diagnostic error analysis measurement & geometry
TRANSCRIPT
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D I AG N O S T I C E R R O R A N A LY S I S
MEASUREMENT & GEOMETRY
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44. CONGRUENCY
Congruency
• Two figures or objects are ___________ if they have the ______ shape size, or if one is the mirror image of the other.• If you place both
images on top of one another, GH and BC line up.
congruent same
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45. SURFACE AREA
• How many sides of a cube are exposed as the surface area?• 26 (This includes the
bottom of model).• What is the surface
area of ONE side?• 3x3=9 sq. in.• 9x26=234 sq. in.
3
3
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46. PYTHAGOREAN THEOREM
• What clues in the picture inform me that I must use the Pythagorean theorem?• a2+b2=c2
• 162+b2=202
• 256+b2=400• Solve for b.
a=
c=
b=?
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47. CONVERSIONS
• Notice the initial units of measurements.
• Notice the conversions offered in the choices.
• You’ll have to convert the units into seconds or minutes.
• Divide the hour (60 minutes) into 6 kilometers.
• 60/6 = 10 minutes• 1 kilometer in 10 minutes.
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48. SCALE MODELS AND PROPORTIONS
• Create the following proportion:
• Solve for x.
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49. AREA OF TRIANGLE
• What is the formula for the area of a triangle?
• Correctly identify the base and height.
• Apply the formula.
base
height
This is NOT the height.
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50. REFLECTION
• Reflection is the_________image across the ____ or _____- axis.• According to the question,
across which axis will the image cross?
• It will be across the y-axis.• POP QUIZ• What happens when
you translate a figure?
mirror
x
y
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REFLECTION VS.
TRANSLATION
REFLECTION
• A figure can be reflected across the y-axis or across the x-axis.
• A problem will always direct you to “reflect across the ____ or ____ axis.”
TRANSLATION
• A figure can be translated up, down, left or right according to specific instructions.
• A problem will always direct you to translate with specific directions like the following:
• “ 2 units up”• “1 unit down and 3 units to
the right”• “1 unit down and 5 units to
the left”
x y
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51. SCALE AND PROPORTION
• What is a key word in this problem?
• Volume is the key word.• How do you get the
volume of a cube?• Multiply the following:
(length)(width)(height)• We can give variables to
the cubes.• Small cube: (x)(x)(x)=
x3
• Large cube:(4x)(4x)(4x)=64x3
• Clearly, the larger cube is 64 times greater.
x
xx
4x
4x4x
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52. PERIMETER
• You must know how to calculate the perimeter.
• The perimeter is the distance ___________ a figure.
• What are the measurements of all four sides?
• 25 + 12.5 + 25 + 12.5• Question: Why do two
sides measure 12.5?• Solve the problem.
around
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53. PROPORTION
• Notice the time measurements.
• Create a proportion.
• Solve for x.• Is there another way you
can solve this problem?
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54. CONVERSION WITH FORMULA
• Is this too easy?• To convert from Celsius to
Fahrenheit, plug in the known variable and solve for the unknown.
• Solve for F.
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55. AREA OF CIRCLE
• How do we know that this question is asking for the area?
• Area is always measured in ___________ units.
• Question: How do I find the radius if they only give me the diameter?
• Label the parts of a circle.• Solve for the area of one
glass top.
square
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56. PLOTTING FIGURES ON GRAPH
• It’s easy to plot the points.
• Now, you must know the definition of all four shapes.
: two bases, usually two parallel sides and two legs not parallel
:same opposite side, diagonals intersect.
:all four sides equal in length
:each opposite pair is parallel and the same length.