Montana Math MT.CORE.ALG.FUN.8

MathGrades 9–12Understand Functions and Expressions

The Standard

Rearrange literal equations to highlight quantities of interest.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students rewrite an equation with several letters so a requested letter stands alone. They use inverse operations on both sides and keep parentheses where needed.
What Mastery Looks Like: Given P=2l+2w, a student can write w=(P-2l)/2. They can check the result by putting in numbers for P and l.
Common Misconceptions: Some students treat letters as labels rather than quantities they can solve for. Others subtract 2l from only one side or forget to divide the whole expression P-2l by 2.
How to Assess It: Exit ticket: Solve P=2l+2w for w. Use P=14 and l=3 to check that your expression gives w=4.

Lesson moves

Give pairs paper rectangles and string; have them cut off both length sections, split the remaining string, and write w=(P-2l)/2.
Ask: Why must you subtract 2l before dividing by 2 in P=2l+2w? Have students explain what happens on both sides.
Write F=ma, A=lw, and P=2l+2w on cards; pairs race to isolate a named variable and check by substitution.
Give students a phone bill with a $15 base charge and $4 per gigabyte; they rearrange C=15+4g to find g when C=35.

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