Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Middle School
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [7.GM]

OREGON MATH STANDARDS (2021): [7.GM]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: 7.GM.A.1

ODE and Oregon Math Project Logo

Cluster: 7.GM.A - Draw construct, and describe geometrical figures and describe the relationships between them.

STANDARD: 7.GM.A.1

 Standards Statement (2021):

Solve problems involving scale drawings of geometric figures.  Reproduce a scale drawing at a different scale and compute actual lengths and areas from a scale drawing.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.GM.A.1

HS.GM.C.10

7.RP.A.2

7.G.A.1

7.GM.A Crosswalk

 Standards Guidance:

Clarifications 

  • Students should understand scale factor as a rate comparison between similar figures and scale drawings.
  • Students should build upon their understanding of proportional relationships.

Teaching Strategies

  • Students should be given opportunities to use technology and tools to reproduce scale drawings.
  • Students should have opportunities to use proportional reasoning to compute unknown lengths by setting up proportions in tables or equations, or they can reason about how the lengths compare multiplicatively.
  • Students should be able to determine the dimensions of figures when given a scale and identify the impact of a scale on actual length (one-dimension) and area (two–dimensions). Students should be able to identify the scale factor given two figures.
  • Opportunity to connect to proportional reasoning to explain why the slope, m, is the same between any two distinct points (7.NRP.A.2).

Progressions

  • Three-dimensional objects can be represented without distortion by scale models such as doll houses, model trains, architectural models, and souvenirs. Students compute or estimate lengths in the real object by computing or measuring lengths in the drawing and multiplying by the scale factor.  Angles in a scale drawing are the same as the corresponding angles in the real object. Lengths are not the same, but differ by a constant scale factor. (Please reference pages 6-7 in the Progression document).

Examples

2021 Oregon Math Guidance: 7.GM.A.2

 ODE and Oregon Math Project Logo

Cluster: 7.GM.A - Draw construct, and describe geometrical figures and describe the relationships between them.

STANDARD: 7.GM.A.2

 Standards Statement (2021):

Draw triangles from three measures of angles or sides.  Understand the possible side lengths and angle measures that determine a unique triangle, more than one triangle, or no triangle.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

 N/A

8.GM.A.1, HS.GM.B.5, HS.GM.B.7

 N/A

7.G.A.2

7.GM.A Crosswalk

 Standards Guidance:

Clarifications

  • Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine unique triangles, more than one triangle, or no triangle.

Boundaries

  • Know when 3 side lengths will form a triangle.
  • Know that the angle measures in a triangle have a sum of 180 degrees.

Teaching Strategies

  • Students should be provided opportunities to draw triangles with ruler and protractor, and with technology.

Progressions

  • By sketching geometric shapes that obey given conditions, students lay the foundation for the concepts of congruence and similarity in Grade 8, and for the practice of geometric deduction that will grow in importance throughout the rest of their school careers.
  • For example, given three side lengths, perhaps in the form of physical or virtual rods, students try to construct a triangle. Two important possibilities arise: there is no triangle or there is exactly one triangle. By examining many situations where there is no triangle, students can identify the culprit: one side that is longer than the other two put together. From this they can reason that in a triangle the sum of any two sides must be greater than the third. (Please reference page 6 in the Progression document).

Examples

  • A triangle with side lengths 3 cm, 4 cm, and 5 cm exists. Use a compass and ruler to draw a triangle with these side lengths. (Modified from Engage NY M6L9)

2021 Oregon Math Guidance: 7.GM.B.3

 ODE and Oregon Math Project Logo

Cluster: 7.GM.B - Solve mathematical problems in authentic contexts involving angle measure, area, surface area, and volume.

STANDARD: 7.GM.B.3

 Standards Statement (2021):

Understand the relationship between area and circumference of circles.  Choose and use the appropriate formula to solve problems with radius, diameter, circumference and area of circles.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.GM.A.1

8.GM.C.9, HS.GM.C.8, HS.GM.C.10

 N/A

7.G.B.4

7.GM.B Crosswalk

 Standards Guidance:

Clarifications

  • Know that a circle is a two-dimensional shape created by connecting all of the points equidistant from a fixed point called the center of the circle.
  • Informally derive and know the formulas for the area and circumference of a circle and use them to solve problems.

Terminology

  • Students should know how to write responses in terms of pi.
  • Special Note:  The terms pi, radius, diameter, and circumference are new academic vocabulary for students.

Boundaries

  • Square roots are an 8th grade expectation.

Teaching Strategies

  • Students should use proportional reasoning to explain the relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is π in order to derive the formulas for the circumference and area of a circle.

Progressions

  • Students have been long familiar with circles and now they undertake a calculation of their perimeters and areas. This is a step forward from their previous methods of calculating area by decomposing figures into rectangles and triangles. Students must now grapple with the meaning of the area of a figure with curved boundary. The area can be estimated by superimposing a square grid and counting squares inside the figure, with the estimate becoming more and more accurate as the grid is made finer and finer. (Please reference page 8 in the Progression document).

Examples

2021 Oregon Math Guidance: 7.GM.B.4

 ODE and Oregon Math Project Logo

Cluster: 7.GM.B - Solve mathematical problems in authentic contexts involving angle measure, area, surface area, and volume.

STANDARD: 7.GM.B.4

 Standards Statement (2021):

Apply facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to determine an unknown angle in a figure.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

4.GM.C.7, 4.GM.C.9

8.GM.A.1, HS.GM.B.6

 N/A

7.G.B.5

7.GM.B Crosswalk

 Standards Guidance:

Clarifications

  • In previous grades, students have studied angles by type according to size: acute, obtuse, and right, and their role as an attribute in polygons. Now angles are considered based upon the special relationships that exist among them: supplementary, complementary, vertical, and adjacent angles.

Terminology

  • Supplementary angles – two angles add up to 180 degrees
  • Complementary angles – two angles add up to 90 degrees
  • Vertical angles – angles opposite each other when two lines intersect
  • Adjacent angles – Two angles that have a common side and a common vertex (corner point), and do not overlap.

Boundaries

  • This includes writing and solving simple equations for an unknown angle in a figure.

Progressions

  • In Grade 7, students build on earlier experiences with angle measurement (see the Grade 4 section of the Geometric Measurement Progression) to solve problems that involve supplementary angles, complementary angles, vertical angles, and adjacent angles.
  • Vertical angles have the same number of degrees because they are both supplementary to the same angle. Keeping in mind that two geometric figures are “the same” in Grade 7 if one can be superimposed on the other, it follows that angles that are the same have the same number of degrees. Conversely, if two angles have the same measurement, then one can be superimposed on the other, so having the same number of degrees is a criterion for two angles to be the same.
  • An angle is called a right angle if, after extending the rays of the angle to lines, it is the case that all the angles at the vertex are the same. In particular, the measurement of a right angle is 90°. In this situation, the intersecting lines are said to be perpendicular.
  • Knowledge of angle measurements allows students to use algebra to determine missing information about particular geometric figures, using algebra in the service of geometry, rather than the other way around. (Please reference page 8 in the Progression document).

Examples

  • The ratio of the measurement of an angle to its complement is 1:2. Create and solve an equation to find the measurement of the angle and its complement. (From Engage NY M5L1)

2021 Oregon Math Guidance: 7.GM.B.5

 ODE and Oregon Math Project Logo

Cluster: 7.GM.B - Solve mathematical problems in authentic contexts involving angle measure, area, surface area, and volume.

STANDARD: 7.GM.B.5

 Standards Statement (2021):

Solve problems in authentic contexts involving two- and three-dimensional figures.  Given formulas, calculate area, volume and surface area.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.GM.A.1, 6.GM.A.2, 6.GM.A.4

8.GM.B.8, HS.GM.C.8, HS.GM.C.9, HS.GM.C.10

 N/A

7.G.B.6

7.GM.B Crosswalk

 Standards Guidance:

Clarifications

  • Students should understand the formulas for prisms as the general statement of the area of the base times the height.  Students may build upon this generalization for volumes of figures in 8th grade.
  • Students should relate the formulas for parallelograms, triangles and trapezoids to the formula for a rectangle.

Terminology

  • Cylinder – any three-dimensional figure with two congruent, opposite faces called bases connected by adjacent curved or flat faces (bases can include circles, triangles, rectangles, or other shapes). 
  • Right prism – any three-dimensional figure with two polygons for bases that are opposite, congruent, and perpendicular to the adjacent faces

Boundaries

  • This includes two- and three-dimensional objects composed of polygons.
  • Cylinders explored in Grade 7 should be limited to right circular cylinders.  Right circular cylinders are three-dimensional solid figures with two congruent, parallel, circular bases that are connected by a curved face that is perpendicular to each base.

Teaching Strategies

  • Students should apply knowledge of cross sections as a strategy for revealing a base of cylinders including right prisms.
  • Students should apply reasoning about the volume of rectangular prisms to explore the volume of cylinders and other three-dimensional objects composed of cubes and right prisms.
  • Students should have opportunities to discover the surface area of a cylinder by decomposing the figure into circles and rectangles.

Progressions

  • In Grade 7, students extend the use of geometric terms and definitions with which they have become familiar: polygons, perimeter, area, volume and surface area of two-dimensional and three-dimensional objects, etc. In Grade 6, students found the area of a polygon by decomposing it into triangles and rectangles whose areas they could calculate, making use of structure (MP.7) to make collections of simpler problems (MP.1). Now they apply the same sort of reasoning to three-dimensional figures, dissecting them in order to calculate their volumes. (Please reference page 7 in the Progression document).

Examples