Montana Math MT.CORE.ALG.MOD.1

MT.CORE.ALG.MOD.1 is a cluster heading. These are the individual standards under it.

• MT.CORE.ALG.MOD.1.a

  Determining if a set of data is best modeled by a linear function, quadratic function, exponential function, or none, and explaining why, and

• MT.CORE.ALG.MOD.1.b

  Understanding that there are contexts where solutions may not lie on the curve.

01

What Students Need to Do

Students use tables and graphs to choose and write a linear, quadratic, or exponential model, or explain why none fits. They use changes in the data to defend their choice and explain why a real measurement might miss the curve.

02

What Mastery Looks Like

Given counts from equally spaced years, students compare first differences, second differences, and ratios, then write a matching equation. They can explain why a count off the curve does not automatically make the model wrong.

03

Common Misconceptions

Students may call any increasing data linear or treat one large jump as proof of exponential growth. They may force an equation onto irregular data or think every observed point must sit exactly on the curve.

04

How to Assess It

Exit ticket: For years 0–3, counts are 8, 16, 32, 64. Name a model, write an equation, and explain whether a year-4 count of 125 would make the model useless.

1. 01

   Have students plot 10,15,20,25; 3,6,11,18; 8,16,32,64; and 5,9,7,14 on graph paper, then sort the patterns.

2. 02

   Ask students to write: If a model predicts 50 bison but a count finds 46, what might explain the difference?

3. 03

   Run a card sort with 4,7,10,13; 2,5,10,17; 3,6,12,24; and 5,8,6,11; students name each model or none.

4. 04

   Use made-up counts, 40, 50, 63, 79, for a Blackfeet bison restoration scenario; discuss why actual counts might miss projections.

• MT.CORE.ALG.MOD.2

  Interpret the coefficients in a linear, quadratic, and exponential model in context. This standard should incorporate cultural context relating to Montana Indig...

• MT.PLUS.ALG.MOD.1

  Model situations in context with polynomial, exponential, logarithmic, and trigonometric functions. This standard should incorporate cultural context relating t...

• MT.PLUS.ALG.MOD.2

  Interpret the coefficients in a polynomial, exponential, logarithmic, and trigonometric model in context. This standard should incorporate cultural context rela...