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01Chapter 1: Friendly Decimals5 pages
02Chapter 2: Tables and Graphs7 pages
03Chapter 3: Averages6 pages
04Chapter 4: Area Calculations7 pages
4.1Choose a Base and Its Perpendicular HeightLesson4.2Cut Composite Figures into Useful PiecesLesson4.3Shared Bases and Shared HeightsLesson4.4Overlap and Cancel Common AreasLesson4.5Complete Figures and Preserve Area DifferencesLesson4.6Equal-Area Partitions and Missing LengthsLesson4.7Chapter 4 Exercise: Area Calculations for Plane FiguresExercise
05Chapter 5: Equal-Area Transformations7 pages
5.1Equal Areas from Shared Bases and HeightsLesson5.2Turn Segment Ratios into Area RatiosLesson5.3Extend Sides and Scale Triangle AreasLesson5.4Area Networks in Trapezoids and ParallelogramsLesson5.5Use an Area Ledger: Add, Subtract, and CompleteLesson5.6Chain Equal-Area TransformationsLesson5.7Chapter 5 Exercise: Equal-Area TransformationsExercise
06Chapter 6: Solid Figures7 pages
6.1Count Unit Cubes, Layers, and Exposed FacesLesson6.2Track Surface Area When Solids Join or SplitLesson6.3Water Displacement, Overflow, and Equal Water LevelsLesson6.4Track Faces, Edges, and Vertices after Cutting and FoldingLesson6.5Fold Nets and Track Opposite FacesLesson6.6Build Open Boxes and Compare VolumesLesson6.7Chapter 6 Exercise: Solid-Figure ProblemsExercise
07Chapter 7: Circular-Track Journeys7 pages
7.1Unwrap the Loop: Meeting and Catch-UpLesson7.2First, Second, and Nth EncountersLesson7.3Reconstruct a Track from Meeting PointsLesson7.4Stops, Corners, and Piecewise MotionLesson7.5Positions on Polygonal Closed TracksLesson7.6Switching Routes and Connected Loop NetworksLesson7.7Chapter 7 Exercise: Travel Problems on Circular TracksExercise
08Chapter 8: Growing Resources8 pages
8.1Build a Growing-Resource ModelLesson8.2Recover Growth, Initial Stock, and TimeLesson8.3Convert Different Consumers to One UnitLesson8.4When the Resource ShrinksLesson8.5Queues: Arrivals versus Service CapacityLesson8.6Replenishing Inventory and Changing RatesLesson8.7Chapter 8 ExerciseExercise8 bonusBalance the Water GridBonus
09Chapter 9: Two-Type Problems7 pages
9.1Assume One Type: Baseline and DifferenceLesson9.2Wheels, Prices, Seats, and Other Two-Type StoriesLesson9.3Use Differences and Hidden RelationshipsLesson9.4Three Types and Integer ConstraintsLesson9.5Scores, Penalties, and Blank AnswersLesson9.6Expected versus Actual Totals and Reverse ProcessesLesson9.7Chapter 9 ExerciseExercise
10Chapter 10: Logical Reasoning: Assumptions7 pages
10.1Assume, Test, and RejectLesson10.2Count True and False Statements PreciselyLesson10.3Rank and Match with a Logic TableLesson10.4Split into Cases and Follow If–Then CluesLesson10.5Truth-Tellers, Liars, and Questions That Work Either WayLesson10.6Solve Multi-Attribute Logic Grids and Order CluesLesson10.7Chapter 10 ExerciseExercise
11Chapter 11: Calculation Logic7 pages
11.1Count Relationships, Complements, and Extreme CasesLesson11.2Match Numbers to Roles and Arithmetic CluesLesson11.3Prove a Minimum with Lower Bounds and ConstructionsLesson11.4Use Score Conservation and StandingsLesson11.5Count the Same Situation Two WaysLesson11.6Enumerate Cases and Test FeasibilityLesson11.7Chapter 11 ExerciseExercise
12Chapter 12: Cycles and Periods7 pages
12.1Find the Period and Use the RemainderLesson12.2Repeating Decimals:Nth Digit and Digit SumLesson12.3Discover Hidden Periods from Equal Window SumsLesson12.4State Cycles: Warm-Up, Repeat, and Jump AheadLesson12.5Last Digits and Recursive Remainder CyclesLesson12.6Combine Cycles and Track Moving PositionsLesson12.7Chapter 12 ExerciseExercise
