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Mathematics Textbook 7B Grade

ArchiMath Publishing LLC

Authors:  Zvezdelina Stankova, Zdravka Paskaleva, Maya Alashka, Raina Alashka

Pages: 216

ISBN: 978-954-779-237-1

Available: Paperback & PDF

In the second part of  our 7th gade math textbooks, students will see great growth in mathematical maturity. They work through a classical axiomatic approach to geometry, beginning with basic axioms and definitions, moving on to a thorough examination of parallel lines, triangle congruence theorems, and the basics of Euclidean constructions. 

They will cover all the 7th garde mathematics material and more.


Emphasis is placed on clear, logical thinking and writing. In algebra, students learn to solve linear equations, as well as equations that reduce to linear ones: reducible quadratics, the absolute value of linear and factored quadratics. The modeling and applications are more advanced, and students learn methods for clearly organizing their thoughts and work as they solve word problems on motion, work, mixtures and alloys, along with basic finance. The year closes with review, giving students a reminder just how much they have grown.

What results can we expect from students that are using Archimath’s Mathematical Textbooks❓
⚠ The present program extends the mathematics taught in elementary school and completes it to a comprehensive K-12 math program that prepares students:
✅to enter high school and college with confidence in their math skills and knowledge;
✅to be successful at any level of high school and first-year college math classes;
✅to develop maturity and a life-long relationship with mathematics that:
☑ will distinguish them among their peers;
☑ will serve them well in any profession and in any endeavor in which they chose to engage.
☑ to effectively learn from a textbook that’s deep, systematic and doable

Chapter 7. Foundations of Geometry

  1. Introduction into Geometry

 (Review with Extensions)

  1. Point, Line, and Segment
  2. Ray, Half-plane, and Angle
  3. Supplementary Angles. Right Angles
  4. Vertical Angles. Perpendicular Lines
  5. Intersecting Two Lines with a Third Line.

 Criterion for Parallel Lines

  1. Criteria for Parallel Lines. Exercises
  2. Axiom of Parallel Lines
  3. Properties of Parallel Lines
  4. Triangle
  5. Sum of the Angles in a Triangle
  6. Exterior Angle of a Triangle
  7. Triangle. Exercises
  8. Summary of “Foundations of Geometry”
  9. Exercises on “Foundations of Geometry”
  10. Test on “Foundations of Geometry”


Chapter 8. Equations

Part I: Linear Equations

  1. Numerical Equalities. Properties.

 Equation with One Unknown

  1. Equivalent Equations
  2. The Equation ax + b = 0. Part I
  3. The Equation ax + b = 0. Part II
  4. The Equation (ax + b)(cx + d) = 0
  5. The Equation |ax + b| = c
  6. Equations that Reduce to Linear Ones
  7. Linear Parametric Equations
  8. Summary of “Linear Equations”
  9. Test on “Linear Equations”

Chapter 8. Equations

Part II: Modeling and Applications

  1. Modeling with Linear Equations. Part I
  2. Modeling with Linear Equations. Part II
  3. Word Problems on Motion. Part I
  4. Word Problems on Motion. Part II
  5. Word Problems on Work. Part I
  6. Word Problems on Work. Part II
  7. Word Problems on Interest Rates and Capital
  8. Word Problems on Mixtures and Alloys
  9. Summary of “Modeling and Applications”
  10. Test on “Modeling and Applications”


Chapter 9. Congruent Triangles

Part I: Criteria for Congruence of Triangles

  1. Congruent Triangles. Introduction
  2. SAS Criterion for Congruence of Triangles
  3. SAS Criterion for Congruence of Triangles. Exercises
  4. ASA Criterion for Congruence of Triangles
  5. SAS and ASA Criteria for Congruence of Triangles. Exercises
  6. Isosceles Triangle
  7. Isosceles and Equilateral Triangle. Exercises
  8. Perpendicular Bisector of a Segment
  9. Perpendicular Bisector of a Segment. Exercises
  10. SSS Criterion for Congruence of Triangles.
  11. Perpendicular from a Point to a Line
  12. Right Triangle with Angle 30°
  13. Right Triangle with Angle 30°. Exercises
  14. Median to the Hypotenuse of

 a Right Triangle

  1. Median to the Hypotenuse. Exercises
  2. SSR Criterion for Congruence

 of Right Triangles

  1. Angle Bisector
  2. Angle Bisector. Exercises
  3. Altitude, Angle Bisector, and Median

 in an Isosceles Triangle

  1. Equivalent Statements
  2. Summary of “Congruent Triangles”
  3. Test on “Congruent Triangles”

Chapter 9. Congruent Triangles

Part II: Euclidean Constructions

  1. Geometric Constructions. Introduction
  2. Constructions w/ a Ruler & Compass, Part I 274
  3. Constructions w/ a Ruler & Compass, Part II 276
  4. Constructing a Triangle by SAS
  5. Constructing a Triangle by ASA
  6. Summary of “Construction Problems”
  7. Quiz 1 on “Euclidean Constructions”
  8. Quiz 2 beyond “Euclidean Constructions”
  9. Test on “Euclidean Constructions”



Chapter 10. Yearly Review

Polyhedral Solids (Review)
Round Solids (Review)
Proportions (Review)
Integer Expressions. Polynomials (Review)
Test with Solutions on 7A Material

 General Tests 1-2 on 7A Material

General Tests 3-4 on 7A Material
Linear Equations. Modeling, Part I (Review)

 Test on Polynomials and Equations

Modeling and Applications, Part II (Review)

 Exercises from Everyday Life

Modeling and Applications, Part III (Review)

 Exercises from Everyday Life

Foundations of Geometry. Logic (Review)
Congruent Triangles.

 Euclidean Constructions (Review)

Yearly Review Test with Solutions
Exit Level: Test 1-2 on 7th Grade Material
Exit Level: Test 3 on 7th Grade Material
Exit Level: Test 4 on 7th Grade Material
Three Types of Averages:

Arithmetic, Geometric, and Harmonic Means

The Arithmetic-Geometric Mean Inequality