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)
No review!  Start out with an Introduction to Number Bases; 
Scientific Notation;  Expanded Notation;  Egyptian Number System

Individual Work (skills and review)
Just work hard to understand the lecture content and the group work.

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work together on Number Bases – Practice Sheet #1

Week 2

Lecture Topics (new topics)
Converting back and forth between octal (base-8) and decimal (base-ten);
Doing arithmetic in the octal system.   

Individual Work (skills and review)
Work on Number Bases – Practice Sheet #2

Group Assignments (puzzles, problem-solving, discovery, etc.)
Discover how to count, represent numbers, and do arithmetic in the octal (base-8) number base;
Work together on Number Bases – Group Sheet #2 and #3.

Week 3

Lecture Topics (new topics)
Introduce other number base systems (hexadecimal, base-five, and binary); 
Place value in different bases;  Arithmetic in different bases; 
Converting between decimal and other bases.

Individual Work (skills and review)
Work on Number Bases – Practice Sheet #3 and #4

Group Assignments (puzzles, problem-solving, discovery, etc.)
Place Value Table for different bases;  Work together on Number Bases – Group Sheet #4

Week 4

Lecture Topics (new topics)
Times tables in different bases;  ASCII code (computer binary-based coding for characters);

More work with converting and arithmetic in different bases

Individual Work (skills and review)
Work on Number Bases – Practice Sheet #5 and #6

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work together on Number Bases – Group Sheet #5 and #7

Week 5

Lecture Topics (new topics)
Start Pythagorean Theorem unit;  Review 7th Grade Geometry
Overview of the two main components of a computer: hardware and software;
The Square Root Algorithm as a computer program;  

Individual Work (skills and review)
Take the Number Bases Test;  Work on Pythagorean Theorem – Practice Sheet #1

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work together on The Mystery Computer Program (Algorithm for Prime Numbers);
Work on Pythagorean Theorem – Group Sheet #1

Week 6  (First week of Geometry Main Lesson)

Lecture Topics (new topics)
Introduce Stereometry – the study of 3-D solids;
Loci – the study of 2-D curves;
Pythagorean Triples

Individual Work (skills and review)
Working with clay – transformation of a cube into an octahedron;
Working with paper – making paper models of a cube, tetrahedron, and octahedron;
Working on loci drawings (in your main lesson book).

Group Assignments (puzzles, problem-solving, discovery, etc.)
Pythagorean Theorem – Group Sheet #2;
How many different nets are there for a cube? ;
Loci puzzle, which introduces The Parabola

Week 7  (Second week of Geometry Main Lesson)

Lecture Topics (new topics)
Duality in solids;  transformation of loci curves, especially the parabola;
Watch extra lecture which shows all the solids – Platonic (5), Archimedean (13), and the Duals (13)

Individual Work (skills and review)
Do Pythagorean Theorem – Practice Sheet #2;
Working with clay – perhaps the dodecahedron, and others;
Working with paper – making paper models of a dodecahedron and an icosahedron;
Working on loci drawings (in your main lesson book).

Group Assignments (puzzles, problem-solving, discovery, etc.)
Do Pythagorean Theorem – Group Sheet #3;
Loci puzzles – leading to the discovery of an ellipse and a hyperbola

Week 8  (Third week of Geometry Main Lesson)

Lecture Topics (new topics)
Conic Sections (Parabola, ellipse, hyperbola);  turning the directrix circle inside-out;
Two formulas for the Pythagorean Theorem;  Using the Pythagorean Theorem to solve triangles.

Individual Work (skills and review)
Do Pythagorean Theorem – Practice Sheet #3;
Working with paper – your final project;
Working on loci drawings (in your main lesson book).

