LONG  WINTER  HOMEWORK    7    LEVEL  1    DUE    1st    class  of  Spring  Semester,  2017.      This  is  a    homework    to  entertain  you    during    the      school    winter  break.    Solve  as  many  problems  as  you  want  –  it  is  not  required  to    solve  all  of  them.    Write  your  arguments  and  solutions    clearly.        

1. Write  the  names  of  the  months  of  the  year  in  order  and  the  number  of  days  in    them.    We  start:    1)    January  (31);        2)    February  (28  or    29);    …                      

2. How  many    full    weeks  are  there  in  one  year?        

 3.      In  the    picture  below    there  are    7  chairs      arranged  around    5    triangular  tables.        

   How    many    chairs    could  be    placed  around  a  similar  arrangement  of  

   

a) 6    triangular    tables?    

       

b) 7  triangular  tables?              

c) 31    triangular  tables?            

4. Find the missing numbers.

 5.    At  a  concert  46    people  were  asked,  if  they    like  classical  music  or    jazz.  It  turned  out    that    25  liked  both,    classical  music    and    jazz,    8    liked  only    classical  music,  6  liked    only      jazz.    How  many      did  not  like  either    type  of  music?  (Draw      Venn  diagram  and  solve  the  problem).                          

 6.  Using  the    digits      1  through  9  once  each,  fill    in  the  boxes  to  make    the    equations    true:    

�   −   �   =   �           ×  

�   ÷   �   =   �           ||  

�   +   �   =   �      7.    Solve  the  problem      posed  by    this  Old  English    children’s    rhyme,  it  was    published    first  time    almost  300  years  ago!    

 As I was going to St. Ives, I met a man with seven wives, Each wife had seven sacks, Each sack had seven cats, Each cat had seven kits: Kits, cats, sacks, and wives, How many were going to St. Ives?

8. Four boys played baseball in the backyard and broke the window. They said the following: Bob: Charlie did it. Charlie: Eric did it. Dave: I didn’t do it. Eric: Charlie lied when he said I did it.

a) If only one of the statements is true, who was guilty?

9. Today 1 Estonian Kroon (currency, money of the country Estonia) equals about 7 Japanese Yen (currency of the country Japan), and about 41 Chilean Peso (currency of the country Chile). What is worth more: 1 Chilean Peso or 1 Japanese Yen? 10. Make an addition problem of two-digit numbers and the answer, using each of the digits 1, 3, 4, 5, 6, 9 only once:

�� + �� = ��

11. What is the smallest counting number that is divisible by numbers a) 2 and 3? b) 2 and 12 ?

b) 2, 4, 6 and 5? 12. To produce each figure, a square was folded twice, punched once, then unfolded. Draw the fold lines.

13. The two the statements below are false. Draw for each of them an example of a shape that illustrates that the statement is false.

A. If all angles of a quadrilateral are equal 90 degrees, then it is a square.

B. If all sides of a quadrilateral have equal length, then it is a square.

14. How many 1x1x1 cubes are in the following stack?

15. For each kid, find the ball with the same answer

16. There  are    5  baseball    teams    with  the  names  A,  B,  C,  D    and  E    in  a  tournament.  Each  team    plays  each  of  the  other    teams  exactly  one  time.    How  many    games  are  played  altogether?    Draw  a  diagram  to    illustrate    the    answer.   17. Match each hat with a scarf that has the same answer

 

 18.  In  the  picture,  the  drawing    on  the  left  shows  a  shape.  The  drawing  on  the  right    tells    you    how  many  cubes    are  on  each  base    square.  The    drawing  on  the  right  is  called  a  base  design.      

 Make  a    base  design    for  the      following  shape: