Note:

• This topic summary is intended for parents and tutors, to just give a quick sense of what is coming up.

Week 1

Lecture Topics (new topics)
Overview of the year

Individual Work (skills and review)
Pre-algebra unit review problems

Group Assignments
“Birthday Magic Trick”;  Puzzles

Week 2

Lecture Topics (new topics)
Rules of Exponents;  HS method for solving basic equations; 
Solving proportions (Moving along diagonals)

Individual Work (skills and review)
Algebra Basics unit – Problem Sets #2-4

• Arithmetic involving fractions
• Arithmetic with positive and negative numbers
• Combining like terms in an expression  
• Using simple formulas (e.g.,  F = C + 32)
• Order of operations
• Distributive property
• Solving simple linear equations. (e.g.,  5x − 6 = 8x + 14)

Group Assignments:   Puzzles

Week 3

Lecture Topics (new topics)
Evaluating expressions;  Rules for signed numbers;  more proportions;  equations with fractions

Individual Work (skills and review)
More Algebra Basics unit – Problem Sets #5-7

Group Assignments:    Puzzles

Week 4

Lecture Topics (new topics)
Solve for Y in terms of X;  Review of everything thus far.

Individual Work (skills and review)
Exponents & Polynomials unit – Problem Sets #2 and #3.  Example problems:

• Simplifying    4x3 + 7x3        →  11x3
                   and    (4x3)(7x3)              →  28x6 
• Simplifying    5x4y3 − 2x4y4  →  can’t
                   and    (5x4y3)(−2x4y4)     →  −10x8y7
• Multiplying    (3x2y3)(x2y3)      →  3x4y6
                   and    (3x2 − y3)(x2 − y3)  →  3x4 – 4x2y3 + y6 
• Squaring    (3pq4)2                  →  9p2q8
               and    (3p + q4)2             →  9p2 + 6pq4 + q8 
  

Group Assignments:   Puzzles

Week 5

Lecture Topics (new topics)
Start Exponents & Polynomial unit;  Intro to F.O.I.L. (multuiply binomials)

Individual Work (skills and review)
Exponents & Polynomials – Problem Sets #4 and #5
Take Algebra Basics Test

Group Assignments
Work together on Problem Set #4;   Puzzles

Week 6  (First week of Descriptive Geometry Main Lesson)

Lecture Topics (new topics)
Geometry: Start 6 photos of a Cube;  House in the Viewing Box;  Three Views of a Stick
Algebra: Selected problems from p22.

Individual Work (skills and review)
Algebra: Exponents & Polynomials – Problem Set #6
Geometry: Finish group work exercises

Group Assignments
Three Views of a House
Problem Set A (from “Desc Geom – Problem Sets”)

Week 7  (Second week of Descriptive Geometry Main Lesson)

Lecture Topics (new topics)
Geometry: Front view of a Dodecahedron
Algebra: Selected problems from p27.

Individual Work (skills and review)
Algebra: Exponents & Polynomials – Problem Set #7
Geometry: Finish group work exercises

Group Assignments
Work together on Exponents & Polynomials – Problem Set #8.
Complete Problem Set C (from “Desc Geom – Problem Sets”)
Three views of a Pentagonal Pyramid
Three views of a Dodecahedron

Week 8  (Third week of Descriptive Geometry Main Lesson)

Lecture Topics (new topics)
Geometry: Finish Three Views of a Dodecahedron; Top View of an Icosahedron;  Edge View
Algebra: base tables and negative exponents

Individual Work (skills and review)
Algebra: Exponents & Polynomials – Problem Set #6
Geometry: Finish group work exercises

Group Assignments
Rotated View of a Dodecahedron. 
Other advanced drawings from my High School Source Book 

Week 9

Lecture Topics (new topics)
Fractions with negative exponents;  Scientific Notation;  GCF

Individual Work (skills and review)
Algebra: Exponents & Polynomials – Problem Sets #9-10

Group Assignments:  Puzzles

Week 10

Lecture Topics (new topics)
Start Factoring unit;  Factoring a Trinomial

Individual Work (skills and review)
Take the Exponents & Polynomials test
Finish group work exercises

Group Assignments
Factoring unit – Problem Sets #1-3

Week 11

Lecture Topics (new topics)
Rules for factoring a trinomial;  

Individual Work (skills and review)
Finish group work exercises

Group Assignments
Factoring unit – Problem Sets #4-5;   Puzzle

Week 12

Lecture Topics (new topics)
Rules for factoring a binomial;  back and forth between multiplying and factoring

Individual Work (skills and review)
Finish group work exercises

Group Assignments
Factoring unit – Problem Sets #5-6;   Puzzles

Week 13

Lecture Topics (new topics)
Mixed factoring;  Solving quadratic equations by factoring

Individual Work (skills and review)
Finish group work exercises

Group Assignments
Factoring unit – Problem Sets #7-8;   Puzzles

Week 14

Lecture Topics (new topics)
More Solving quadratic equations by factoring

Individual Work (skills and review)
Finish group work exercises

Group Assignments
Factoring unit – Problem Sets #9-10;  Puzzles

Week 15

Lecture Topics (new topics)
Practice for factoring test

Individual Work (skills and review)
Factoring unit – Problem Sets #11-12

Group Assignments
Puzzles

Week 16

Lecture Topics (new topics)
Algebraic word problems (two-number riddles);  Math magic trick;  Systems of Equations

Individual Work (skills and review)
Take Factoring test

Group Assignments
Math Magic Trick;  Common solution to two equations;  Word Problem unit – Problem Sets #1-2

Week 17

Lecture Topics (new topics)
Show how to solve last week’s math magic trick;  More word problems, incl. consecutive integers

Individual Work (skills and review)
Create your own two-number riddles.  Finish group work problems.

