The Power of Exponents

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

7, 8

Overview

In this activity, students will begin thinking about the power of exponents. They are given a choice of receiving 500 coins right now or receiving one coin the first day and doubling the amount each day for a month. Students will watch a free video tutorial to guide them through why exponents are used, how to simplify the same-base number with exponents, and how to show equivalent expressions to bases containing negative exponents. The video tutorial explains exponents in a way that all students can understand. Then, the students will revisit their choices by watching another video and work problems posed to see if their choice was wise considering the power of exponents. This activity can be used as an introduction to a lesson on exponents. 

This activity results from the ALEX Resource Department Summit.

Phase

Before/Engage
Mathematics (2019) Grade(s): 7

MA19.7.14

Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.

UP:MA19.7.14

Vocabulary

  • Probability model
  • Uniform model
  • non-uniform model
  • observed frequencies

Knowledge

Students know:
  • the probability of any single event can be expressed using terminology like impossible, unlikely, likely, or certain or as a number between 0 and 1, inclusive, with numbers closer to 1 indicating greater likelihood.
  • A probability model is a visual display of the sample space and each corresponding probability
  • probability models can be used to find the probability of events.
  • A uniform probability model has equally likely probabilities.
  • Sample space and related probabilities should be used to determine an appropriate probability model for a random circumstance.

Skills

Students are able to:
  • make predictions before conducting probability experiments, run trials of the experiment, and refine their conjectures as they run additional trials.
  • Collect data on the chance process that produces an event.
  • Use a developed probability model to find probabilities of events.
  • Compare probabilities from a model to observed frequencies
  • Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Understanding

Students understand that:
  • long-run frequencies tend to approximate theoretical probability.
  • predictions are reasonable estimates and not exact measures.
Mathematics (2019) Grade(s): 8

MA19.8.3

Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

UP:MA19.8.3

Vocabulary

  • Integer Exponent

Knowledge

Students know:
  • that whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced.

Skills

Students are able to:
  • Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents.

Understanding

Students understand that:
  • just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
  • The exponent can be translated (visually, listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense.

Learning Objectives

Students:
- can apply their understanding of exponents as repeated multiplication to create equivalent expressions and justify integer exponent properties.

Activity Details

Distribute the worksheet titled The Power of Two Worksheet (one per student). Read aloud the choices to the students and have them highlight their choice. (Students will highlight their choice so they can not change their choice later). 

Show students the video, Apply Properties of Integer Exponents to Generate Equivalent Expressions Part 1.

Bring students' attention back to The Power of Two Worksheet.

Show the students the Power of Exponents video. Then, ask the students if their choice might have changed.

Have the students complete the table starting with one coin on the first day and then double that amount each day until the end of the month. How many coins did they receive on the last day? Did they choose wisely?

Assessment Strategies

The students will be assessed on the completion of The Power of Two Worksheet. Did they choose wisely?

What is the amount of coins received on the last day of the month?

Variation Tips

The worksheet can be completed with partners, groups, or individually. If the teacher sees students who are struggling, they might wish to place those students in groups with a strong partner. The teacher can use closed caption on the videos if needed.

Background / Preparation

The teacher will need an internet device to show the videos.

The teacher will need to make copies of The Power of Exponents worksheet. 

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