Group Assignments (puzzles, problem-solving, discovery, etc.)
Curves of Cassini;  Puzzles 

Week 9

Lecture Topics (new topics)
Review of 7th Grade Ratios;  The Four Ratios of π.  The Shear & Stretch;  

Individual Work (skills and review)
Do Pythagorean Theorem – Practice Sheet #4 and #5

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on the challenge problems from Pythagorean Theorem – Practice Sheet #4 and #5; 
Baravalle’s proof of the Pythagorean Theorem;  Ptolemy’s Quadrilateral Theorem 

Week 10

Lecture Topics (new topics)
Start Mensuration unit;  Areas of rectangles, triangles, etc.; 
Intro to Volume;  3-D Shear & Stretch;  Height of a Pyramid;  

Individual Work (skills and review)
Take the Pythagorean Theorem Test;  Do Mensuration – Practice Sheet #1

Group Assignments (puzzles, problem-solving, discovery, etc.)
Deriving the formula for the Area of a Circle;  Do Mensuration – Group Sheet #1

Week 11

Lecture Topics (new topics)
Area of a Trapezoid, and Area of a Circle;  Formulas for a Cone and a Pyramid;  Archimedes’ Ratio

Individual Work (skills and review)
Do Mensuration – Practice Sheet #2

Group Assignments (puzzles, problem-solving, discovery, etc.)
Making a Tilted Pyramid;  Do Mensuration – Group Sheet #2

Week 12

Lecture Topics (new topics)
Surface area;  Review methods/formulas for finding all areas and volumes; 
Area and Volume practice problems;  Heron’s formula for the area of a triangle

Individual Work (skills and review)
Do Mensuration – Practice Sheet #3 

Group Assignments (puzzles, problem-solving, discovery, etc.)
Derive a formula for the volume of a sphere;  Do Mensuration – Practice Sheet #3 and #4

Week 13

Lecture Topics (new topics)
Archimedes’ proof of his ratio;  Portions of Circles

Individual Work (skills and review)
Finish Mensuration – Practice Sheet #4;  Start Mensuration – Practice Sheet #5

Group Assignments (puzzles, problem-solving, discovery, etc.)
Do Mensuration – Group Sheet #3;  Puzzle

Week 14

Lecture Topics (new topics)
Practice everything from the Mensuration unit

Individual Work (skills and review)
Finish Mensuration – Practice Sheet #5;  Start Mensuration – Practice Sheet #6

Group Assignments (puzzles, problem-solving, discovery, etc.)
Laws regarding scale factors and areas of similar figures;  Puzzles

Week 15

Lecture Topics (new topics)
Laws regarding scale factors and areas of similar figures and solids;  More practice

Individual Work (skills and review)
Finish Mensuration – Practice Sheet #6;  Prepare for test

Group Assignments (puzzles, problem-solving, discovery, etc.)
Scale factor puzzles.;  Cone challenge problem;  Puzzle

Week 16

Lecture Topics (new topics)
Start Percents & Growth unit; Thorough review of 7th Grade Percents

Individual Work (skills and review)
Take the Mensuration Test;  Work on Percents Review Sheets;  Work on Percents Flashcards.

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Percents Review Sheets;  Puzzle

Week 17

Lecture Topics (new topics)
Rewording Increase/Decrease Percents problems → 30% more = 130% of = 1.3 times
Continue 7th Grade Percents Review

Individual Work (skills and review)
Do Percents & Growth – Practice Sheet #1

Group Assignments (puzzles, problem-solving, discovery, etc.)
Do Percents & Growth – Group Sheet #1;  Puzzles

Week 18 

Lecture Topics (new topics)
Using the Growth Rate Table;  Exponential Growth (constant % growth) with populations

Individual Work (skills and review)
Do Percents & Growth – Practice Sheet #2 and #3

Group Assignments (puzzles, problem-solving, discovery, etc.)
Do Percents & Growth – Group Sheet #2;  Puzzles

Week 19 

Lecture Topics (new topics)
Reverse Percent problems;  Compound Interest;  Rule of 72;  Rules for using a Calculator

Individual Work (skills and review)
Do Percents & Growth – Practice Sheet #4

Group Assignments (puzzles, problem-solving, discovery, etc.)
Do Percents & Growth – Group Sheet #3;  Puzzle

Week 20 

Lecture Topics (new topics)
Analysis of the population of USA since 1800;  Review of everything in the unit thus far

Individual Work (skills and review)
Work on Percents & Growth – Practice Sheet #5;  Start Practice Sheet #6

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Percents & Growth – Practice Sheets #5 and #6;  Puzzles

Week 21

Lecture Topics (new topics)
Start Proportions & Dimensional Analysis unit
Review 7th grade Measurement, Ratios, and Average Speed;  Map Scales;  Proportions;  Similar Figures