Group Assignments
Share your two-number riddles;  Problem Sets #1-4 from the Word Problem unit

Week 18 

Lecture Topics (new topics)
Weighted average;  Coins problems;  Sum of squares problems

Individual Work (skills and review)
Finish group work problems.

Group Assignments
Problem Sets #4-5 from the Word Problem unit

Week 19 

Lecture Topics (new topics)
Airline ticket problem;  Rate/Time/Distance problems

Individual Work (skills and review)
Problem Sets #5-6 from the Word Problem unit

Group Assignments
Problem Sets #6-7 from the Word Problem unit;   Puzzles

Week 20 

Lecture Topics (new topics)
Age problems;  Percent problems;  three-number riddles
Start Mid-Year Review, including percents, rates, dimensional analysis (unit conversions)

Individual Work (skills and review)
Finish group work problems.

Group Assignments
Problem Sets #7-9 from the Word Problem unit

Week 21 (First week of Possibility & Probability Main Lesson)

Lecture Topics (new topics)
Street problem;  Wardrobe problem;  Seating chart problem;  Menu problem;  Prize problem
Continue Mid-Year Review

Individual Work (skills and review)
Take the Word Problem test;  Create main lesson book pages;  Midyear Review unit Problem Sets #1-2

Group Assignments
Work on Seating Chart Problem, Menu Problem, License Plate Problem, Seating Chart Problem

Week 22 (Second week of Possibility & Probability Main Lesson)

Lecture Topics (new topics)
Intro to Probability;  Word Scrambling;  Committee problem;  Pascal’s Triangle
Possible ways to roll two dice;  How to use a spreadsheet with formulas
Continue Mid-Year Review

Individual Work (skills and review)
Create main lesson book pages;  Midyear Review unit Problem Sets #3-4

Group Assignments
Prize Problem and Committee Problem;  Use a spreadsheet for Rolling Two Dice.

Week 23 (Third week of Possibility & Probability Main Lesson)

Lecture Topics (new topics)
Conclusions for Rolling Two Dice;  Street problem;  Birthday problem;  Thorough review
Continue Mid-Year Review

Individual Work (skills and review)
Create main lesson book pages;  Midyear Review unit Problem Sets #5-6

Group Assignments
Pascal’s Triangle;  Solving P&P problems;  

Week 24

Lecture Topics (new topics)
Go over P&P challenge problems;  What types of equations can we solve thus far? 
Start Quadratic Formula unit;  Absolute value equations

Individual Work (skills and review)
Finish group work problems.

Group Assignments
Problem Set #1 from the Quadratic Formula unit;  Puzzles

Week 25

Lecture Topics (new topics)
Intro to solving quadratic equations using completing the square;  Start reading al Khwarizmi’s book

Individual Work (skills and review)
Finish group work problems.

Group Assignments
Solving a Quadratic Equation by Completing the Square; 
Problem Set #1 from the Quadratic Formula unit;  Puzzles

Week 26

Lecture Topics (new topics)
More solving quadratic equations using completing the square; 
Al Khwarizmi’s solution to x2 + 10x = 39

Individual Work (skills and review)
completing the square;  Finish group work problems.

Group Assignments
Quadratic Formula unit – Problem Set #6;  Math Magic Trick!

Week 27

Lecture Topics (new topics)
Al Khwarizmi’s proof of the quadratic formula

Individual Work (skills and review)
Finish group work problems.

Group Assignments
Derivation of the Quadratic Formula!!;  Quadratic Formula unit – Problem Sets #8-9

Week 28

Lecture Topics (new topics)
Show proof of the quadratic formula;  5 ways to solve x2 + 8x = 20;  practice using the quadratic formula.

Individual Work (skills and review)
Quadratic Formula unit – Problem Set #11;  practice using the quadratic formula.

Group Assignments
Quadratic Formula unit – Problem Sets #12-13;  Puzzles

Week 29

Lecture Topics (new topics)
Intro to Logarithms;  Rational exponents (e.g., 9½)

Individual Work (skills and review)
Take the test on the Quadratic Formula unit

Group Assignments
Logarithms unit – Problem Set #1;  Puzzles

Week 30

Lecture Topics (new topics)
Using the Annual Growth Formula to solve problems;  Using logs to solve equations.

Individual Work (skills and review)
Logarithms unit – Problem Set #4;  begin Year-End Review Practice 

Group Assignments
Logarithms unit – Problem Sets #2-3

Week 31

Lecture Topics (new topics)
Finish logarithms;  Review Possibility & Probability

Individual Work (skills and review)
Year-End Review Practice sheets;  Logarithms unit – Problem Set #4

Group Assignments
Possibility & Probability – Problem Sets #1-2.

Week 32

Lecture Topics (new topics)
Intro to simplifying square roots;  Practice Possibility & Probability problems

Individual Work (skills and review)
Take the Year-End Test;  Finish group work problems.

Group Assignments
Possibility & Probability – Problem Sets #3-4

Week 33-55 (Extra Unit for Advanced Students only)

Completely cover Fractions & Square Roots unit