Mathematics Unit Planner

Mathematics Unit Plan Grade: 7 Unit: Growing Exponentially Time: 5 to 10 periods Textbook(s) Impact Math, Course 2 – Chapter 3

Unit Overview

Note: This unit plan deviates significantly from the CAB. If you wish to use some or all of this unit plan, discuss it with your Math Coach first. Students will have had some exposure in previous years to the concepts of powers and scientific notation. These concepts, for many students, will not be secure. This chapter will build on this past knowledge. Note that the text goes further than that required in the Scope and Sequence for 7th Grade. Powers Students need to be able to write a product such as 2 x 2 x 2 as a power, i.e. 2 x 2 x 2 = 23, and vice versa. Students need to be able to evaluate powers with smallish bases and smallish exponents, e.g. 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64. Through exposure to such numbers, students should know which small numbers (e.g. up to 144) can be written as powers. For example a student should know that 16 = 24 = 42, and 64 = 26 = 43 = 82. Students should be able to read and write numbers through to billions using place value and expanded form. Students need to be able to write a large number such as 2,300,000 (known as standard notation) in scientific notation and vice versa. This is all that is required in the Scope and Sequence for 7th Grade. Laws of Exponents The laws of exponents are a Grade 8 topic. If the citywide test follows the Scope and Sequence, they will not be assessed on this test. However, there are some good reasons why you should consider teaching this topic:  The laws are not difficult, and can be easily discovered using an investigative approach.  The Grade 8 Impact Math text will assume that these have been taught in Grade 7. To me, the approach used in the text – stretching machines, repeaters, super-repeaters – takes a simple topic and complicates it. Students can discover the laws of exponents in this chapter by knowing no more than the definition of a power, e.g. 23 x 24 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 27 2创 2 2 创 2 2 创 2 2 27  23 = = 24 2创 2 2 (22 ) 3 = 2 x 2 x 2 x 2 x 2 x 2 = 26.

(2 x 3)3 = 2 x 3 x 2 x 3 x 2 x 3 = 2 x 2 x 2 x 3 x 3 x 3 = 23 x 33. In fact students can simplify these expressions without knowing anything about the laws of exponents. If you choose to teach this topic (recommended if you have time) and choose to not use the model of repeaters and super-repeaters, you will have to create your own Activities and Exercises, for the most part. Growing Exponentially While outside of the Scope and Sequence for Grade 7, you might consider teaching aspects of this topic. Given a situation that involves exponential growth (e.g. how many thicknesses if a I fold a newspaper once, twice, three times, etc.), a nice investigation is making a table of thickness versus the number of folds, finding the rule and drawing the graph. Kids love the “rice on the chessboard” activity. It is worth doing, if you have the time. A lovely open-ended question – on which square is there enough rice to feed this whole class? Scientific Notation Section 3.4 is the heart of the chapter, and where the bulk of the time should be spent.

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Learning Objectives

At the completion of this topic, students should be able to  Express a product as a power and vice-versa.  Evaluate powers (with smallish bases and smallish exponents).  Write small numbers (up to 144) as powers, where possible.  Read and write numbers up to billions using place value and expanded notation.  Write numbers up to billions in scientific notation.  Convert numbers expressed in scientific notation to standard form.  Use knowledge of scientific notation is real-life contexts. Optional learning objectives  Know and use the Laws of Exponents for Multiplication and Division.  Know and use the Law of Exponent for Raising a Power to a Power.  Understand the concept of exponential growth.  Be able to express simple exponential growth models as a table, a rule and as a graph.

Vocabulary The student should be able to spell, know the definition of, give an example of and (where appropriate) draw a diagram of: base exponent exponential growth power scientific notation standard notation

Additional Resources

None required

Homework, Systematic Review and Extended Response Test Preparation

Math Now! Math Now! sheets, as appropriate. Homework You will need to create some homework questions.

Topic Planner Note: This assumes that you have decided to not use the model of repeaters and super-repeaters.

Topic Periods Page Suggested Activities Comments Powers 2 to 3 - Write a repeated product as a power and vice versa. Evaluate powers with smallish bases and smallish exponents Read and write numbers through to billions using place value and expanded form. Laws of Exponents 1 to 3 - Optional. Discover and apply the Laws of Exponents for products and quotients. Growing Exponentially 1 to 4 - Optional. Given a situation that involves exponential growth, express the situation as a table, a rule and a graph. The “rice on the chess table” activity is inherently interesting. Describing Large 3 to 4 190 Selectively use some of the questions in the text; there are some Numbers -202 interesting questions. Alternatively, buy a copy of the latest Guiness Book of World Records; it has even more interesting data.

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