Answer:
Enduring Understandings:
The square roots of perfect squares are rational numbers.
The square roots of non-perfect squares are irrational numbers.
Many geometric properties and attributes of shapes are related to
measurement.
General Learning Outcomes:
Develop number sense.
Use direct or indirect measurement to solve problems.
Specific Learning Outcome(s): Achievement Indicators:
8.N.1 Demonstrate an understanding
of perfect squares and square
roots, concretely, pictorially, and
symbolically (limited to whole
numbers).
[C, CN, R,V]
Represent a perfect square as a square
region using materials, such as grid paper
or square shapes.
Determine the factors of a perfect square,
and explain why one of the factors is the
square root and the others are not.
Determine whether or not a number is
a perfect square using materials and
strategies such as square shapes, grid paper,
or prime factorization, and explain the
reasoning.
Determine the square root of a perfect
square, and record it symbolically.
Determine the square of a number.
8.N.2 Determine the approximate
square root of numbers that are
not perfect squares (limited to
whole numbers).
[C, CN, ME, R, T]
Estimate the square root of a number that
is not a perfect square using the roots of
perfect squares as benchmarks.
Approximate the square root of a number
that is not a perfect square using technology
(e.g., calculator, computer).
continued
4 Grade 8 Mathematics: Suppor t Document for Teachers
Specific Learning Outcome(s): Achievement Indicators:
Explain why the square root of a number
shown on a calculator may be an
approximation.
Identify a number with a square root that is
between two given numbers.
8.SS.1 Develop and apply the
Pythagorean theorem to solve
problems.
[CN, PS, R, T, V]
Model and explain the Pythagorean
theorem concretely, pictorially, or by using
technology.
Explain, using examples, that the
Pythagorean theorem applies only to
right triangles.
Determine whether or not a triangle
is a right triangle by applying the
Pythagorean theorem.
Solve a problem that involves determining
the measure of the third side of a right
triangle, given the measures of the other
two sides.
Solve a problem that involves Pythagorean
triples (e.g., 3, 4, 5 or 5, 12, 13).
Prior Knowledge
Students may have had experience with the following:
Q Demonstrating an understanding of regular and irregular 2-D shapes by
Q recognizing that area is measured in square units
Q selecting and justifying referents for the units cm² or m²
Q estimating area by using referents for cm² or m²
Q determining and recording area (cm² or m²)
Q constructing different rectangles for a given area (cm² or m²) in order to
demonstrate that many different rectangles may have the same area
Q Solving problems involving 2-D shapes and 3-D objects
Q Designing and constructing different rectangles given either perimeter or area, or
both (whole numbers), and drawing conclusions
Q Identifying and sorting quadrilaterals, including
Q rectangles
Number 5
Q squares
Q trapezoids
Q parallelograms
Q rhombuses
according to their attributes
Q Developing and applying a formula for determining the
Q perimeter of polygons
Q area of rectangles
Q volume of right rectangular prisms
Q Constructing and comparing triangles, including
Q scalene
Q isosceles
Q equilateral
Q right
Q obtuse
Q acute
in different orientations
Background Information
Squares and Square Roots
A square is a 2-dimensional (2-D) shape with all four sides equal.
The total area the square covers is measured in square units.
To determine the side length of a square when given the area, the square root must be
determined.
A perfect square can be described as
Q a square with whole number sides (e.g., 1 × 1, 2 × 2, 3 × 3)
Q a number whose square root is an integer (e.g., 4 = 2 or –2)
A non-perfect square can be described as
Q a square with non-whole number sides (e.g., 1.2 × 1.2)
Q a number whose square root is not a whole number (e.g., 2)
Rounding is often used to determine the approximate square root of non-perfect
squares.
Step-by-step explanation: