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Partitioning Rectangles

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Basics on the topic Partitioning Rectangles

What is Area in Maths?

If you want to know the size of a shape in maths, you want to know the size of the surface area of that shape. If that shape happens to be a rectangle, you can find the area of that rectangle by dividing the shape using horizontal and vertical lines.

Area is the size of a surface and we can divide up one larger surface area into lots of smaller ones by partitioning. A rectangle is a flat, four-sided shape with straight sides and four vertices. When we partition a rectangle with same-sized squares, we are dividing it into equal parts. This helps us count the space or the area inside. There are many ways to partition, or divide, a rectangle evenly.

How to Partition Rectangles

To partition rectangles, one way is to use horizontal and vertical lines, or rows and columns of equal size to make the parts the same size. Rows go across, from side to side.

25641_SEO-L14.svg Columns go up and down.

25641_SEO-L15.svg To evenly partition a rectangle, first, make equal rows across. To help us, we can connect the markers.

25641_SEO-L18.svg Then, make equal columns up and down. Again, we can use the markers shown on the rectangle and draw lines connecting them.

25641_SEO-L20.svg Finally, we count all the squares that were made. This rectangle has six equal squares.

25641_SEO-L22.svg

Partitioning Rectangles – Summary of Steps

Remember: partitioning rectangles means to divide a rectangular shape into equal parts. This is applicable in many ways. For this text, we used a rectangular cake as an example. In order to make sure everybody gets equal pieces, you need to follow these steps to partition your cake:

Step # What to do
1 Make equal rows across.
2 Make equal columns up and down.
3 Count all the squares that were made.
  • First, make equal rows across.

  • Then, make equal columns up and down.

  • Finally, count all the squares that were made.

Have you practiced yet? After watching the video, you can also find interactive exercises, worksheets and further activities on how to partition rectangles.

Transcript Partitioning Rectangles

Nia and Nico are getting ready for Nia’s family reunion. They have all the decorations and food ready! All the food that is except for the tray bake. When they picked it up from the bakery, it looked delicious, but it is in one, large piece. How will they feed all of Nia's family members? Let's help Nia and Nico by learning about partitioning rectangles! You might have learned that a rectangle is a two dimensional shape with four straight sides and four right angles. When we partition a rectangle into equal-sized squares, we are dividing it into equal parts. This helps us count the space inside. There are many ways to partition, or divide, a rectangle evenly. One way is to use rows and columns of equal size to make the parts the same size. Rows go across, from side to side and columns go up and down. To evenly partition a rectangle, first, make equal rows across. To help us, we can connect the markers. Then, make equal columns up and down. Again, we can use the markers and draw lines connecting them. Finally, count all the squares that were made. This rectangle has six equal squares. Now, let's try partitioning Nia's cake! First, we make three equal rows across. Then, we make four equal columns up and down. Finally, we count all the squares that were made. This rectangular cake has twelve equal squares which means there are twelve equal slices of cake to share! This is perfect because twelve family members just arrived. Uh-oh! More relatives are here! We'll need to partition the entire rectangle again to make sure everyone gets a piece. What is our first step? Our first step is to make equal rows across. This time we'll make four. What is the next step? The next step is to make equal columns up and down. This time we'll make five. Now we count all the squares to see how many squares fit inside the rectangle. How many squares are there? There are twenty squares which means we have twenty equal slices and everyone can have cake! As Nia serves her guests, let's remember! Today we learned about partitioning rectangles into equal-sized squares. We use rows and columns of the same size to help partition into equal-sized squares. Rows go across, from side to side. Columns go up and down. To partition a rectangle into equal-sized squares, first, make equal rows across. Then, make equal columns up and down. Finally, count all the squares that were made. "Nico, would you like a slice?" "Yes!" "Oh thanks?"

Partitioning Rectangles exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Partitioning Rectangles.
  • How do we cut the cake?

    Hints

    This is how the cake is cut when rows are made.

    This is how the cake is cut when columns are made.

    Equal means the same. We want the pieces to all be the same, not different.

    Solution
    • First, they make slices across so that the cake is divided into rows.
    • Then, they make markers at the top and bottom and cut the cake into columns.
    • Now they have pieces that are all equal in size.
  • How many pieces?

    Hints

    Count how many pieces are inside the cake. The fewest means the smallest amount, so this goes first in the order.

    The cake with the most pieces has the biggest number. This goes last in the order.

    Solution

    The cakes in order from those with fewest pieces to most pieces is:

    • Pink cake - this has 10 pieces
    • Yellow cake - this has 12 pieces
    • White cake - this has 18 pieces
    • Purple cake - this has 20 pieces

  • Are they equal sized squares?

    Hints

    Remember that each piece needs to be exactly the same size and a square.

    A square means that the length of each side is exactly the same. This is a square.

    Solution

    This cake has been cut into 15 equal sized square pieces.

  • How can we make eight equal pieces?

    Hints

    The cake should first be cut across into two rows, using a horizontal line.

    The cake should then be cut into columns using vertical lines.

    The cake should have 8 equal sized pieces when finished.

    Solution

    The cake has been cut into 8 equal sized squares using the lines shown here.

  • Equal sized squares.

    Hints

    Equal sized squares means that each piece of cake needs to be the same size.

    Solution

    This cake has been divided into square pieces that are all equal in size.

  • How many pieces of cake are made?

    Hints

    This has been cut into three rows that go across.

    This rectangle has 2 rows and 3 columns. There are 6 pieces in total.

    Try drawing each option and counting how many pieces have been made.

    Solution

    The image shows the answer where 12 pieces are made:

    • 3 rows & 4 columns (3 x 4 = 12)
    • 2 rows & 6 columns (2 x 6 = 12)

    8 pieces:

    • 4 rows & 2 columns (4 x 2 = 8)

    18 pieces

    • 3 rows & 6 columns (3 x 6 =18)
    • 2 rows & 9 columns (2 x 9 = 18)