Montana Math MT.8.G.3
The Standard
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students plot vertices and find their new coordinates after translations, rotations, reflections, and dilations. They explain how the coordinates change and whether the figure changes size.
What Mastery Looks Like
- A student can give the new coordinates for every vertex, not just one. They can name a transformation from the original and new coordinates and explain that a dilation changes size.
Common Misconceptions
- Students may change only one vertex, reverse the wrong coordinate when reflecting, or turn clockwise instead of counterclockwise. For a dilation by 2 about the origin, they may add 2 to each coordinate instead of multiplying by 2.
How to Assess It
- Exit ticket: Plot A(1,1), B(3,1), C(1,2). Give the new vertices and coordinate rule for a shift right 2, a reflection across the y-axis, a 90° counterclockwise turn about the origin, and a dilation by 2 about the origin.
Lesson moves
Ways to Teach It
Trace a triangle onto clear plastic over grid paper; slide, flip, and turn it, marking the new coordinates after each move.
Write: '(2,3) becomes (-2,3), and (4,5) becomes (-4,5). Which transformation fits, and how do you know?'
Give pairs coordinate-rule cards and triangle cards; have them match each rule to an image, then draw a dilation by 2.
Print a public map of Salish Kootenai College, a tribal college in Pablo; grid three building locations and translate their triangle two units east.
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