AIDE Pre-Algebra Assignment Guide and Key Points
Chapter 8 "Exponents, Square Roots, and the Pythagorean Theorem"
Lesson 1 "Exponents"
Turn to Pages 209 Look at the picture on the facing page and predict how it relates to Pre-algebra.
On Page 209 Read the short introduction to Chapter 8
On Page 209 Read the goals you will achieve this chapter.
Scan Pages 210; focus on the purple colored boxes, which contain the key vocabulary terms.
Read Through Pages 210-211 and work through the 5 examples (take notes of important ideas)
Select 3 problems from Exercise A, 4 from B, 2 from C and complete them. (This is for practice you will be graded only on the quiz and tests)
(Compare your answers with these. If you missed any do three more from that section until you get them right.)
Do you know the vocabulary words? (See Key Points below for help)
Take the quiz on Lesson 1 "Exponents" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Review answers on the quiz and print it out. This will be very useful when you are studying for the test.
Lesson 1 Key Points
Vocabulary Terms
Power - the product of multiplying any number by itself once or many times.
Exponent - number that tells how many times another number is a factor.
Base - the number being multiplied.
Section Review Answers
Did you learn these Objectives?
Can you define and identify exponent and base?
Are you able to express factors in exponential form?
Can you find the values of powers of numbers?
Lesson 2 "Multiplying with Exponents"
Scan Page 212; focus on the purple colored boxes, write the information there in your notes and try to memorize the "Rule"
Scan Pages 213 read the box outlined in green.
Read Through Page 212 and work through the example (take notes of important ideas)
Select 5 problems from Exercise A, 5 from B and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 2 "Multiplying with Exponents" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 2 Key Points
none
Are you able to multiply numbers with the same base by adding exponents?
Can you identify the accuracy of such multiplications?
Lesson 3 "Dividing with Exponents"
Scan Page 214; focus on the purple colored boxes, write the information there in your notes and try to memorize the "Rule"
Read Through Page 214 and work through the example (take notes of important ideas)
Read the box outlined in green on Page 214
Select 4 problems from Exercise A, 4 from B and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 3 "Dividing with Exponents" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 3 Key Points
None
Did you learn this Objective?
Are you able to divide numbers with the same base by subtracting exponents.
Can you identify the accuracy of such division problems?
Lesson 4 "Squares"
Scan Page 216; focus on and read the purple colored boxes, which contain the key vocabulary terms.
Read Through Page 216 and work through the 2 examples (take notes of important ideas)
Select 2 problems from Exercise A, 2 from B, 2 from C and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 4 "Squares" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 4 Key Points
Area - the number of square units inside a closed region.
Square - a four-sided shape with sides of equal length and four right angles.
Can you recognize the relationship of the length and width of a square with the factors of s2 ?
Are you able to find the area of a square given the length of a side?
Lesson 5 "Cubes"
Scan Page 218; focus on and read the purple colored boxes, which contain the key vocabulary terms.
Read Through Pages 218-219 and work through the 3 examples (take notes of important ideas)
Select 1 problem from Exercise A, 2 from B, 2 from C, and 1 from D and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 5 "Cubes" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 5 Key Points
Volume - the number of cubic units that fills the interior of a solid.
Cube - a solid with six square faces.
Can you understand volume as area times height, or the number of units that completely fill a solid?
Are you able to recognize that the volume of a cube is equal to the length of its side to the third power?
Can you find the volume of a cube given the length of a side?
Lesson 6 "Square Roots"
Scan Page 220; focus on and read the purple colored boxes, which contain the key vocabulary terms.
Read Through Pages 220-221 and work through the 4 examples (take notes of important ideas)
Select 6 problems from Exercise A, 3 from B and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 6 "Square Roots" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 6 Key Points
Root - An equal factor of a number.
Square root - a factor of a power of two.
Did you learn this Objectives?
Are you able to perceive finding the root as the opposite of finding the area of a square – that is, discovering the "length of a side"?
Can you identify a as the square root of a2?
Are you able to estimate and calculate square roots of whole numbers?
Lesson 7 "Irrational Numbers and Square Roots"
Scan Page 224; focus on and read the purple colored boxes, which contain the key vocabulary terms.
Scan Pages 224-225 for square boxes in the margins outlined in green. Read the info there.
Read Through Pages 224-225 and work through the 3 examples (take notes of important ideas)
Select 5 problems from Exercise A and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 7 "Irrational Numbers and Square Roots" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 7 Key Points
Irrational Number - a real number such as √2 that cannot be written in the form a/b in which a and b are whole numbers and b∫0.
Graph - a diagram showing how one quantify depends on another.
Are you able to differentiate numbers whose roots are irrational from those whose roots are rational?
Can you use a graph to estimate square roots involving decimals?
Lesson 8 "Pythagorean Theorem"
Scan Page 226; focus on and read the purple colored boxes, which contain the key vocabulary terms.
Read Through Page 226-228 and work through the 3 examples (take notes of important ideas)
Select 2 problems from Exercise A, 2 from B and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 8 "Pythagorean Theorem" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 8 Key Points
triangle - a closed figure with three sides.
right triangle - a three-sided figure, or triangle, with one right, or 90º angle.
Angle - a figure made up of two sides or rays with a common endpoint.
Right Angle - a 90º angle.
hypotenuse - the longest side in a right triangle.
Pythagorean theorem - a formula that states that in a right triangle, the length of the hypotenuse c square is equal to the length of side a squared pulse the length of side b squared. a2 + b2 = c2
Are you able to visualize why the hypotenuse of a right triangle squared equals the sum of the other two sides squared?
Can you use the Pythagorean theorem to find the length of an unknown side of a right triangle?
Lesson 9 "More about Triangles"
Scan Page 230; focus on and read the purple colored boxes, which contain the key vocabulary terms.
Read Through Page 230-231 and work through the 3 examples (take notes of important ideas)
Select 3 problems from Exercise A and complete them. (This is for practice you will be graded only on the quiz and tests)
Take the quiz on Lesson 9 "More about Triangles" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Lesson 9 Key Points
Scalene triangle - a triangle with no equal sides.
Isosceles triangle - a triangle with two sides of equal length.
Equilateral triangle - a triangle with three equal sides.
Can you identify triangles according to the relative lengths of their sides?
Are you able to identify triangles as right triangles given only the lengths of their sides?
Application of Pre-Algebra from Chapter 8
Look at the picture on the bottom of page 232 and guess how it relates to pre-algebra.
Read from the top of page 232 and complete the Example.
Complete 2 problems from the exercises at the bottom. (This is for practice you will be graded only on the quiz and tests)
(Compare your answers with these. If you missed any do three more from that section until you get them all right.)
Take the quiz on Applying Chapter 8 , "Applying the Pythagorean Theorem" (You may use the book, notes and Key Points for help on the quizzes. NOT ON TESTS!)
Application 1 Key Points
Are you able to map distances and diagram heights in geographic and architectural contexts?
Can you compute unknown measures of distance using the Pythagorean theorem?
Preparing for Chapter 8 Test
Turn to Pages 233-235 and work through all even numbered problems, (2,4,6,8,...).
Check your answers with these. (This is for practice you will be graded only on the quiz and tests)
If you missed more than 4 problems work through all the odd numbered problems on pages 233-235.
Check your answers with those in the Chapter Review answers.
If you missed more than 4 problems this time contact your instructor for extra help: marble@yksd.com
Take the Chapter 8 Test "Exponents, Square Roots, and the Pythagorean Theorem"
Review the answers then print the results for your records.
Congratulations, if you completed all the items above, you finished Chapter 8 !!