Here’s a question from Marion Small www.onetwoinfinity.ca on algebraic reasoning :
Notice this pattern:
4 x 5 = 4 x 4 + 4
5 x 6 = 5 x 5 + 5
6 x 7 = 6 x 6 + 6
How can you say the pattern in words? using visuals? using algebra?
Often we try to solve the problem by finding the pattern or inputting the formula. How often do we take the time to really understand what these equations and expressions mean? How many students that are in grade 10, 11 and 12 that don’t realize the difference between an expression and an equation? Sometimes by showing a different way to the same problem can help clarify understanding.
Scroll down for two examples on how you can use algebra and manipulatives on how you could represent your answer.
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Algebraically, you represent n for any number… and n(n + 1) = n^2 + n, which you can see after expanding the left side of the equation. This is how we usually expect to find the answer to this question.
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What happens if we use manipulatives to show the same equation ?
Mathworkz 