Manipulating Formulas for Geometric Shapes
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L3 MATHS LITERACY
T
OPIC
2 –LESSON 1
S
PACE
AND
SHAPE
MANIPULATION OF
FORMULAE
SUBJECT OUTCOME/S: (this is what you need to
understand and apply)
2.2.5 Manipulate given formulae to calculate the
unknown values when the perimeter/circumference
and area of the following shapes are given:
•
Square
•
Rectangle
•
Triangle
•
Circle
•
Semi-circle
compiled by B Adams
1
In order for us to understand the above outcome, we must first make sure
that we know our formulas. In L2 you were expected to just work out the
perimeter, area or volume. But for L3, we give you the worked out
perimeter, area or volume.
You then need to find the missing
dimension (length, breath, height, radius etc.)
This means that when we have our formula (Halleluja) we can substitute
the values that they have given us into the formula. Look at the examples
on the
following slides:
compiled by B Adams
2
L
ET
’
S
LOOK
AT
SOME
EXAMPLES
:
Length – 6m
Step 1
– What did the question ask?
Step 2
– What shape do you see/or did the
question mentioned?
Step 3
– Is the dimensions in the same unit
(meters, centimeters or millimeters)
Step 4
– What is the related formula (look at
step 1 and 2)
Step 5
– Write the formula down and substitute
what was given in the Question.
compiled by B Adams
3
C
ONTINUE
:
EXAMPLE
2
Height
10cm
Step 1
– What did the question ask?
Step 2
– What shape do you see/or did the
question mentioned?
Step 3
– Is the dimensions in the same
unit (meters, centimeters or millimeters)
Step 4
– What is the related formula (look
at step 1 and 2)
Step 5
– Write the formula down and
substitute what was given in the Question.
compiled by B Adams
4
L
ET
’
S
DO
A
FEW
NOW
TO
PRACTICE
:
Go to page 124 Exercise 2.6
Do the following Questions
1, 2,3,4 and 5
Please use the steps as given above for
each question. After substitution you
need to work out the answer.
You can do this guys. If there were NO picture with the
question – draw it, visualise it for yourself and write the
dimensions in.
Good luck and shout if you are stuck!
compiled by B Adams
5
How to calculate unknown values by manipulating formulas for shapes like squares, rectangles, triangles, circles, and semi-circles when the perimeter/circumference and area are given. Follow step-by-step examples to practice the concept.
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Presentation Transcript
L3 MATHS LITERACY TOPIC 2 LESSON 1 SPACE AND SHAPE MANIPULATION OF FORMULAE SUBJECT OUTCOME/S: (this is what you need to understand and apply) 2.2.5 Manipulate given formulae to calculate the unknown values when the perimeter/circumference and area of the following shapes are given: Square Rectangle Triangle Circle Semi-circle compiled by B Adams 1
In order for us to understand the above outcome, we must first make sure that we know our formulas. In L2 you were expected to just work out the perimeter, area or volume. But for L3, we give you the worked out perimeter, area or volume. You then need to find the missing dimension (length, breath, height, radius etc.) This means that when we have our formula (Halleluja) we can substitute the values that they have given us into the formula. Look at the examples on the following slides: compiled by B Adams 2
LETSLOOKATSOMEEXAMPLES: Example 1: The area of a rectangular room is ????. The length of the one side is 6m. What is the breath? Step 1 What did the question ask? Step 2 What shape do you see/or did the question mentioned? Step 3 Is the dimensions in the same unit (meters, centimeters or millimeters) Step 4 What is the related formula (look at step 1 and 2) Step 5 Write the formula down and substitute what was given in the Question. compiled by B Adams Area = 30?2 Length 6m 1. Work out the breath 2. A rectangle was mentioned in the question (if you are unsure draw the shape for yourself) 3. The dimensions are in the same unit - meters 4. ???? ?? ? ????????? = ???? ? ????? 5. Substitute what was given in the question 30?2= 6m ????? 30?2 5? = ????? 6? =6m ????? (divide both sides by 6m) 3 6?
CONTINUE: EXAMPLE 2 The Volume of a cylinder is 282,6??3. Calculate the radius of the cylinder if the height is 10cm. Step 1 What did the question ask? Step 2 What shape do you see/or did the question mentioned? Step 3 Is the dimensions in the same unit (meters, centimeters or millimeters) Step 4 What is the related formula (look at step 1 and 2) Step 5 Write the formula down and substitute what was given in the Question. compiled by B Adams Volume = 282,6??3 Height 10cm 1. 2. 3. 4. 5. Work out the radius A cylinder Dimensions is the same in centimeters ?????? ?? ??linder = ?2 Substitute into the formula: ?????? ?? ??linder = ?2 282,6??3= 3,14 ?2 10?? (You are allowed to swapped both sides of the equal = sign) 3,14 ?2 10?? = 282,6??3 31,4?? ?2 = 282,6??3 (divide both sides with 31,4cm) ?2= 9??2 ?2= 9??2 ? = 3?? 4
LETSDOAFEWNOWTOPRACTICE: Go to page 124 Exercise 2.6 Do the following Questions 1, 2,3,4 and 5 compiled by B Adams Please use the steps as given above for each question. After substitution you need to work out the answer. You can do this guys. If there were NO picture with the question draw it, visualise it for yourself and write the dimensions in. 5 Good luck and shout if you are stuck!