13Chapter 13: Page Numbers7 pages
13.1Read Page Numbers as Digits and Solve Digit CluesLesson13.2Count the Digits Used to Number a BookLesson13.3Count How Often a Chosen Digit AppearsLesson13.4Work Backward from a Digit BudgetLesson13.5Find Missing or Repeated Pages from SumsLesson13.6Use Facing Pages, Sheets, and Odd–Even StructureLesson13.7Chapter 13 Exercise — Page Number ProblemsExercise
14Chapter 14: Number-Filling Diagrams7 pages
14.1Count Shared Positions and Discover Magic-Square InvariantsLesson14.2Construct Grids with Equal or Distinct SumsLesson14.3Fill Connected Regions Using Frequency and AdjacencyLesson14.4Build Sum Pyramids and Work BackwardLesson14.5Arrange Number Rings under Neighbor RulesLesson14.6Solve Number Networks with Global Totals and ConstraintsLesson14.7Chapter 14 ExerciseExercise
15Chapter 15: Divisibility7 pages
15.1Understand Divisibility and Build a Test ToolkitLesson15.2Split Large Numbers into BlocksLesson15.3Combine Conditions and Fill Missing DigitsLesson15.4Work Backward after Inserting a Decimal PointLesson15.5Track Repeated Elimination with Remainder ClassesLesson15.6Construct and Enumerate Divisible NumbersLesson15.7Chapter 15 ExerciseExercise
16Chapter 16: Remainders8 pages
16.1Build the Division Story: Quotient and RemainderLesson16.2Find a Hidden Divisor from the RemainderLesson16.3Recover Hidden Dividends, Divisors, and QuotientsLesson16.4Transform and Align RemaindersLesson16.5Find What Stays the SameLesson16.6Follow Remainder CyclesLesson16.7Chapter 16 ExerciseExercise16 bonusFind Full-Time TimestampsBonus
17Chapter 17: Primes and Composite Numbers7 pages
17.1Decide Whether a Number Is Prime or CompositeLesson17.2Use Parity and Remainders to Pin Down PrimesLesson17.3Decompose Numbers into Distinct Prime SumsLesson17.4Build Prime Numbers from Digits and OptimizeLesson17.5Recover Primes from Equations and Reciprocal SumsLesson17.6Group Prime-Power Packets into Coprime Composite NumbersLesson17.7Chapter 17 ExerciseExercise
18Chapter 18: Prime Factorization7 pages
18.1Build Standard Prime FactorizationsLesson18.2Count and Sum Divisors from Prime ExponentsLesson18.3Reconstruct Consecutive Numbers and Real-World Roles from ProductsLesson18.4Arrange Prime Factors to Fit Digit PatternsLesson18.5Balance Prime Exponents for Squares, Coprime Factors, and Equal ProductsLesson18.6Use Factor Pairs, Bounds, and Shared Divisors to Recover Hidden CountsLesson18.7Chapter 18 ExerciseExercise
19Chapter 19: GCD and LCM7 pages
19.1Read GCD and LCM from Prime ExponentsLesson19.2Use Short Division and the Euclidean AlgorithmLesson19.3Synchronize Cycles, Spacing, and Consecutive SumsLesson19.4Recover Numbers from GCD, LCM, and ProductLesson19.5Maximize Common Factors and Share Quantities EquallyLesson19.6Build Pairwise-Coprime Groups and Test Mixed ConstraintsLesson19.7Chapter 19 ExerciseExercise
20Chapter 20: Perfect Squares7 pages
20.1Recognize, Count, and Locate Perfect SquaresLesson20.2Balance Prime Exponents to Make a Perfect SquareLesson20.3Test Squares with Last Digits and Digit PatternsLesson20.4Connect Squares, Cubes, and Divisor CountsLesson20.5Work Backward with Square Roots, Gaps, and ShiftsLesson20.6Use Square Remainders, Identities, and SumsLesson20.7Chapter 20 ExerciseExercise
21Chapter 21: Digit Sums and Number Strings8 pages
