Montana Math MT.PLUS.ALG.POLY.2.b
The Standard
- MT.PLUS.ALG.POLY.2
- Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by: Choosing the form strategically based on given information and intended use when writing an expression, Converting between factored and standard form symbolically and using representations (e.g., area model), and Interpreting the relationship between the factored form of the expression and the zeros of the function.
Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by: Converting between factored and standard form symbolically and using representations (e.g., area model), and
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students multiply factors and combine like terms to write a polynomial in standard form. They factor a polynomial to go the other way. They use an area grid to show why the forms match.
What Mastery Looks Like
- Given (2x+3)(x-4), a student fills all four grid cells and gets 2x²-5x-12. They can factor the result back, find the zeros from the factors, and find the constant term in standard form.
Common Misconceptions
- Students may multiply only the first and last terms, leaving out the two middle products. They may combine unlike terms, such as 2x² and -5x, or lose a negative sign when factoring.
How to Assess It
- Exit ticket: Use a four-cell grid to expand (2x+3)(x-4), then factor your answer back. Circle the constant term and write the two zeros.
Lesson moves
Ways to Teach It
Give pairs one x² tile, five x tiles, and six unit tiles; have them build a rectangle and record its side lengths.
Ask students to explain in writing why (x+3)(x+2) equals x²+5x+6, not x²+6, using a four-cell grid.
Set out cards showing (x+2)(x+3), (x+1)(x+4), x²+5x+6, and x²+5x+4; pairs match them and check by expanding.
Draw a garden with sides x+2 and x+3 meters; have students split it into four sections and write two formulas for its area.
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