Montana Math MT.CORE.ALG.QUAD.1
The Standard
Understand that quadratic functions do not have a constant rate of change but have a constant second difference over equal intervals and identify the constant second difference in tables.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Read a table with equal steps in x and find how much y changes each step. Compare those changes to find the second differences and decide whether the table shows a quadratic pattern.
What Mastery Looks Like
- Given evenly spaced x-values, students correctly list the first and second differences. They identify the repeated second difference and explain that the first differences show a changing rate of change.
Common Misconceptions
- Students may call a pattern linear because its outputs go up at every step. Some compare outputs two rows apart instead of subtracting adjacent first differences. Others look for constant second differences when the x-steps are unequal.
How to Assess It
- Exit ticket: For x = 0, 1, 2, 3, 4 and y = 4, 1, 0, 1, 4, list the first and second differences. Is the rate of change constant?
Lesson moves
Ways to Teach It
Build 1-by-1 through 4-by-4 squares with tiles; record tile totals, first differences, and second differences in a table.
Have students explain why y-values 0, 1, 4, 9, 16 have changing first differences but constant second differences.
Deal table cards for x^2, 2x+1, and 2^x at x = 0, 1, 2, 3, 4; partners sort them by their differences.
Sketch square gardens with sides of 1, 2, 3, and 4 meters; list their areas and find both rows of differences.
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Printable MT.CORE.ALG.QUAD.1 Worksheet
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