The purpose of this Warm-up is to introduce students to cube roots by providing an opportunity to use cube root language and notation during the discussion. Encourage students to use estimated values for d and e to order the values before using a calculator. As students work, identify students who use different strategies for ordering, such as using a number line or using multiplication to guess and check.
Arrange students in groups of 2. Give students 2–3 minutes of quiet work time, and follow with a whole-class discussion.
For this activity, it is best if students do not have access to a calculator with a square root button. Encourage them to use estimation to order the values.
Let a, b, c, d, e, and f be positive numbers.
Given these equations, arrange a, b, c, d, e, and f from least to greatest. Explain your reasoning.
a2=9
b3=8
c2=10
d3=9
e2=8
f3=7
The order from least to greatest is f, b, d, e, a, c. Sample reasoning: We know that a=9, which is equal to 3. Since e=8, it is slightly less than 3. Since c=10, it is slightly greater than 3. We know that b=38, which is equal to 2 because 23=8. Since d=39, it is slightly greater than 2. Since f=37, it is slightly less than 2.
The purpose of this discussion is to introduce cube roots and cube root notation. Ask students to share their order of a, b, c, d, e, and f from least to greatest. Record and display their responses for all to see. If the class is in agreement, select previously identified students to share their strategies for ordering the values. If the class is in disagreement, ask students to share their reasoning until an agreement is reached.
Introduce students to cube root language and notation. Remind students that they previously learned that the equation c2=10 has a solution c=10. Similarly, we can say that the equation d3=9 has a solution d=39. Ask students to write a solution to f3=7. (f=37)
Finally, tell students that while square roots are a way to write the exact value of the side length of a square with a known area, cube roots are a way to write the exact value of the edge length of a cube with a known volume.
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The purpose of this Warm-up is to introduce students to cube roots by providing an opportunity to use cube root language and notation during the discussion. Encourage students to use estimated values for d and e to order the values before using a calculator. As students work, identify students who use different strategies for ordering, such as using a number line or using multiplication to guess and check.
Arrange students in groups of 2. Give students 2–3 minutes of quiet work time, and follow with a whole-class discussion.
For this activity, it is best if students do not have access to a calculator with a square root button. Encourage them to use estimation to order the values.
Let a, b, c, d, e, and f be positive numbers.
Given these equations, arrange a, b, c, d, e, and f from least to greatest. Explain your reasoning.
a2=9
b3=8
c2=10
d3=9
e2=8
f3=7
The order from least to greatest is f, b, d, e, a, c. Sample reasoning: We know that a=9, which is equal to 3. Since e=8, it is slightly less than 3. Since c=10, it is slightly greater than 3. We know that b=38, which is equal to 2 because 23=8. Since d=39, it is slightly greater than 2. Since f=37, it is slightly less than 2.
The purpose of this discussion is to introduce cube roots and cube root notation. Ask students to share their order of a, b, c, d, e, and f from least to greatest. Record and display their responses for all to see. If the class is in agreement, select previously identified students to share their strategies for ordering the values. If the class is in disagreement, ask students to share their reasoning until an agreement is reached.
Introduce students to cube root language and notation. Remind students that they previously learned that the equation c2=10 has a solution c=10. Similarly, we can say that the equation d3=9 has a solution d=39. Ask students to write a solution to f3=7. (f=37)
Finally, tell students that while square roots are a way to write the exact value of the side length of a square with a known area, cube roots are a way to write the exact value of the edge length of a cube with a known volume.