Montana Math MT.CORE.ALG.LIN.3

MT.CORE.ALG.LIN.3 is a cluster heading. These are the individual standards under it.

• MT.CORE.ALG.LIN.3.a

  Identifying the rate of change and initial value in each representation.

• MT.CORE.ALG.LIN.3.b

  Converting between representations, and

• MT.CORE.ALG.LIN.3.c

  Writing equations for a line perpendicular or parallel to a given line that passes through a given point.

01

What Students Need to Do

Students show one linear relationship as a story, table, graph, and equation. They find the rate of change and the value at zero in each form. They write equations for parallel and perpendicular lines through a given point, then check them with a graphing tool.

02

What Mastery Looks Like

A student can find the rate and starting value even when a table does not include zero. They can move between the four forms without changing what the numbers mean. Their parallel and perpendicular lines have the right slopes and pass through the given point.

03

Common Misconceptions

Students may call the first value in a table the starting value, even when the table begins at an input other than zero. They may give parallel lines the same intercept instead of the same slope. For perpendicular lines, they may change only the slope's sign instead of taking its negative reciprocal.

04

How to Assess It

Exit ticket: A table shows (0, 6), (2, 10), and (4, 14) for posters ordered and total cost at a local community event. Write a cost story and equation, graph the points, label the rate and starting cost, then write parallel and perpendicular line equations through (2, 7).

1. 01

   Give pairs graph paper, string, and cards marked (0, 1), (1, 3), and (2, 5); have them build the line and write its equation.

2. 02

   Ask students to explain how a $5 starting charge appears in a table, graph, equation, and spoken description.

3. 03

   Give teams y = 2x + 1 and (3, 4); have them write parallel and perpendicular equations, then check both with a graphing tool.

4. 04

   Use a hypothetical printing quote for a Salish Kootenai College event, $15 setup plus $0.20 per flyer; graph costs for 0, 50, and 100 flyers.

• MT.5.G.2

  Represent problems including problems in context by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in t...

• MT.CORE.ALG.FUN.3

  Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically by: Understa...

• MT.CORE.ALG.QUAD.2

  Represent quadratic functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cul...

• MT.CORE.ALG.EXP.4

  Represent exponential functions using tables, graphs, equations, and verbal situations; using technology strategically. This standard should incorporate cultura...