8th Grade Parents:

Students are beginning Chapter 6, Exponential Equations and Functions.

The sequence of numbers 2, 4, 8, 16, 32, 64,… grows exponentially while the sequence 2, 4, 6, 8, 10, 12,… grows linearly. If you remember the ancient story regarding the chess board in which 2 cents are placed on the first square, 4 cents on the second square, 8 cents on the third square and so on, the last square will have almost $200 million billion on it (2^64 cents is approximately $1.8 x 10^19). By contrast, 2 cents placed on the first square, 4 cents on the second square, 6 cents on the third, and so on will result in $1.28 on the last square. In general, a sequence grows exponentially (or geometrically) if its rate of growth is proportional to the amount of the quantity present – i.e., if each number in the sequence comes from multiplying its predecessor by the same factor. A sequence grows linearly (or arithmetically) if its rate of growth is constant – i.e., if each number in the sequence comes from adding the same factor to its predecessor.

Like money in a compound-interest account, populations (whether of people or bacteria) tend to grow exponentially, and like money earning simple interest, food production tends to increase only linearly. The early-nineteenth-century British economist Thomas Malthus put these two observations together and concluded that poverty and famine were unavoidable. THE ARGUMENT IS FLAWED AND CAN BE ATTACKED ON A NUMBER OF POINTS.

Listed below are the students’ textbook sections aligned with Khan Academy. Over this 3 day weekend, I would advise the students go to Khan Academy, Algebra I, and the chapter entitled Rational Exponents and Radicals, and peruse the beginning videos and practice problems

NOTE: Students will be reviewing ideas/skills from Khan Academy, 8th grade, Numbers and Operations

Student Textbook (Khan Academy > Algebra I > Rational Exponents and Radicals)

6.1 Properties of Square Roots

6.2 Properties of Exponents

6.3 Radicals and Rational Exponents

Student Textbook (Khan Academy > Algebra I > Exponential Growth and Decay)

6.4 Exponential Functions

6.5 Exponential Growth

6.6 Exponential Decay

Student Textbook (Khan Academy > Algebra I > Sequences)

6.7 Geometric Sequences

 

7th Grade Parents

Students are beginning Chapter 5 – Similarity and Transformations

5.1 Identifying Similar Figures

• Two figures are similar if corresponding side lengths are proportional and corresponding angles have the same measure

5.2 Perimeters and Areas of Similar Figures

• If two figures are similar, then the ratio of their perimeters is equal to the ratio of their corresponding side lengths
• If two figures are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths

5.3 Finding Unknown Measures in Similar Figures

5.4 Scale Drawings

5.5 Translations

5.6 Reflections

5.7 Rotations