This lesson teaches students about several of the rules regarding exponents. It uses a situation from Alice in Wonderland in which Alice's height is doubled or reduced by half depending on what she consumes to introduce negative exponents and the rules for dividing powers.

In this activity, the students will demonstrate the ability to represent numbers in scientific notation and use geometry to solve problems about planets in the solar system.

In this video segment from Cyberchase, Harry plays a game of chess with a young friend and suggests a wager on the game. Harry?s friend uses a story to explain how putting a penny on the first square and then doubling the amount on each square of the chessboard can generate a tremendous amount of money over time. Teaching tips are also provided that discuss frame, focus and follow-up suggestions for using this video in a math lesson.

The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow.

Lesson plan using a Cyberchase activity, students are introduced to a problem that gives them a sense of how quickly exponential growth accrues in the classic problem about a chess board and grains of rice. The context is extended to consider applications using money growth and chain letters. They are introduced to the algebraic representation for exponential growth.

Students partner up and take turns guessing each others decimals. Students must read the decimals correctly and match them up with the correct decimal in standard form.

This lesson unit is intended to help you assess how well students are able to: Perform arithmetic operations, including those involving whole-number exponents, recognizing and applying the conventional order of operations; Write and evaluate numerical expressions from diagrammatic representations and be able to identify equivalent expressions; apply the distributive and commutative properties appropriately; and use the method for finding areas of compound rectangles.

In this video segment from Cyberchase, the CyberSquad is trying to escape from a desert island by crossing a large body of water. They find a special lily pad that was left for them by the Red Warrior. When the lily pad is put in water it doubles and the number of lily pads keeps on doubling. The CyberSquad tries to use this doubling effect to help them create a lily pad bridge to cross the water and escape. Teaching tips are also provided that discuss frame, focus and follow-up suggestions for using this video in a math lesson.

This general math site offers reference material on a host of math topics, plus a math message board and links to relevant material online. The tables cover a range of math skills, from basic fraction-decimal conversion to the more advanced calculus and discrete math. The information is presented in notation form, with diagrams, graphs, and tables. The site is available in English, Spanish, and French. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/

Expressions

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Write and evaluate simple expressions that record calculations with numbers.
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.
Interpret numerical expressions without evaluating them.

Lesson Flow

Students learn to write and evaluate numerical expressions involving the four basic arithmetic operations and whole-number exponents. In specific contexts, they create and interpret numerical expressions and evaluate them. Then students move on to algebraic expressions, in which letters stand for numbers. In specific contexts, students simplify algebraic expressions and evaluate them for given values of the variables. Students learn about and use the vocabulary of algebraic expressions. Then they identify equivalent expressions and apply properties of operations, such as the distributive property, to generate equivalent expressions. Finally, students use geometric models to explore greatest common factors and least common multiples.

Students play an Expressions Game in which they describe expressions to their partners using the vocabulary of expressions: term, coefficient, exponent, constant, and variable. Their partners try to write the correct expressions based on the descriptions.Key ConceptsMathematical expressions have parts, and these parts have names. These names allow us to communicate with others in a precise way.A variable is a symbol (usually a letter) in an expression that can be replaced by a number.A term is a number, a variable, or a product of numbers and variables. Terms are separated by the operator symbols + (plus) and – (minus).A coefficient is a symbol (usually a number) that multiplies the variable in an algebraic expression.An exponent tells how many copies of a number or variable are multiplied together.A constant is a number. In an expression, it can be a constant term or a constant coefficient. In the expression 2x + 3, 2 is a constant coefficient and 3 is a constant term.Goals and Learning ObjectivesIdentify parts of an expression using appropriate mathematical vocabulary.Write expressions that fit specific descriptions (for example, the expression is the sum of two terms each with a different variable).

Adapted from mathematicsvisionproject.com’s Material Overview:
The Mathematics Vision Project (MVP) was created as a resource for teachers to implement the Common Core State Standards (CCSS) using a task-based approach that leads to skill and efficiency in mathematics by first developing understanding. The MVP approach develops the Standards of Mathematical Practice through experiential learning. Students engage in mathematical problem solving, guided by skilled teachers, in order to achieve mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The MVP authors created a curriculum where students do not learn solely by either “internalizing what a teacher or book says or, on the other hand, solely by inventing mathematics on their own.”
The MVP classroom experience begins by confronting students with an engaging problem and allows them to grapple with solving it. As students’ ideas emerge, take form, and are shared, the teacher deliberately orchestrates the student discussions and explorations toward a focused math goal. Students justify their own thinking while clarifying, describing, comparing, and questioning the thinking of others leading to refined thinking and mathematical fluency. What begin as ideas become concepts that lead to formal, traditional math definitions and properties. Strategies become algorithms that lead to procedures supporting efficiency and consistency. Representations become tools of communication which are formalized as mathematical models. Students learn by doing mathematics.

This video goes over several examples of the properties of exponents. The resource has been edited to include 10 practice problems.