lesson 3 (area, permeter and volume) 2017.notebook€¦ · lesson 3 (area, permeter and volume)...

Lesson 3 (Area, Permeter and Volume) 2017.notebook

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June 02, 2017

6SS3.3 Explain, using models, how the perimeter of any polygon can be determined.

(For any rectangle:Area is what you would color is you were asked to color it.Perimeter is the distance around a shape and can be traced with you finger.)

Polygon is any enclosed shapes with three or more sides (polygon meaning “many sided figure”).

6SS3 Develop and apply a formula for determining the:• perimeter of polygons• area of rectangles• volume of right rectangular prisms.


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June 02, 2017

Find the perimeter of these shapes.

A BC

D

E

F


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June 02, 2017


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June 02, 2017

Go back and find the perimeter of triangles A to F using a formula for perimeter.(linear units are used to measure 1‐dimensional shapes. There is no need for an exponent on the unit.)

Shape A: Shape D:

Shape B: Shape E:

Shape C: Shape F:


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June 02, 2017

6SS3.4 Generalize a rule (formula) for determining the perimeter of polygons, including rectangles and squares.

Which sides are congruent (ie. same length)?

3 cm

‐ We place a small mark on the sides that are equal to indicate that they are equal.‐ We can use repeated addition or multiplication to find the perimeter when sides are congruent.


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June 02, 2017

t

t

w w

Sides with same measure are indicated using the same hatch mark or variable.

The sum of these congruent sides can be found through repeated addition and therefore, by multiplication.

For example, in the rectangle below you can write the combined width as

w + w or 2 × w OR 2w and 2l Therefore we can write

Perimeter = 2w + 2l OR Perimeter = w + w + l + l

We can write multiplication involving a variable and a number without using the multiplication symbol. For example, 2 × w would be written as 2w.


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June 02, 2017

Example 1:

Example 2: In the regular hexagon below the side length is unknown so we use the variable s to represent it.

s


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June 02, 2017

Example 3:

Example 4:Create shapes using pattern blocks then write an expression to represent the perimeter of each shape.


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June 02, 2017

Farmer’s Fence Activity‐ You have a variety of polygons (square, rectangles, and triangles) with common side lengths labelled with a variable. ‐ Each polygon represents a different shaped field on a farm. ‐ Each different variable indicates the length of each side.

‐ You (The Farmer) want to build a fence around your farm. Write a formula for the perimeter of your farm.

‐ In groups students can arrange the polygons to create various combinations of different shaped farms. Write and record a formula for the farm's perimeter.

Example:The formula for this farm would be P = 3b + 2a + c + e


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June 02, 2017

Farmer’s Fence Activity‐ You have a variety of polygons (squares, rectangles, triangles) with side lengths labelled with a variable. ‐ Each polygon represents a different shaped field on a farm. Each different variable indicates the length of each side. ‐ In groups arrange the polygons to create various combinations of different shaped farms.

Use your formulas to find the perimeter of each of your farms.

For example: if a = 5 metres, b = 2 metres, c = 3 metres, e = 4 metres. The perimeter of the farm above would be P = 3(2) + 2(5) + 3 + 4 P = 6 + 10 + 3 + 4 = 23 metres


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June 02, 2017

a = 5 metres, b = 2 metres, c = 3 metres, e = 4 metres.

P = 4a + 3b + c + d + eP = 4(5) + 3(2) + 3 + 2 + 4P = 20 + 6 + 3 + 2 + 4P = 35


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June 02, 2017

Independent seat work June 5, 2013(Finish for homework)

Text page 246 questions: 5, 11Text page 252 questions: 4, 6Text page 257 questions: 4, 5Text page 260 questions 2Text page 263 question 3Text pages 268‐269 questions 4, 6, 8Text page 272‐273 questions 3, 4Text page 276 question 3


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June 02, 2017

6SS3.1 Explain, using models, how the area of any rectangle can be determined.

What's the area of this rectangle?

Each square unit on the grid paper has a 2‐D area of 1 cm2 meaning it has linear dimensions of 1 cm in height and 1 cm in width.

Measurement Notes #3 (Area)


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June 02, 2017


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June 02, 2017

A

B C

D

E F


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June 02, 2017

What do you notice?

By viewing the dimensions of a rectangle as groups of square units (width x length) the area of the rectangle can be found.

Changing the unit of measurement (mm2, cm2, m2) simply means that the size of each unit within the rectangle has changed but the area can still be determined in the same way.


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June 02, 2017

We can write the formula for perimeter as either:

Perimeter = 2w + 2l OR Perimeter = 2l + 2w

AND Area = l x w OR Area = w x l

The commutative property simply shows that the order in which terms are added or multiplied does not affect the final outcome. For example:

2 + 4 = 6 and 4 + 2 = 6

5 × 2 = 10 and 2 × 5 = 10


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June 02, 2017

6SS3.2 Generalize a rule (formula) for determining the area of rectangles.

A formula is a rule (process) that can be used to find a desired quantity or measurement.

In words: The area of a rectangle can be found by multiplying its length by its width.

As a formula: A = l × w, where A = area, l = length and w = width

Area can be thought of as what they would be colouring in if asked to colour a shape.


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June 02, 2017

Go back and find the area of triangles A to F using the formula for Area.(Square units are used to measure 2‐dimensional shapes. The exponent of 2 or squared on any unit means 2‐dimensional.)

Rectangle A: Rectangle D:

Rectangle B: Rectangle E:

Rectangle C: Rectangle F:


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June 02, 2017

Solving problems involving perimeter and areaJudy has designed a rectangular quilt 2m by 3m. What is the perimeter of the quilt?

John is making a display board for his Science Fair project. The display board is 1m by 2m. He wants to add a border around the display. If the border costs $3.00 per meter, how much will it cost?


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June 02, 2017

Solving problems involving perimeter and areaEllen has a flower garden that measures 6m by 8m. If one bag of fertilizer covers 16 square meters, how many bags would she need to fertilize her entire garden?

Felicia is training for a race. She runs a trail that is the shape of a regular hexagon. If the total distance she runs is 12km, how long is each leg (side) of the trail?


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June 02, 2017


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June 02, 2017

6SS3.5 Explain, using models, how the volume of any right rectangular prism can be determined.

Volume is measured in cubed units such as (mm3, cm3, m3). (You may think of the exponent 3 as meaning 3‐dimensional.)

Each cube has a volume of 1cm3, the total volume can initially be found by counting the number of cubes in the prism.


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June 02, 2017

There are 3‐dimensions to a rectangular prims: • Length• Width• Height

‐ We can count the number of cubes along the length, width and height. ‐ These dimensions are linear distances and are not measured in cubed units. ‐ The height of the prism will indicate how many layers of cubes are in the prism. ‐ First find the volume of one layer. V = l x w x h‐ Then find the number of layers. ‐ Multiply volume of one layer and the number of layers

There are 4 layers and each has a volume of 20 cm3, the total volume of the prism must be 80 cm3 (4 groups of 20 cm3)


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June 02, 2017

Group activity:‐ Each group create the largest rectangular prism possible with the blocks given. (random amount)‐ Record dimensions and record them in the chart given.‐ Calculate and record the volume.


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June 02, 2017

lesson 3 (area, permeter and volume) 2017.notebook€¦ · lesson 3 (area, permeter and volume)...

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