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UNIT 3 - FACTORING

REASONING ROUTINES

DESIGNED TO GET YOUR STUDENTS ENGAGED FROM THE MINUTE THEY WALK INTO YOUR CLASS

Created by: THE HCPS MATHEMATICS CURRICULUM DEVELOPMENT TEAM

http://blogs.henrico.k12.va.us/math

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Hand Signals

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Number Talks - Number Strings

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Alike and Different

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Number Talks

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Fill in the Blank

so that

is a factorable quadratic expression.

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Which One Doesn’t Belong?

http://wodb.ca/

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Mystery Function

I have two binomial factors

One of my factors is also a factor of x² - 9

My other factor is also a factor of x² + 5x - 24

Both factors are the sum of two terms

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Quick Image

Source: https://myscres.com

Topic: Factoring

Routine: The teacher will click to display the image. The image will only be shown for 3 seconds. Once the image disappears, students are asked to tell the quantity or draw what they can remember seeing. When the teacher sees that most students have drawn all they can, he/she will click to display the image for three more seconds. Once the image disappears again students will continue drawing. At this time, students can compare drawings and either discuss in pairs or as a whole class how they developed their drawings. The Quick Images routine develops mental imagery, builds vocabulary, improves spatial memory, and teaches students to analyze mental images.

Guiding questions: “What did you see?” “How did you draw it?” “What are figures that you see?”

Sample Responses/Teacher Talking Points:

Students may see (x-2)(x-3) or x²-5x+6 or both

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Alike and Different

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Which One Doesn’t Belong?

http://wodb.ca/

Topic: Factoring Quadratics

Routine (Which One Doesn’t Belong): Students will determine which figure(s)/statement(s) they think do not belong and provide a justification. There is no correct solution, but rather students should be encouraged to use their knowledge of symmetry to figure out a reason why each shape may not belong. This routine will strengthen students skills in comparative thinking, connecting and communicating mathematical ideas, and critical thinking.

Sample Responses/Teacher Talking Points:

Top Left is (x+4)(x+2) = x²+ 6x + 8 and is different because it is the only non-perfect square trinomial.

Top Right is x(x+6) = x² + 6x and is different because it is the only quadratic without a constant term.

Bottom Left is (x+3)(x+3) +1 = x² +6x+9+1 = x² + 6x + 10 and is different because it is the only one that is a factored trinomial plus a constant.

Bottom Right is (x+3)(x+3) = x² +6x + 9 and is different because it is the only perfect square trinomial.