standard_description: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about square roots by estimating the value of each expression. The values given as choices are close in range to encourage students to use the square roots they know to help them estimate ones they do not. These understandings will be helpful for students in upcoming activities where they will be applying the Pythagorean Theorem.
While four problems are given, it may not be possible to share every strategy. Consider gathering only two or three different strategies per problem.
Launch
Display one problem at a time. Give students 30 seconds of quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all previous problems displayed throughout the talk. Follow with a whole-class discussion.
Student Facing
Which estimate is closest to the actual value of the expression? Explain your reasoning.
\(\sqrt{24}\)
4
4.5
5
\(\sqrt7\)
2
2.5
3
\(\sqrt{42}\)
6
6.5
7
\(\sqrt{10}\)
+
\(\sqrt{97}\)
13
13.25
13.5
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. After each student shares, ask if their chosen estimate is more or less than the actual value of each expression.
Speaking: MLR8 Discussion Supports.
: Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because . . ." or "I noticed _____ so I . . . ." Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)


aligns: no