19
Squares, Cubes and
Number Shapes
LEARNING and TEACHING POINT
LEARNING and TEACHING POINT
Use square arrays of dots and square
grids to explain square numbers. Connect
the square of a number with the area of a
square grid, given by counting the number of square units in the grid.
Explicitly teach children the calculator
sequence for finding square numbers on a
basic non-scientific calculator (number, ×, =).
LEARNING and TEACHING POINT
LEARNING and TEACHING POINT
Encourage children when learning their
multiplication tables to take a special
interest in the square numbers and to
locate them in the table of multiplication
results (see Figure 11.1).
LEARNING and TEACHING POINT
Cube numbers can be explored by older
and more able children in the primary
school. Get them to construct cubes from
cubic units. Connect the cube of a number
with the volume of the cube, given by
counting the number of cubic units used
to construct it.
Children can explore properties of square
numbers using the visual image of a
square array. For example, can you make
a square of side 7 units from strips of 6
units (and so on)? How many 3 by 3
squares do you need to make a 6 by 6
square? Do all positive whole numbers
have an even number of factors? In seeking to answer such questions children
would be ‘following a line of enquiry,
conjecturing relationships and generalizations’ (see Chapter 4).
LEARNING and TEACHING POINT
Squaring and finding a square root are
excellent examples of inverse processes to
discuss with children. Inverse processes
are those where one process undoes the
effect of the other.
LEARNING and TEACHING POINT
LEARNING and TEACHING POINT
Give children opportunities to investigate the relationships between sequences
of geometric patterns and numerical
sequences. The kind of thinking involved
is an introduction to algebraic reasoning,
involving the recognition and articulation of generalizations.
To introduce primary children to the
method of trial and improvement using a
calculator, get them to solve puzzles such
as: ‘I am thinking of a number; I add 23 to
it and multiply the answer by my number.
The result is 2124. What is my number?’