20771_Problem_solving_Year_6_Background_information_resources

INTRODUCTION
The following problem shows how these
understandings can be used.
A small sheet of paper
has been folded in half
and then cut along
the fold to make two
rectangles.
Many dice are made in the shape of a cube with
arrangements of dots on each square face so that
the sum of the dots on opposite faces is always 7.
An arrangement of squares that can be folded to
make a cube is called a net of a cube.
The perimeter of each
rectangle is 18 cm.
What was the
perimeter of the
original square sheet
of paper?
Reading the problem carefully and analysing the
diagram shows that the length of the longer side
of the rectangle is the same as the one side of the
square while the other side of the rectangle is half
this length. Another way to obtain this insight is to
make a square, fold it in half along the cutting line and
then fold it again. This shows that the large square is
made up of four smaller squares:
Since each rectangle contains two small squares, the
side of the rectangle, 18 cm, is the same as 6 sides of
the smaller square, so the side of the small square is
3 cm. The perimeter of the large square is made of 6
of these small sides, so is 24 cm.
Similar thinking is used with arrangements of twodimensional
and three-dimensional
shapes and in visualising how they can
fit together or be taken apart.
Which of these arrangements of squares forms a
net for the dice?
Greengrocers often
stack fruit as a
pyramid.
How many oranges
are in this stack?
Measurement sense is dependent on both number
sense and spatial sense as attributes that are one-,
two- or three-dimensional are quantified to provide
both exact and approximate measures and allow
comparison. Many measurements use aspects
of space (length, area, volume), while others use
numbers on a scale (time, mass, temperature).
Money can be viewed as a measure of value and
uses numbers more directly, while practical activities
such as map reading and determining angles require
a sense of direction as well as gauging measurement.
The coordination of the thinking for number and
space, along with an understanding of how the metric
system builds on place value, zero and renaming, is
critical in both building measurement understanding
and using it to come to terms with and solve many
practical problems and applications.
Measurement sense includes:
• understanding how numeration and computation underpin measurement
• extending relationships from number understandings to the metric system
• appreciating the relative size of measurements
• a capacity to use calculators, mental or written processes for exact and approximate calculations
• an inclination to use understanding and facility with measurements in flexible ways.
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Problem-solving in mathematics www.ricpublications.com.au R.I.C. Publications ®