Montana Math MT.PLUS.ALG.POLY.2

MT.PLUS.ALG.POLY.2 is a cluster heading. These are the individual standards under it.

• MT.PLUS.ALG.POLY.2.a

  Choosing the form strategically based on given information and intended use when writing an expression,

• MT.PLUS.ALG.POLY.2.b

  Converting between factored and standard form symbolically and using representations (e.g., area model), and

• MT.PLUS.ALG.POLY.2.c

  Interpreting the relationship between the factored form of the expression and the zeros of the function.

01

What Students Need to Do

Students move between factored and expanded forms by multiplying or using an area model. They choose the form that makes a task easier and find zeros from factors.

02

What Mastery Looks Like

Given (x-3)(x+2), a student writes x²-x-6 and finds the zeros 3 and -2. They use factored form to find zeros and standard form to read the y-intercept.

03

Common Misconceptions

Students may name -3 and 2 as the zeros because they do not set each factor equal to zero. They may miss the middle terms when multiplying or mistake the constant term for an x-intercept.

04

How to Assess It

Exit ticket: Given f(x)=(x-2)(x+3), expand it, find both zeros, and say which form makes finding the y-intercept quicker.

1. 01

   Give pairs algebra tiles to build a rectangle with sides x+2 and x+3, then record its area in both forms.

2. 02

   Write (x-4)(x+1) and x²-3x-4 on the board; ask which form finds zeros faster and which shows the y-intercept.

3. 03

   Put factored and expanded polynomial cards on desks; have pairs match equivalent forms and write the zeros on each matched pair.

4. 04

   Give h(t)=-5t(t-4) for a tossed ball; ask when it hits the ground and what each zero means.

• MT.CORE.ALG.QUAD.3

  Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writi...

• MT.CORE.ALG.QUAD.3.b

  Converting between factored, standard, and vertex forms symbolically and using representations,