Montana Math MT.7.EE.4
The Standard
Use variables to represent quantities and construct simple equations and inequalities to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: Solving, accurately and efficiently, problems in context leading to equations of the form p · x + q = r and p(x + q) = r, where p, q, and r are specific rational numbers, comparing an algebraic solution to an arithmetic solution, and identifying the sequence of the operations used in each approach, and Solving problems in context leading to inequalities of the form p · x + q > r or p · x + q < r, where p, q, and r are specific rational numbers graphing the solution set of the inequality, and interpreting the solution in context.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students choose a variable and write an equation or inequality from a situation involving decimals or fractions. They solve equations with and without parentheses, then compare arithmetic and algebraic steps. They graph inequality solutions and explain which values fit the situation.
What Mastery Looks Like
- For three kits with x pencils and two erasers each, totaling 30 items, a student writes 3(x+2)=30 and finds x=8. They compare dividing 30 by 3, then subtracting 2, with the matching algebra steps. They graph x<6 with an open circle at 6 and identify 0 through 5 as possible whole-number notebook counts.
Common Misconceptions
- Students may divide before subtracting in 2.5x+3=18 or rewrite 3(x+2) as 3x+2. They may include 6 for x<6 or count fractional notebooks as valid.
How to Assess It
- Exit ticket: Three kits each contain x notebooks and two pens, with 30 items in all. Write an equation, solve it using arithmetic and algebra, and list the operations in each solution.
Lesson moves
Ways to Teach It
Give pairs play money and a $3 delivery card; build an $18 order with $2.50 notebooks, then write and solve the equation.
Ask: For 3(x+2)=30, how does dividing 30 by 3 and subtracting 2 compare with solving using algebra?
In pairs, solve 2.5x+3=18 and 3(x+2)=30, then swap papers and check each answer by substitution.
Plan a hypothetical book drive for Salish Kootenai College: at $2.50 per notebook plus $3 delivery, graph whole-number counts costing under $18.
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