MATHEMATICS GRADE 8
HOUSTON ISD PLANNING GUIDE
4TH SIX-WEEKS
Planning Guide User Information
Unit 12: Spatial Relationships in Geometric Solids
Time Allocations
Unit
2 lessons (90-minutes each)
or
4 lessons (45-minutes each)
Unit Overview
Spatial Relationships in Geometric Solids – Students investigate spatial relationships by matching drawings of front,
top, and side views of geometric solids to the solid; drawing given solids from different perspectives; and using spatial
visualization skills to build concrete representations of solids.
TEKS/SEs (district clarifications/elaborations in italics)
Ⓢ MATH.8.7A Draw three-dimensional figures from different perspectives and match drawings of top, front, and side
views to figures.
Ⓢ MATH.8.7B Use geometric concepts (including symmetry, similarity, congruence, and transformations) and
properties of two- and three-dimensional figures to solve problems in fields such as art and architecture.
MATH.8.14A Identify and apply mathematics to everyday experiences, to activities in and outside of school, with
other disciplines, and with other mathematical topics.
MATH.8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical,
numerical, physical, or algebraic mathematical models.
 English Language Proficiency Standards
ELPS C.3d Speak using grade-level content area vocabulary in context to internalize new English words and build
academic language proficiency.
College and Career Readiness Standards
CCRS 3.A1 Identify and represent
the features of plane and space
figures.
CCRS 3.B2 Identify the symmetries
of a plane figure.
CCRS 10.A2 Connect mathematics
to the study of other disciplines.
CCRS 9.C1 Communicate
mathematical ideas, reasoning,
and their implications using
symbols, diagrams, graphs, and
words.
Key Concepts
geometric solid
visualization
Academic Vocabulary
concrete
draw
relationship
surface area
volume
Content-Specific Vocabulary
area
Essential Understandings / Guiding Questions
Visualization of spatial relationships is used to construct, draw, describe, and compare geometric solids.
1. How are the front, top, and side views of geometric solids related?
2. How is the floor plan of a geometric solid related to the solid itself?
3. Why is spatial visualization important?
 - English Language Proficiency Standards (ELPS)
- Literacy Leads the Way Best Practices
- Aligned to Upcoming State Readiness Standard
- State Process Standard Ⓡ - State Readiness Standard Ⓢ - State Supporting Standard Ⓣ - TAKS Tested Objective (only 11th grade)
© Houston ISD Curriculum
2012 – 2013
Page 1 of 4
MATHEMATICS GRADE 8
HOUSTON ISD PLANNING GUIDE
4TH SIX-WEEKS
Assessment Connections
Performance Expectation – Students will construct, draw, describe, and compare geometric solids and spatial
relationships by matching drawings of front, top, and side views.
Draw & Write – students respond to the following scenario in their interactive notebook.
o A pet iguana lives in an aquarium with a height of 3 units and a rectangular base 5 units long and 4 units wide.
Use isometric dot paper to sketch the aquarium. Then draw and label the top, front, and side views of the
aquarium.
o Suppose one of your classmates is absent the day this assignment was given. Write a brief paragraph
explaining the process above.
Formative Assessment – Front, Top, and Side View – students determine different perspectives of various objects.
Exit Ticket – have students explain whether a top-front-side view diagram always provides enough information to
draw a figure. If not, provide a counterexample.
®
SpringBoard Course 2 – Embedded Assessment #1: “Under the Sea” – #1, 2
STAAR Sample Item – Item #8 (MATH.8.7B)
Texas English Language Proficiency Assessment System (TELPAS): End-of-year assessment in listening,
speaking, reading, and writing for all students coded as LEP (ELL) and for students who are LEP but have parental
denials for Language Support Programming (coded WH). For the Writing TELPAS, teachers provide five writing
samples – one narrative about a past event, two academic (from science, social studies, or mathematics), and two
others.
Instructional Considerations
Information in this section is provided to assist the teacher with the background knowledge needed to plan instruction
that facilitates students to internalize the Key Concepts and Essential Understandings for this unit. It is recommended
that teachers thoroughly read this section before implementing the strategies and activities in the Instructional
Strategies section.
Prerequisites and/or Background Knowledge for Students
The concept of drawing solids from different perspectives was introduced in elementary school.
