options: Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
problem_activity: Warm-up
This Math Talk encourages students to think about the relationship between base 10 logarithms and exponential expressions. Students have a chance to rewrite decimals, fractions, and base 10 numbers as powers of 10 in order to see which power of 10 the number is equal to and so find its base 10 logarithm. They will use this skill later in the lesson and in future lessons in order to calculate or estimate different logarithms.
Launch
Remind students that logarithms with no specified base are base-10 logarithms.
Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Representation: Internalize Comprehension.
To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Student Facing
Evaluate mentally.
\(\log 10\)
\(\log 10,\!000\)
\(\log 0.1\)
\(\log \frac{1}{1,000}\)
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
“Who can restate
\(\underline{\hspace{.5in}}\)
’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to
\(\underline{\hspace{.5in}}\)
’s strategy?”
“Do you agree or disagree? Why?”
If not already mentioned, make sure students recall that numbers such as 0.1 and
\(\frac{1}{1,000}\)
are still powers of 10 but they have negative exponents (that is, 0.1 is
\(10^{\text -1}\)
, and
\(\frac {1}{1,000}\)
is
\(\frac{1}{10^3}\)
or
\(10^{\text-3}\)
). This suggests that the logarithms of numbers that are less than 1 would be negative.
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)


correct_option_index: 7