Students will use algebra tiles and the student handout (found in the attachments of the file), guided by the teacher using this file, to create the formula for Completing the Square.
Below I have included three sample pages from the file.
There is an intro story - I had created worksheets for today's lesson but accidentally spilled ink all over it. Since I didn't have time to remake the worksheets, you need to help me figure out the missing numbers. I set up all the expressions so that you could build a perfect square out of each expression. What number is missing? We would build the first factored form together once they have built the square. After than they should have no problem writing it for the perfect squares.
A discussion would then need to occur regarding patterns. Students are then asked to...
Since they can't build it using algebra tiles (I remind them they are not allowed to deface school property by breaking any of the pieces), they should be aware they have to do it just with paper and pencil although they might try to draw it.
Then we start to deal with expressions that have too many and too few pieces. The story is that a little munchkin snuck into my classroom and either added to or took away unit pieces out of the algebra tile bags that I had created again for class. They originally started with the exact number needed to make perfect squares. Help me figure out how many extra/too few pieces there are. Once they have built it and determined the number of extra pieces (write that in the circle), we would discuss that it is a perfect square - which would be (x + 3)^2 but has 2 extra pieces so we represent it as (x + 3)^2 + 2.
We repeat the discussion again for "missing" pieces but when we are missing pieces we have a perfect square minus whatever we're missing.
Aligns to Alberta Curriculum: Math 20-1
This lesson addresses the process for "Completing the Square" in order to address the following outcome:
*Analyze quadratic functions of the form y=ax^2+bx+c to identify characteristics of the corresponding graph, including vertex, domain and range, direction of opening, axis of symmetry, x and y intercepts and to solve problems.
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