21.1Locate Digits in Concatenated Number StringsLesson21.2Sum Digits over Complete Blocks and RangesLesson21.3Count Numbers with Exact or Modular Digit SumsLesson21.4Follow Recursive Digit and Decimal CyclesLesson21.5Track Digit Sums through Carries and ProductsLesson21.6Solve Digit-Sum Equations and Build Extremal NumbersLesson21.7Chapter 21 ExerciseExercise21 bonusMake 100 with Digit StringsBonus
22Chapter 22: Consecutive Numbers and Sums7 pages
22.1Build Consecutive Sequences with a Middle TermLesson22.2Count Long Consecutive Ranges without ListingLesson22.3Use Divisibility to Find Consecutive SumsLesson22.4Turn Divisibility Claims into Remainder ClassesLesson22.5Pair Terms and Recover Missing SumsLesson22.6Construct and Optimize with Digits and Group SumsLesson22.7Chapter 22 ExerciseExercise
23Chapter 23: The Pigeonhole Principle7 pages
23.1Find the Objects, Drawers, and Guaranteed CountLesson23.2Group Numbers to Force a RelationshipLesson23.3Build the Largest Safe Set and Prove It Is BestLesson23.4Partition Shapes to Force Closeness or Small AreaLesson23.5Use Color Patterns and Grid Signatures as DrawersLesson23.6Count the Worst Case before a Match Is ForcedLesson23.7Chapter 23 ExerciseExercise
24Chapter 24: Systematic Counting7 pages
24.1Build Complete, Non-Overlapping Case TablesLesson24.2Count Digit Patterns by Position, Equality, and DifferenceLesson24.3Classify by Remainders and Construct Every CaseLesson24.4Count Runs, Peaks, and Boundary PatternsLesson24.5Count Shapes, Tilings, and Assemblies SystematicallyLesson24.6Count Prime-Factor Contributions and Product ConditionsLesson24.7Chapter 24 ExerciseExercise
25Chapter 25: Defined Operations7 pages
25.1Decode a Defined Operation and Substitute in OrderLesson25.2Evaluate Nested Operations One Layer at a TimeLesson25.3Work Backward to Recover Inputs and Hidden ParametersLesson25.4Follow Recursive Definitions and Discover Repeated PatternsLesson25.5Use Number Functions, Congruence, and Selection OperatorsLesson25.6Test Order, Symmetry, and AssociativityLesson25.7Chapter 25 ExerciseExercise
26Chapter 26: Binary and Place Value7 pages
26.1Read Place Value and Count in BinaryLesson26.2Convert Between Decimal and BinaryLesson26.3Add and Subtract with Binary Carries and BorrowsLesson26.4Multiply, Divide, and Evaluate Binary ExpressionsLesson26.5Use Bit Patterns for Powers, Divisibility, and SubsetsLesson26.6Design Exact-Quantity Boxes and Brackets with Binary ChoicesLesson26.7Chapter 26 ExerciseExercise
27Chapter 27: Puzzle Workshop I9 pages
27.1Think Like a Puzzle Solver: Decompose, Reassemble, and Trace PathsLesson27.2Partition Grid Shapes into the Fewest SquaresLesson27.3Place Digits to Make Arithmetic Statements TrueLesson27.4Pair Points with Every Required Segment LengthLesson27.5Draw and Optimize Closed Orthogonal PathsLesson27.6Complete Latin Squares from Ranked Line NumbersLesson27.7Select Grid Cells to Maximize Repeated Line-Sum ScoresLesson27.8Fill Neighbor-Counting Grids with Parity RulesLesson27.9Solve Skyscraper Latin Squares from Visibility TotalsLesson
28Chapter 28: Puzzle Workshop II10 pages
28.1Close Circular Arithmetic Chains with Inverse OperationsLesson28.2Draw Grid Squares from Marked-Vertex ConstraintsLesson28.3Pack T-Shaped Tanks from Row-and-Column CluesLesson28.4Arrange and Move Cards to Control Line SumsLesson28.5Swap Tiles through a Single Empty SpaceLesson28.6Build paired-digitspacing sequencesLesson28.7Minimize non-touching squares in irregular grid regionsLesson28.8Number points to draw a nonintersecting pathLesson28.9Build Latin squares with trailing-zero place valuesLesson28.10Move the last digit to the front by multiplicationLesson