Math

This week we will review area particularly applying areas of rectangles to solve problems. It's important that you understand the difference between area and perimeter and recognize the different types of problems. 

Area of a rectangle = Length x Width 

Area is measured in square units e.g. mm², cm², m², km²

^{It is the amount of square units cover a two-dimensional shape. It's the INSIDE of the shape.}

^{Examples of area problems:}

• ^{flooring in a room}
• ^{space to plant a garden or grass or a patio}
• ^{size of a school yard or field}
• ^{size of a border around a picture}

^{Perimeter of a Rectangle = (Length + Width) x 2} 

^{Perimeter of a Rectangle  = 2 x Length + 2 x Width}

^{Perimeter of a Rectangle = Length + Length + Width + Width}

^{All of these formulas will work, but the first one is the most important when solving problems.}

Perimeter is measured in linear units e.g. mm, cm, m, km

^{Perimeter is a measure of the distance around the OUTSIDE of a two-dimensional shape.}

^{Examples of perimeter problems:}

• ^fencing
• ^framing
• ^{border (can be both)}
• ^trim

Practice questions:

A rectangular garden has a length of 25 m and a width of 10 m. How much would it cost to fence the garden if fencing is $10 a metre? How much would it cost to lay sod (grass) if sod is $5 a square metre?

A backyard has an area of 45 m², what are possible lengths and widths?

What are the area of 3 rectangles that have a perimeter of 30 cm?

A picture frame has a length of 12 cm and a perimeter of 96 cm. What is the width of the frame?

A frame has a length of 30 cm and a width of 20 cm. It has a 5 cm border around the picture. What is the area of the picture inside?

We began on Friday to look at APPLYING our knowledge of the area of rectangles to find the area of shapes that are not rectangles. 

A right-angled triangle if really half of a rectangle. So if you multiply the length and width then divide the answer by 2, you will get the area of the triangle.

Area of right-angled triangle = Length x Width ÷ 2

                                               = 8 cm x 6 cm ÷ 2

                                               = 48 cm² ÷ 2

                                               = 24 cm²

Noticed how I solved the problem. I showed all of my steps line by line.

How many 2 cm² tiles are needed to cover a square wall that is 6 cm by 6 cm?

Hmm...... now you are grouping your square units into two. Anytime you are grouping, it is a DIVISION problem.

First find the area of the wall. Then divide the answer by 2.

Area = Length x Width

         = 6 cm x 6 cm

         = 36 cm²

Because each tile is 2 cm²  you have to divide by 2.

Number of square tiles = 36 cm²÷ 2 cm²

                                      = 18 tiles

Notice the answer does not have a unit. It is just the number of tiles. 

Find the area and perimeter.

To find the perimeter, you must find the length of the unknown side first (15 cm - 7 cm = 8 cm).

Then you add the sides.

Perimeter = Sum of all the sides

                = 15 cm + 3 cm + 8 cm + 8 cm + 7 cm + 11 cm

                = 52 cm

To find the area, you need to divide the shape into two rectangles, find the area of both rectangles then add them together.

There are two ways you can divide this shape into rectangles. Both ways will give you the correct answer.

 Area 1 = Length x Width                                                Area 1 = Length x Width

                = 3 cm x 8 cm                                                              = 15 cm x 3 cm

                = 24  cm²                                                                     = 45 cm²

Area 2 = Length x Width                                                Area 2 = Length x Width

           = 11 cm x 7 cm                                                                = 8 cm x 7 cm

           = 77 cm²                                                                          = 56 cm²

Total Area = Area 1 + Area 2                                         Total Area = Area 1 + Area 2

                  = 24 cm² + 77 cm²                                                          = 45 cm² + 56 cm²

                  = 101 cm²                                                                        = 101 cm²

What is the area of the photo? What is the area of the border around the photograph?

To find the area of the photograph, subtract 10 cm from the length and width of the large rectangle.

Length of photo = 25 cm - 10 cm

                           = 15 cm

Width of photo = 16 cm - 10 cm

                         = 6 cm

Area of photo = Length x Width

                       = 15 cm x 6 cm

                       = 90 cm² 

To find the area of the border around the photo, you find the area of the large rectangle and subtract it from the area of the photo. You are essentially cutting out the photo to get the border.

Area of Large Rectangle = 25 cm x 16 cm

                                        = 400 cm² 

Area of Photo = 90 cm² 

Area of border = 400 cm²   - 90 cm² 

                         = 310 cm² 

Area test will be on THURSDAY.

Lent

On Wednesday we begin the holy liturgical season of LENT. We will be celebrating Ash Wednesday with a mass at school on that day.

The day before Ash Wednesday is of course Shrove Tuesday or Pancake Tuesday. In the morning each student is welcome to a pancake or two (no charge). Syrup will be provided. You are welcome to bring in any extra toppings for yourself. Please remember we have nut allergies in our classroom.

Tubing

We had absolutely the best day this winter for tubing. Everyone had a fantastic time! Special thank you to Carter's mom for joining us for the day.

Reminders:

• Mathletics assignments
• STUDY TIMES TABLE
• Interesting fact about the skin for Monday 
• Pancake Tuesday
• Ash Wednesday Mass at St. Nicholas @ 2:00 pm
• Area / Perimeter test on Thursday