
Explain that 10, however, is not a perfect square. Display images such as shown here, emphasizing that 10 small squares can not be arranged into a large square (the way 9 small squares can).
Tell students that in this warm-up they will find more numbers that are perfect squares. Give students 2 minutes of quiet think time to complete the activity.
Student Task
- The number 9 is a "perfect square." Find four numbers that are perfect squares and two numbers that are not perfect squares.
- A square has side length 7 in. What is its area?
- The area of a square is 64 sq cm. What is its side length?
Sample Response
- Sample response: Perfect squares: 9, 25, 4, 49, 100. Not perfect squares: 21, 2, 3, 10.
- 49 square inches
- 8 centimeters
Activity Synthesis (Teacher Notes)
Invite students to share the examples and non-examples they found for perfect squares. Solicit some ideas on how they decided if a number is or is not a perfect square.
If a student asks about 0 being a perfect square, wait until the end of the lesson, when the exponent notation is introduced. 0 is a perfect square because 02=0.
Briefly discuss students’ responses to the last two questions, the last one in particular. If not already uncovered in discussion, highlight the reasoning for finding the side length of a square given its area. The area of a square is found by multiplying its two equal side lengths. So, if we know the area, we can find the side length by answering the question ”What number times itself equals the area?”
Math Community
Display the Math Community Chart. Remind students that norms are agreements that everyone in the class shares responsibility for, so it is important that everyone understands the intent of each norm and can agree with it. Tell students that today’s Cool-down includes a question asking for feedback on the drafted norms. This feedback will help identify which norms the class currently agrees with and which norms need revising or removing.
Anticipated Misconceptions
If students do not recall what the abbreviations km, cm, and sq stand for, provide that information.
Students may divide 64 by 2 for the third question. If students are having trouble with this, ask them to check by working backward i.e., by multiplying the side lengths to see if the product yields the given area measure.
Standards
- 4.MD.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <em>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</em>
- 4.MD.A.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <span>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</span>
10 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Squares and Cubes
5 min
Teacher Prep
Setup
Narrative
This activity introduces the concept of “perfect squares.” It also includes opportunities to practice using units of measurement, which offers insights about students’ knowledge from preceding lessons.
Some students may benefit from using physical tiles to reason about perfect squares. Provide access to square tiles, if available.
As students work, notice whether they use appropriate units for the questions about area.
Launch
Tell students, “Some numbers are called ‘perfect squares.’ For example, 9 is a perfect square. Nine copies of a small square can be arranged into a large square.” Display a square like this for all to see:
Explain that 10, however, is not a perfect square. Display images such as shown here, emphasizing that 10 small squares can not be arranged into a large square (the way 9 small squares can).
Tell students that in this warm-up they will find more numbers that are perfect squares. Give students 2 minutes of quiet think time to complete the activity.
Student Task
- The number 9 is a "perfect square." Find four numbers that are perfect squares and two numbers that are not perfect squares.
- A square has side length 7 in. What is its area?
- The area of a square is 64 sq cm. What is its side length?
Sample Response
- Sample response: Perfect squares: 9, 25, 4, 49, 100. Not perfect squares: 21, 2, 3, 10.
- 49 square inches
- 8 centimeters
Activity Synthesis (Teacher Notes)
Invite students to share the examples and non-examples they found for perfect squares. Solicit some ideas on how they decided if a number is or is not a perfect square.
If a student asks about 0 being a perfect square, wait until the end of the lesson, when the exponent notation is introduced. 0 is a perfect square because 02=0.
Briefly discuss students’ responses to the last two questions, the last one in particular. If not already uncovered in discussion, highlight the reasoning for finding the side length of a square given its area. The area of a square is found by multiplying its two equal side lengths. So, if we know the area, we can find the side length by answering the question ”What number times itself equals the area?”
Math Community
Display the Math Community Chart. Remind students that norms are agreements that everyone in the class shares responsibility for, so it is important that everyone understands the intent of each norm and can agree with it. Tell students that today’s Cool-down includes a question asking for feedback on the drafted norms. This feedback will help identify which norms the class currently agrees with and which norms need revising or removing.
Anticipated Misconceptions
If students do not recall what the abbreviations km, cm, and sq stand for, provide that information.
Students may divide 64 by 2 for the third question. If students are having trouble with this, ask them to check by working backward i.e., by multiplying the side lengths to see if the product yields the given area measure.
Standards
- 4.MD.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <em>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</em>
- 4.MD.A.3·Apply the area and perimeter formulas for rectangles in real world and mathematical problems. <span>For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.</span>