Sunday, December 13, 2009

Getting a Square Idea.

Three heads are better than one.  I have a brilliant teacher candidate this term.  She really knows her stuff.  I also have a great mentor at this school that always tells me the analogy of slow learning (drawing a turtle on the board) to make me remember the need to go slow when necessary.

Together all three of us yesterday came up with a great activity to get kids to understand the idea of squares.  More specifically.... Can you make a square out of 2 squares tiles, 3 squares tiles etc.  What we came up with was a stroke of genius.

Supplies you will need for this activity are a sheep of cm grid paper and a piece of coloured paper.  On the grid paper you need to cut out 4 10 by 10 squares.  My paper only goes 18 across.  You will get one 10 by to and one 8 by 10 rectangle.  Take a 2 by 10 rectangle to complete the 8 by 10 into a 10 by 10 square.

When we are all done the students have a great representation of how to create the squares of 1, 2, 3, and 4.
Step 1
Glue one 10 by 10 square onto the large foldable sheet of paper.  Get the students to understand the difference between the 100 squares and that this represents 1 whole square.
Once this has been done complete the chart at the top of your paper.  Show the side measure of the square and how 1 x 1 is 1.

You now have to use your second square.  Get the students to figure out the largest square you can make with the second square that has 100 smaller squares in it.  Most students will start to see the pattern of 1.1 x 1.1 is 1.21(11 x 11 =121) and so on.  When you are done this part of the foldable your page should look like this.

The largest square is using 196 smaller squares or 14 x 14.  This is really 1.4 x 1.4 which is 1.96.  Complete the chart like the previous one and have all squares up to 1.4 on the chart. 

Continue with the third square.  If students have not coloured them yet it might be a good idea.  Colour enhances the foldable showing the different squares

You should have completed the blue part of the foldable now.  This means that you have made the largest square possible with 3 squares.  1.7 x 1.7 (17 x 17).

Complete the chart to show that you now have 3 new squares possible.

You now are ready for the last square.  This is the 4th square.  You need to get the students to understand that they now have a perfect square.  2 x 2 = 4. To achieve this they will use the remaining square and all the leftover pieces from the last 2 squares.  Adding 111 small squares will give you a square with the area of 400 little squares or 4 larger squares. 

 Finish the chart to complete it up to 2 x 2 = 4.

This is a great conceptual idea for showing Squares and Square Roots.

Hope you enjoyed the lesson.  Now on to the next post.

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