ContentsLetʼs review what you have learned
at elementary school ··································· 4Chapter

1Signed numbers

1 Signed numbers ·················································· 11
Signed numbers / Inequality signs, The number
line and size of numbers / Absolute values
2 Addition and subtraction ····························· 15Addition / Laws of addition / Subtraction /Calculations with both addition and subtraction
3 Multiplication and division ························· 22
Multiplication / Multiplication with three or morenumbers / Powers and exponents / Division /Calculations with both multiplication and division /Calculations with the four arithmetic operations /Making calculations easy / Determining the sign /Sets of numbers and the four arithmetic operations
4 Using signed numbers ····································· 32
Using signed numbers / Signed numbers and tables

Comprehension test for Chapter 1,
End-of-chapter problems ···································· 36

Chapter

2Algebraic expressions

1 How to write algebraic expressions ······· 39
Expressions that use variables / How to express
products / How to express quotients / The productand quotient of numbers and algebraic expressions /How to express calculations with the four arithmetic
operations
2 How to express quantities, Evaluating
expressions ··························································· 45
How to express costs and numbers / How toexpress averages and units / How to express areasand volumes / How to express rates and speed /Evaluating expressions
3 Calculating linear expressions ················· 51
Terms and coef ficients / Combining terms /Addition and subtraction of linear expressions /Multiplication and division of linear expressions andnumbers / Various calculations

4 Using algebraic expressions ······················· 57
Applying calculations with algebraic expressions /Calculations with algebraic expressions andregularity / How to express the relationships
between quantities

Comprehension test for Chapter 2,
End-of-chapter problems ···································· 62

Chapter

3Equations

1 Equations and how to solve them ··········· 65
Equations and their solutions / Proper ties ofequalities / How to solve equations using theproperties of equalities / How to solve equations /How to solve equations containing parentheses /How to solve equations containing decimals / Howto solve equations containing fractions / Proportional
expressions
2 Using equations (1) ········································· 74
Problems about the values for variables / Problems
about numbers / Problems about prices and thenumber of items / Problems about surpluses andshortages / Problems about distribution / Problems
using ratios / Problems about age and average
3 Using equations (2) ········································· 81Problems about speed / Problems about profit /Problems about salt water / Problems about changes
in number / Problems about figures / Problems
about moving points in figures / Problems about
regularities

Comprehension test for Chapter 3,
End-of-chapter problems ···································· 90Complements

How to solve inequalities ·················· 92

7th grade

Chapter

4Proportion and inverseproportion

1 Proportion and inverse proportion ········ 95
Functions / Variables and domains / Proportion /Proportional expressions / Inverse proportion /Inversely proportional expressions
2 Coordinates and graphs ······························ 102
Points and coordinates / Reflection of a point,Midpoint, Moving a point / Graphing proportion /Expressing proportional graphs / Graphing inverseproportion / Expressing inversely proportionalgraphs
3 Applying coordinates and graphs tofigures ···································································· 111
Coordinates and the area of figures / Coordinatesof parallelograms / Graphs and figures / Graphs
and using equations

Comprehension test for Chapter 4,
End-of-chapter problems ·································· 116

Chapter

5Plane figures

1 Lines and angles ·············································· 119
Lines and angles / Parallel and perpendicularlines / Circle arcs and chords, Tangents /Properties of symmetric figures
2 Figure transformation ·································· 124
Translation / Rotation / Reflection
3 Figure construction ······································· 128
Constructing triangles / Constructing perpendicularbisectors / Constr ucting angle bisectors /Constructing perpendicular lines / Constructing
angles / Circles and figure construction / Symmetryand figure construction / Transformation and figure
construction4 Sectors ··································································· 139
Sectors / Combined figures / Rolling figures

Chapter

6Space figures

1 Positional relationships between lines
and planes ··························································· 149
Determination of a plane / Positional relationships
between two lines / Positional relationships betweenlines and planes / Positional relationships between
two planes
2 Prisms, cylinders, pyramids, cones, andspheres ·································································· 154
Prisms, cylinders, pyramids, and cones / Nets ofprisms and cylinders / Volume and surface area ofprisms and cylinders / Nets of pyramids and cones /Volume and surface area of pyramids / Volume andsurface area of cones / Volume and surface area ofspheres / Solids of revolution
3 Various ways of looking at solids ··········· 165
Regular polyhedra / Projections / Using nets /Cutting cubes

Comprehension test for Chapter 6,
End-of-chapter problems ·································· 170

Chapter7

Organizing and making
use of data

1 Organizing and making use of data ······ 173
Frequency distribution tables / Histograms /Relative frequency / Mean / Tentative mean /Median, Mode / Approximate values and errors,
Significant figures

Comprehension test for Chapter 7,
End-of-chapter problems ·································· 180○Letʼs review·························································· 182●Final test······························································· 190

Comprehension test for Chapter 5,
End-of-chapter problems ·································· 144
Complements
circumcenter

Sets of points, Incenter and···························································· 146

Key points learned during the first yearof junior high school ············································ 192