
Division, Multiplication, & Algebra Discovered by
Playing with Blocks
Purpose: students will demonstrate multiplication,
division, and algebra by arranging blocks, students will
show a relationship between algebra and geometry with
blocks.
Background: these lessons were proposed for a
1st2nd grade class (too late in the year to be tried) 
Reformatted: January 2010 

Division Demonstrated with Blocks
[1] Give students a set of blocks. Have them make rectangles using
as many blocks as possible. Have them describe their arrangement of
blocks by the dimensions. How many blocks long are each side?

This arrangement is 3 blocks by 5 blocks with 2
left over, totaling 17 blocks,
or 3x5 remainder 2

This is 13 blocks arranged as 3 blocks by 4
blocks with 1 left over,
or 3x4 remainder 1.


Vocabulary:
 by & x : these symbolize multiply, students will see
them as references to geometry also
 left over & remainder : these words from division
will mean to students how many blocks did not fit into the
rectangles.

Related pages at this site


Factoring and Winning Demonstrated by Playing with Blocks
Purposes: to demonstrate factoring concepts, to demonstrate
that more is not always a winning strategy
 Have students work in pairs.
 Tell students that they will arrange their blocks in
rectangles. They must use all their blocks in each rectangle. The
student who creates the most rectangles "wins."
 From the following set of choices the first student may pick
which number of blocks he wants to use:
6 or 7

9 or 10

12 or 13

15 or 16

24 or 25

The other student gets the other number.
 In each case, the student with the smaller number of blocks
will win by creating more rectangles that use all of his blocks.
 Have students discuss what they learned about winning
strategies for this game.
Comments: The number of rectangles that you may make
depends on how many ways that each number can be factored. For
example, in the first set: 6 = 1x6, 6=6x1, 6=2x3, 6=3x2 and 7=1x7,
7=7x1. Students should discuss whether they think that 2x3 is the
same as, or different from 3x2.
Algebra Demonstrated by Playing with Blocks
Purpose: to represent some geometrical ideas that occur in
algebra
 Have students arrange blocks into a rectangle
 Have them group the blocks to describe the rectangle as being
made of parts
 Have them try again to show a similar arrangement with a
different size rectangle

Here we see a square represented as
 4 corners, 4 sides made of 3 blocks each, and a
center 3x3 square of 9 blocks
 Corners + sides + center = total
 4 + 4x3 + 3x3 = 25

This anticipates the form:
N^{2} = A^{2} + 4AB+ 4B^{2} 

Here we see a square represented as
 a series of blocks forming a corner around a smaller
square
 1+3+5+7+9 = 25

This anticipates the form:
N^{2} = Sum (odds)

?

What groupings can students think of to represent parts
of rectangles? How would they show them?



