Bases - Activity 3

 

Materials Needed:    Base five units and longs.

 

All answers should be written as base five numerals.

 

Understanding Multiplication as Repeated Addition

 

1.         Use base five pieces to model 2_five  3_five as two groups of three each.

 

            What addition problem does this represent?

 

            Therefore 2_five  3_five =

 

2.         Use base five pieces to model 3_five  42_five as three groups of 42_five.

 

            What addition problem does this replacement?

 

            Therefore 3_five  42_five =

 

Creating a Base Five Multiplication Table

 

1.         Use the base five pieces to solve the problems:

 

            1_five  1_five =                             1_five  1_five =

            1_five  2_five =                             2_five  1_five =    

            1_five  3_five =                             3_five  1_five =

            1_five  4_five =                             4_five  1_five =

 

Use the solutions to fill in the appropriate spaces in the base five multiplication table.

           

 

2.         Use base five pieces and the associated addition problems to solve the following.

 

            2_five   2_five  =                            2_five  2_five =

            2_five   3_five  =                            3_five  2_five =

            2_five   4_five =                            4_five  2_five =

 

            Use the solutions to fill in the appropriate spaces in the base five multiplication table.

 

            What property of multiplication is demonstrated by the fact that 2_five  3_five =  3_five  2_five?

 

3.         Use base five pieces and the associated addition problems to solve the following.

 

            3_five  3_five =                             3_five  3_five =

            3_five  4_five =                             4_five  3_five =

 

            Use the solutions to fill in the appropriate spaces in the base five multiplication table.

 

4.         Use base five pieces to solve 4_five  4_five.

 

            Fill the solution in the appropriate spaces in the base five multiplication table.

 

5.         Solve:               0_five   0_five =                            0_five   0_five =

                                    0_five   1_five =                            1_five   0_five =

                                    0_five   2_five =                            2_five   0_five =

                                    0_five   3_five =                            3_five   0_five =

                                    0_five   4_five =                            4_five   0_five =

 

            Use the solutions to fill in the appropriate spaces in the base five multiplication table.

 

6.         a)  How does the Commutative Property of Multiplication appear in the table?

 

 

            b)  How does the table show the Zero Property of Multiplication?

 

 

            c)  How does the table show that one is the multiplicative identity?

 

 

Using Base Five Multiplication Tables                   

 

 

Use the base five multiplication table and base five addition to find the following products.

 

	fives	ones			fives	ones			twenty-fives	fives	ones
1.	1	4five		2.	2	3five		3.	1	0	2five
		3five				4five					4five

 

 

4.         23_five                                         5.         304_five                           6.         444_five   44_five =

         13_five                                                    32_five

 

 

7.         Greg's dad motivates him to save, by promising to contribute twice what Greg saves.  Greg has saved 1 quarter, 2 nickels and three pennies.

 

            a)  If his dad's donation is in quarters, nickels and pennies, what is the minimum number of

     each his Dad  donates?

 

b)  Greg has a small bank, so his mother trades him pennies for nickels, and nickels for

     quarters.  What  is the minimum number of quarters, nickels, and pennies which Greg has

     after his dad's contribution?

 

c)  His younger sister wants to trade Greg's coins for her penny collection.  How many

     pennies must she give to Greg?