Gr. 7 Unit: 7.G.A.1-3: Draw, Construct, and Describe Geometrical Figures and Describe the Relationships Between Them

Unit Overview

This unit builds on student understanding of ratio concepts and reasoning, as well as on proportional relationships to create scale drawings. The unit also focuses on the origin of two-dimensional figures that result from slicing three-dimensional figures.

Teacher Notes:

Enduring Understandings:

At the completion of this unit on drawing, constructing, and describing geometrical figures and their relationships, the student will understand that:

Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):

Possible Student Outcomes:

Students will be able to:

Evidence of Student Learning:

The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.

Fluency Expectations and Examples of Culminating Standards:

PARCC has no fluency expectations related to drawing, constructing, and describing geometrical figures.

Common Misconceptions:

Students may

Interdisciplinary Connections:

Interdisciplinary connections fall into a number of related categories:

Literacy standards within the Maryland Common Core State Curriculum

Science, Technology, Engineering, and Mathematics standards

Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others.

Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:

Items purchased from vendors

PARCC prototype items

PARCC public release items

Maryland Public release items

Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)

Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.

Part I – Focus Cluster
Use Properties of Operations to Generate Equivalent Expressions

right rectangular prism:

a. b. c.

A right rectangular prism is a 6-sided polyhedron in which all faces are quadrilaterals that meet to form right angles at the vertices (see prism a. and prism b.). Prism c is an oblique rectangular prism because not all faces meet to form right angles at the vertices.

right rectangular pyramid:

a. b.

A right rectangular pyramid has a rectangle as the base and four isosceles triangles as the faces (see pyramid a.). An oblique rectangular pyramid has a rectangle as the base, with two scalene triangles and two isosceles triangles as faces (see pyramid b.).

Part II – Instructional Connections outside the Focus Cluster

unit rate: Unit rate is the ratio of two different measurements in which the second term
is 1. Example: 6:1 6 miles/one gallon, , (In fraction form, the denominator is 1.)

ratio: A ratio is a comparison of 2 quantities. It is written as the quotient of two numbers
  (part to part and part to whole). The three ways of writing a ratio include: 9 to 10, and 9:10
  and .

complex fraction: A complex fraction has a fraction for the numerator or denominator or both.

proportional relationship: A proportional relationship is a collection of pairs of
   numbers that are in equivalent ratios (Example: A proportional relationship also can be described by an equation of the form y = kx, where k is a positive constant (often called a “constant of proportionality”)

proportion: A proportion is a statement of equality of two ratios; that is written as an
   equation. Example: 3:9 = 4:12 or =

identify that a proportional relationship intersects (0, 0): As shown on the graphs below, when the value of x is 0, the value of y is also 0, or (0, 0). For example, (a) when zero electricity is being generated, zero pounds of carbon are emitted; (b) when zero ounces of oregano are weighed, the cost is zero dollars; (c) when a cone has a height of zero, the cone flattens into a 2-dimensional circle, and thus, has volume of zero.

within ratios: A ratio of two measures in the same setting is within ratios. Example: If a person walks 4 miles in 2 hours, how many miles will she walk in 3 hours? Let m = miles.

between ratios: A ratio of two corresponding measures in different situations is considered between ratios. Example: If a person walks 4 miles in 2 hours, how many miles will she walk in 3 hours? Let m = miles.

additive reasoning versus multiplicative reasoning: Proportional situations are based on
  multiplicative relationships. Equal ratios result from multiplication or division, not addition
  or subtraction.
  Consider any proportion, for example What operation was used to convert to ?Was additive reasoning used: ?Or was multiplicative reasoning used:

The example below shows an application of multiplicative reasoning:

Last month, two bean plants were measured at 9 inches tall and 15 inches tall. Today they are 12 inches tall and 18 inches tall, respectively. Which bean plant grew more during the month, the 9-inch bean plant or the 15-inch bean plant?

Using additive reasoning, we know that each plant added 3 inches in a month. To determine
   plant grew more, however, we use multiplicative reasoning. In other words,
  we want to know what proportion of the original plant height is represented by 3 inches.
   The 3-inch increase represents of the first plant’s growth, whereas the 3-inch increase represents of the second plant’s growth. Since > (or > , the 9-inch plant grew more.

a.    b.

c.

determine other points using (1, r), where r is the unit rate: In the ordered pair (1, r),
   x-value “1” represents one standard of measurement. The y-value “r” represents
   a given specific quantity.

For example in the table “A Moving Automobile,” the x-value is time (hours). The y-value “r” is distance traveled (miles). The unit rate is r miles per hour, or According to the graph, unit rate is (1, 50) or To determine other points: 1. multiply by 2. identify (2, 100) or, (3, 150) or ; and (6, 300) or , respectively.

percent error: We often assume that each measurement we make in mathematics or science is true and accurate.  However, sources of error often prevent us from being as accurate as we would like.  Percent error calculations are used to determine how close to the true values our experimental values actually are. The value that we derive from measuring is called the experimental, or observed, value. A true, ortheoretical, value can be found in reference tables.

The percent error can be determined when the theoretical value is compared to the experimental value according to the equation below:

percent error =

Example:  A student measured the volume of a 2.50 liter container to be 2.38 liters. What is the percent error in the student's measurement?
   percent error =

Additional Resources: