Fractions, Decimals, &
Percents
Geometry
Measurement
EDU 592
Class 3
Developing Fraction Concepts
• Fractional parts are equal shares or equal sized
portions of a whole or a unit. A unit can be an
object or a collection of objects. More abstractly,
the unit is counted as 1. On the number line, the
distance from 0 to 1 is the unit.
• Fractional parts have special names that tell how
many parts of that size are needed to make the
whole. For example, thirds require three parts to
make a whole.
Developing Fraction Concepts
• The more fractional parts used to make the
whole, the smaller the parts. For example,
eighths are smaller than fifths.
• The denominator of a fraction indicates by
what number the whole has been divided in
order to produce the type of part under
consideration. The denominator is a divisor.
It names the kind of fractional part under
consideration.
What fraction of the large square is
shaded…
Developing Fraction Concepts
• The numerator tell how many of these
fractional parts are under consideration. It is
a multiplier - it indicates a multiple of the
given fractional part.
• Two equivalent fractions are two ways of
describing the same amount by using
different-sized fractional parts.
Decimal and Percent Concepts
• Decimal numbers are simply another way of
writing fractions. Both notations have value,
and students need to understand how the two
symbol systems are related.
• Our base-ten place-value system extends
infinitely in both directions. Between any two
place values, the 10:1 ratio remains the same.
Match the Decimal Number with
the closest fraction expression:
1
5
.41
.804
7
8
.6271
.211
1
3
5
8
Decimal and Percent Concepts
• The decimal point is simply a convention that
has been developed to indicate the units
position.
• Percents are hundredths. They are another
way of writing fractions and decimals.
• Addition and subtraction with decimals are
based on the fundamental concept of adding
and subtracting numbers in like position
values.
Decimal and Percent Concepts
• Multiplication and division of two numbers
will produce the same digits, regardless of the
positions of the decimal point. Computations
should be performed as whole numbers with
the decimal point placed using estimation.
.6 x 2.5 =
Think: 6 x 25 = 150
What would be reasonable?
Geometric Thinking
• Many different geometric properties influence
what makes shapes alike and different. For
example, shapes have sides that are parallel,
perpendicular, or neither; they have a line of
symmetry, rotational symmetry or neither;
they are similar, congruent, or neither.
• Shapes can be moved in a plane or in space
(translations, rotations, reflections).
Geometric Thinking
• Shapes can be described in terms of their
location in a plane or in space- coordinate
systems can be used to describe these
locations precisely.
• Shapes can be seen from different
perspectives, which helps us understand
relationships between 2 and 3-dimensional
figures.
Name the Property
Have it:
Don’t have it:
Name the Property
Which of these has it?
Developing Measurement Concepts
• Measurement involves a comparison of an
attribute with a unit that has the same
attribute (length to length, time to time, etc.).
• Meaningful measurement and estimation of
measurements depend on a personal
familiarity with the unit of measure being
used.
Developing Measurement Concepts
• Estimation of measures and the development
of personal benchmarks for frequently used
units of measure help students increase their
familiarity with units and help to prevent
errors.
• Measurement tools replace the need for
actual measurement units. We need to
understand how they are used to accurately
and meaningfully use them.
Developing Measurement Concepts
• Area and volume formulas provide a method
of measuring these attributes by using only
measures of length.
• Area, perimeter, and volume are related to
each other, although not precisely or by
formula.
Developing Measurement Concepts
How many different rectangles can you make
with an area of 36 square units?
• For each rectangle, record the perimeter.
• Make a conjecture about the relationship you
see.