Montana Math MT.CORE.ALG.FUN.7
The Standard
Understand that expressions can be rewritten in equivalent forms to make different characteristics or features visible.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite expressions without changing their value. They choose a form that makes zeros, a starting value, or a maximum easier to see.
What Mastery Looks Like
- A student can rewrite x²-6x+8 as (x-2)(x-4) and find its zeros at 2 and 4. They can rewrite it as (x-3)²-1 and find its minimum value of -1.
Common Misconceptions
- Students may think expressions that look different must give different values. They may factor x²-6x+8 as (x+2)(x+4), or read (x-3)²-1 as having its minimum at x=-3.
How to Assess It
- Exit ticket: Rewrite x²-6x+8 in factored form, name both zeros, and multiply your factors to check.
Lesson moves
Ways to Teach It
Give pairs algebra tiles for x²+5x+6; have them build a rectangle and write its side lengths as factors.
Show three forms of x²-6x+8; ask which form reveals the zeros and which reveals the minimum.
Give pairs cards with expanded and factored quadratics; have them match equivalent expressions and name the zeros.
For ticket sales, show R(p)=-2p²+40p=-2(p-10)²+200; ask which ticket price gives the highest revenue.
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Printable MT.CORE.ALG.FUN.7 Worksheet
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Related Standards
- MT.7.EE.2
Understand that rewriting an expression in different forms in a problem in context can show how the quantities in it are related.
- 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.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 strat...
- MT.6.EE.3
Apply the properties of operations including the distributive property, to generate equivalent expressions and determine when two expressions are equivalent.
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