Perfect Squares and Patterns
If you have been following my last blog, you may find this new post helpful for you in solving questions of Pythagorean Theorem.
Firstly, I am going to talk about perfect squares.
The following are some examples and non-examples of perfect squares from the online resource:
http://www.mathwarehouse.com/arithmetic/numbers/what-is-a-perfect-square.php.
Examples of perfect squares
- 9
- 9 is a perfect square because it can be expressed as 3 * 3 (the product of two equal integers)
- 16
- 16 is a perfect square because it can be expressed as 4 * 4 (the product of two equal integers)
- 25
- 25 is a perfect square because it can be expressed as 5 * 5 (the product of two equal integers)
Non examples of perfect squares
- 8
- 8 is a not perfect square because you cannot express it as the product of two equal integers
- 5
- 5 is a not perfect square because it cannot be expressed as the product of two equal integers
- 7
- 7 is a not perfect square because you cannot express it as the product of two equal
- integers
Hopefully, these above examples has helped you understand more about perfect squares.
Secondly, I would like to introduce some easier and faster ways for students to calculate their questions as I did in my last post.
Usually, students would just know the square of one digit number which is from 12 up to 92. However, it would be even better if students can memorize up to 192. They could either memorize them just by memorizing or they could memorize them using a pattern.
1) Perfect Squares - Pattern 1
#’s Squares Difference between squares Difference increases by
112 = 121 [+23] +2
122 = 144 [+25] +2
132 = 169 [+27] +2
142 = 196 [+29] +2
152 = 225 [+31] +2
162 = 256 [+33] +2
172 = 289 [+35] +2
182 = 324 [+37] +2
192 = 361
Pattern: the difference between 112 and 122 is +23, and then the difference increases by +2 as the number increases by 1.
2) Perfect Squares - Pattern 2
#’s Squares Difference between squares Difference increases by
152 = 225 +400 +200
252 = 625 +600 +200
352 = 1225 +800 +200
452 = 2025 +1000 +200
552 = 3025 +1200 +200
652 = 4225 +1400 +200
752 = 5625 +1600 +200
852 = 7225 +1800 +200
952 = 9025
Pattern: the difference between 152 and 252 is +400, and then the difference increases by +200 as the number increases by 10.
By knowing and memorizing these patterns, students can calculate squares faster.
Hope this post helps you in calculating squares as well.
I like this strategy, I have struggled getting this point across to students in the past. If students are able to recognize patterns then it will make it easier for them to understand the topic so I will try this out next time. Do you have any other strategies that involve patterns to make other topics easier for students to understand?
ReplyDeleteThanks for sharing! I really like this strategy, and it's pretty useful for the intermediate grades. I think using visuals, and showing students patterns helps them grasp understanding of this concept. Knowing this information transcends into other areas of Math, especially in measurement and geometry when students are working with squares as shapes, or when finding surface area or volume of cubes. Using geoboards and elastics is great for small numbers, but this is excellent for the larger numbers.
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