Square Roots
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to continue developing their understanding of square roots. Students find the areas of three squares, estimate their side lengths using tracing paper, and write their exact side lengths using square root notation.
Launch
Arrange students in groups of 2. Provide access to geometry toolkits, including tracing paper. Since the goal of this activity is for students to estimate square roots and not find exact values, do not provide access to calculators. Remind students about the meaning and use of square root notation.
Student Task
Find the area of each square and estimate the side lengths using your geometry toolkit. Then write the exact length for the sides of each square.
Sample Response
Sample response:
A: Area is 29 square units; any side length between 5 and 6 units in reasonable; s=29
B: Area is 18 square units; any side length between 4 and 5 units in reasonable; s=18
C: Area is 13 square units; any side length between 3 and 4 units in reasonable; s=13
Activity Synthesis (Teacher Notes)
The purpose of this discussion is for students to connect the estimate made with tracing paper to the exact length of the side of a square written in square root notation. This helps students to see that a square root is still a number, and it can be approximated by a value that is easier to see.
For each square, invite several students to share their estimate for the side length and display the results for all to see. Here are some questions for discussion:
-
“What do you notice about the estimates?” (The estimates are all close to each other. Some have more decimal places than others.)
-
“How can we check the accuracy of our estimates?” (We can take our estimate and square it to see how close we are to the area of the square.)
Standards
- 8.EE.2·Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
- 8.EE.A.2·Use square root and cube root symbols to represent solutions to equations of the form <span class="math">\(x^2 = p\)</span> and <span class="math">\(x^3 = p\)</span>, where <span class="math">\(p\)</span> is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that <span class="math">\(\sqrt{2}\)</span> is irrational.
15 min
10 min
Knowledge Components
All skills for this lesson
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Square Roots
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to continue developing their understanding of square roots. Students find the areas of three squares, estimate their side lengths using tracing paper, and write their exact side lengths using square root notation.
Launch
Arrange students in groups of 2. Provide access to geometry toolkits, including tracing paper. Since the goal of this activity is for students to estimate square roots and not find exact values, do not provide access to calculators. Remind students about the meaning and use of square root notation.
Student Task
Find the area of each square and estimate the side lengths using your geometry toolkit. Then write the exact length for the sides of each square.
Sample Response
Sample response:
A: Area is 29 square units; any side length between 5 and 6 units in reasonable; s=29
B: Area is 18 square units; any side length between 4 and 5 units in reasonable; s=18
C: Area is 13 square units; any side length between 3 and 4 units in reasonable; s=13
Activity Synthesis (Teacher Notes)
The purpose of this discussion is for students to connect the estimate made with tracing paper to the exact length of the side of a square written in square root notation. This helps students to see that a square root is still a number, and it can be approximated by a value that is easier to see.
For each square, invite several students to share their estimate for the side length and display the results for all to see. Here are some questions for discussion:
-
“What do you notice about the estimates?” (The estimates are all close to each other. Some have more decimal places than others.)
-
“How can we check the accuracy of our estimates?” (We can take our estimate and square it to see how close we are to the area of the square.)
Standards
- 8.EE.2·Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
- 8.EE.A.2·Use square root and cube root symbols to represent solutions to equations of the form <span class="math">\(x^2 = p\)</span> and <span class="math">\(x^3 = p\)</span>, where <span class="math">\(p\)</span> is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that <span class="math">\(\sqrt{2}\)</span> is irrational.