Download GM5-10W

STRAND:
Geometry and Measurement
LEVEL:
5
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
They will solve problems and model situations that require them to:
GM4-5 Identify classes of two- and
three-dimensional shapes by their
geometric properties.
GM5-10 Apply trigonometric ratios and Pythagoras’
theorem in two dimensions.
LEARNING INTENTION:
I am learning to identify situations where trigonometric ratios can be used to find
angles and lengths in right angle triangles.
I am learning to identify situations where the use of Pythagoras’ Theorem is
appropriate.
I am learning to apply Pythagoras’ Theorem and trigonometric ratios to practical
situations.
PRIOR KNOWLEDGE:
Triangle and right-angled triangle properties.
Rounding to decimal places and significant figures.
GM6-6 Use trigonometric ratios and
Pythagoras’ theorem in two and three
dimensions.
SUCCESS CRITERIA: Know, understand and do.
I can identify sides of a right angled triangle relative to a given angle.
I can choose the appropriate trigonometric ratio to find sides.
I can choose the appropriate trigonometric ratio to find angles.
I can use Pythagoras’ Theorem to find the length of the hypotenuse of a right
angled triangle.
I can use Pythagoras’ Theorem to find the length of a short side of a right angled
triangle.
I can interpret and solve word problems.
LINKED OBJECTIVES:
Solve algebraic equations.
Using calculator functions.
Similar triangles.
Rounding, using decimals, estimation.
VOCABULARY: sine, cosine, tangent, hypotenuse, opposite, adjacent, degrees, angle, right-angled, Pythagoras, Theorem, trigonometric, ratio,
SOHCAHTOA, square root, relationship.
DIAGNOSTIC SNAPSHOT:
GM5-10 Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.
KEY COMPETENCIES:
INTRODUCING:
Thinking Relating to others Using language, symbols and texts Managing self Participating and contributing
Bridge building (EQUALS trig book ETB)
How high?
M, P
Geometer’s Sketchpad (or Cabri
Geometry or CAS) investigation of
areas of squares on sides of rightangled triangle.
U
T
Investigation of squares on scalene
triangles
M, T
Investigation or areas of other figures
eg circles, equilateral triangles on
triangles
T
Same shape triangles (ETB)
T
Find the height of tree/ building etc
(field work, ETB)
R
Cooperative logic (ETB)
P
Finding the gradient of stairs – field
work
M, P
Cost distance problem (Nelson 9)
Find the point of minimum cost using
table, graph, Geometer’s Sketchpad. T
EXTENDING:
Pythagorean triples
T
Vector problems such as rowing
across a river.
T