Level 3

Operations

    AAA.1     

Properties

    BBB.1

Ratios and proportions

    CCC.1       

Problem solving (Velocity)

    DDD.1    Replacement of long hand and hour hand           

    DDD.2    Three persons moving on a circular pond          

    DDD.3    The 3rd hand on a circular clock          

    DDD.4    Two persons moving on an annular road            

    DDD.5    Two persons walking on a moving walkway            

    DDD.6    Going back and forth two points            

    DDD.7    Hour hand, minute hand and second hand           

    DDD.8    Three points moving on a circumference            

Transformations

    EEE.1    Three points moving on a rectangle

    EEE.2    Two points moving in a square

    EEE.3    Change of gas rate in several months

    EEE.4    Taxi fare of two types of cars

Problem solving (Sum and difference)

    FFF.1    Number of songs at concerts           

    FFF.2    Questionnaire on three subjects          

    FFF.3    Election of class representative           

    FFF.4    Put water in four vessels

    FFF.5    Candies for children gathering

Number sense / theory

    GGG.1    Put 48 balls into five boxes            

    GGG.2    Ten students roll three dice           

    GGG.3    Multiple of continued integers          

    GGG.4    Multiple of every number of each digit      

    GGG.5    Sum total of every number of each digit              

    GGG.6    Quotient is rounded off at 1st decimal place        

Number of cases / Probability

    HHH.1    Way of putting spots on the die         

    HHH.2    Same birthday in the class of 50 people          

    HHH.3    Take out balls from the bag          

    HHH.4    Three blue cards and five red cards           

    HHH.5    Arrangement of squares in order            

    HHH.6    Number of inverse order          

    HHH.7    Put 1~8 in a frame            

Patterns / Regularity

    III.1    Lottery of "Amidakuji"

    III.2    Two machines displaying numbers on the rule

    III.3    Table of integers written clockwise 

    III.4    Triangle of integers written counterclockwise

    III.5    365 cards with date of one year

    III.6    Time of display of crossing for trains

    III.7    Removing cards based on the rule

Geometry (Plane figure)

    JJJ.1    Rectangle moves and overlaps triangle            

    JJJ.2    Connected parallelograms

    JJJ.3    Two circles moving in triangle

    JJJ.4    Overlapping hexagon and heptagon

    JJJ.5    Partition of right triangle

    JJJ.6    Straight line dividing figure into three

    JJJ.7    Circle moving around a figure

    JJJ.8    Circle moving around hexagon

    JJJ.9    Square moves in a triangle

    JJJ.10    Compare area of black and white square

    JJJ.11    Area ratio divided in sector

    JJJ.12    Area ratio divided in parallelogram

    JJJ.13    Area ratio divided in triangle

    JJJ.14    Right dodecagon

    JJJ.15    Tape winded around rectangular board

    JJJ.16    Reflection in rectangle

    JJJ.17    Triangle covered by squares

Geometry (Solid figure)

    KKK.1    Piling up cubes and put red seals

    KKK.2    Paint inside of rectangular prism

    KKK.3    Cut surface of cube

    KKK.4    Cut right quadrangular pyramid

    KKK.5    Cut another quadrangular pyramid

    KKK.6    Shadow of rectangular wall

    KKK.7    Solid made by cutting cylinder

    KKK.8    Volume ratio after cutting rectangular prism

    KKK.9    Number of dice to be cut or not

    KKK.10    Cutting line based on development view

    KKK.11    Development view of solid with six faces of lozenge

    KKK.12    Square pyramid and homothetic ratio

    KKK.13    Shadow of block by streetlight

    KKK.14    Shadow of box by stand light

    KKK.15    Cut rectangular prism with planes parallel to faces

    KKK.16    Rectangular prism and triangular pyramid

    KKK.17    Piling up cubes and cut

    KKK.18    Hollowing out rectangular prism

    KKK.19    Cut piling up eight cubes 

    KKK.20    Number of cut to make development view

    KKK.21    Vessel, water and bar
    KKK.22    Assembling development views of two solids
   KKK.23    Image solid from development view

 Logical reasoning

    LLL.1    Find the way to go           

    LLL.2    Find the road to paradise        

    LLL.3    Volleyball tournament of five teams