Grade 06 Mathematics - EC: M06.C-G.1.1.4

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

Instructional activities designed to be integrated into planned lessons
Questions/activities that grow in complexity
Opportunities for differentiation for each student’s level of performance

Grade Levels

6th Grade

Course, Subject

Mathematics

Related Academic Standards / Eligible Content

M06.C-G.1.1.4 M06.C-G.1.1.4

Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided.

Activities

Given the points on the graph, calculate its area.

Given the points on the graph, find the area of the triangle.

Given the points A(3, 5), B(-2, 5), C(-5, 0) and D(0, 0), calculate the area of the parallelogram. Explain.

Given the points A(7, 6), B(-6, 5), C(-6, -1), and D(7, -7). Identify the shape drawn and calculate the area. Show all your work, including the graph.

Look at the points of the rectangle on the graph. If point C changes to (-4, -6) what other point(s) would have to change, and to what, so that it will stay a rectangle? What are the new side lengths of the rectangle and what is the area of the new rectangle? Explain/show your work.

What is the area of the triangle on the grid? Predict what would happen to the area if you change point A to (-2, 4). Verify your prediction and explain your answer.

Answer Key/Rubric

25 units²

15 units²

25 units²

Acceptable responses may include, but are not limited to:

Plot the points on the graph.

Identify the height of the parallelogram by dropping a line perpendicular to the x-axis; height is 5 units.

Calculate the area:

Trapezoid with an area of 123.5 units²

Acceptable work may include, but is not limited to:

Graph points:

Identify shape as a trapezoid.

Identify height of the trapezoid by drawing a line perpendicular to the y-axis from one base to the other; height is 13 units.

Calculate the area:

Student work might include, but is not limited to:

The other points that would have to change are B and D

Point B would have to move to (-4, 3)

Point D would have to move to (3, -6)

The new length and width are 9 by 7.

Area of rectangle = 63 units²

Student work might include, but is not limited to:

Area of triangle = 17.5 units²

Students need to make a prediction and test it.

If you move point A to (-2, 4) the area of the new triangle would not be changed.

The triangle that is made with the new point A will have the same length base and same length height; therefore the area would remain the same.