Individual Work (skills and review)
Finish Percents & Growth – Practice Sheet #6;  Do the Practice Test

Group Assignments (puzzles, problem-solving, discovery, etc.)
Puzzles

Week 22

Lecture Topics (new topics)
Measurement Conversions between US and Metric systems;  Four Ways to write a Ratio;
Method of “Moving along Diagonals” to solve proportions;  Currency conversions; 
Intro to the Chain Method for Unit Conversions

Individual Work (skills and review)
Take the Percents & Growth Test 

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Proportions & Dimensional Analysis Practice Sheet #1 and Group Sheet #1;
Grains of Rice puzzle

Week 23

Lecture Topics (new topics)
Intro to Density → Calculating weight, volume, and density

Individual Work (skills and review)
Work on Measurement Flashcards;  Proportions & Dimensional Analysis Practice Sheet #2 and #3

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Proportions & Dimensional Analysis Practice Sheet #2 and #3;  Puzzles

Week 24

Lecture Topics (new topics)
Practice problems involving Density, Map Scales, Unit Conversions, Proportions

Individual Work (skills and review)
Keep working on Measurement Flashcards;  Proportions & Dimensional Analysis Practice Sheet #4

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Proportions & Dimensional Analysis Group Sheet #2;  Puzzles

Week 25

Lecture Topics (new topics)
Archimedes’ Principle (for floating and sinking objects);  More practice using the Chain Method

Individual Work (skills and review)
Keep working on Measurement Flashcards;  Proportions & Dimensional Analysis Practice Sheet #5

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Proportions & Dimensional Analysis Group Sheet #3;  Puzzles

Week 26

Lecture Topics (new topics)
Go over Group Sheet #3 (“Are there too many people in the world?”);
Thorough review of everything in the unit.

Individual Work (skills and review)
Work on Proportions & Dimensional Analysis Practice Sheets #6 and #7;  Prepare for PDA test

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Proportions & Dimensional Analysis Practice Sheets #6 and #7;  Puzzle

Week 27

Lecture Topics (new topics)
Start Algebra unit;  What is an equation?  Thorough review of 7th Grade Algebra;
Intro to Distributive Property;  Intro to Order of Operations

Individual Work (skills and review)
Take the Proportions and Dimensional Analysis Test; 
Work on Algebra Practice Sheets #1 and #2

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on the Proportions and Dimensional Analysis – Practice Test ; 
Work on Algebra Practice Sheets #1 and #2;  Puzzle

Week 28

Lecture Topics (new topics)
Lots of Algebra practice;  Solving equations with fractions

Individual Work (skills and review)
Work on Algebra Practice Sheets #3 and #4

Group Assignments (puzzles, problem-solving, discovery, etc.)
Work on Algebra Practice Sheets #3 and #4;  Puzzles

Week 29

Lecture Topics (new topics)
Lots of Algebra practice;  Algebra problems with greater difficulty;
Start Problem-Solving unit

Individual Work (skills and review)
Work on Algebra Practice Sheets #5 and #6

Group Assignments (puzzles, problem-solving, discovery, etc.)
Problem Solving → Number Circle Magic Trick;  Clock Hands;  Card Trick;  Factors – Part I

Week 30

Lecture Topics (new topics)
Go over last week’s group Problem Solving exercises, and introduce new ones.

Individual Work (skills and review)
Take the Algebra Test

Group Assignments (puzzles, problem-solving, discovery, etc.)
Problem Solving → Number Magic;  Catching Up;  Factors – Part II;  Two-Ant Problem

Week 31

Lecture Topics (new topics)
Go over last week’s group Problem Solving exercises, and introduce new ones.

Individual Work (skills and review)
Work on Year-End Review – Practice Sheets #1 and #2

Group Assignments (puzzles, problem-solving, discovery, etc.)
Problem Solving → Factors and Remainders;  Nines Magic;  Chinese Remainder Theorem

Week 32

Lecture Topics (new topics)
Go over last week’s group Problem Solving exercises

Individual Work (skills and review)
Work on Year-End Review – Practice Sheets #3 and #4

Group Assignments (puzzles, problem-solving, discovery, etc.)
Problem Solving → Factors;  Greatest Common Factors;  Two-Variable Equations