Seventh-grade students sketched solids given the front, top, and side views (FTS) or drew FTS
views of given solids constructed from a group of cubes such as the figure shown to the right.
Background Knowledge for Teacher
Critical Content
Use spatial visualization skills to identify and draw front, top, and side views of geometric solids.
Instructional Accommodations for Diverse Learners
 As students are building and discussing solids in cooperative groups (MATH.8.15A), they should also be using
and reviewing previous knowledge about the concepts of area, surface area, and volume and relating them to the
constructions (MATH.8.7B). C.3d
As students develop their spatial skills, they also need to be able to recognize the top view of a figure not built from
cubes such as the one shown below.
Use the Sketching Solids PowerPoint presentation on front, top, and side view to engage students who may have
difficulties with fine motor skills or lack of visualization. Allow students to practice sketching the front, top, and side
view using the Front, Top, and Side View practice document.
 - English Language Proficiency Standards (ELPS)
- Literacy Leads the Way Best Practices
- Aligned to Upcoming State Readiness Standard
- State Process Standard Ⓡ - State Readiness Standard Ⓢ - State Supporting Standard Ⓣ - TAKS Tested Objective (only 11th grade)
© Houston ISD Curriculum
2012 – 2013
Page 2 of 4
MATHEMATICS GRADE 8
HOUSTON ISD PLANNING GUIDE
4TH SIX-WEEKS
Instructional Strategies / Activities
The strategies and activities in this section are designed to assist the teacher to provide learning experiences to
ensure that all learners achieve mastery of the TEKS SEs for this unit. It is recommended that the strategies and
activities in this section be taught in the order in which they appear.
Summarizing and Note-Taking
KWL (Turn The Light On)
As an engagement activity, direct the students to create a KWL chart to show everything they know about the
concept of drawing solids from different perspectives similar to the one below.
Know
Want
to
Know
Learned
In groups, have students "popcorn" what they remember about solids as they take notes on chart paper.
Debrief the activity by having each group make a brief presentation while the audience compares and contrasts the
information on each chart. (MATH.8.7A, MATH.8.15A)
Nonlinguistic Representations
If students do not have the background to solve problems matching solids to FTS views and vice versa, allow
students to progress through a series of hands-on activities (Activities: Spatial Visualization Tasks, Activity 8.7A 3D
Models in the Mathematics Toolkit – see Resources).
Summarizing and Note-Taking
Two-Column Notes (Pen/cil To Paper)
Students should use cubes to build a solid, sketch it on isometric grid paper, and draw the FTS views as well as a
“floor plan” that indicates the height of the figures.
Using a two-column note-taking strategy will help students make the connections between the two types of
representations (i.e. 3-D sketch and floor plan). An example of a figure and its floor plan is shown below:
1
2
1
2
1
2
2
1
1
Front
Students should also complete activities that begin with a floor plan or FTS views and work backwards to the creation
®
of a sketch and/or the building of a concrete representation of the matching solid. (SpringBoard Mathematics with
Meaning: Middle School 2, Activity 4.2 “Sketching Solids”) (MATH.8.8.7A)
 - English Language Proficiency Standards (ELPS)
- Literacy Leads the Way Best Practices
- Aligned to Upcoming State Readiness Standard
- State Process Standard Ⓡ - State Readiness Standard Ⓢ - State Supporting Standard Ⓣ - TAKS Tested Objective (only 11th grade)
© Houston ISD Curriculum
2012 – 2013
Page 3 of 4
MATHEMATICS GRADE 8
HOUSTON ISD PLANNING GUIDE
4TH SIX-WEEKS
Instructional Strategies / Activities
Instructional Accommodations for Diverse Learners
Generating and Testing Hypotheses
Using Building Houses, allows students to “play” with 3-D figures (“cube houses”) and their various perspectives and
views in an informal and non-threatening manner. Students generate and test their own hypotheses relating to the
figures – see Resources. (MATH.8.7A, MATH.8.7B, MATH.8.14A)
For additional strategies to assist diverse learners, access Recommendations for Accommodating Special Needs
Students: Math 8, Cycle 4, Unit 12.
Homework and Practice
Using Cubes and Isometric Drawings is a complete unit with annotated lesson plans using a computer-based
drawing tool – see Resources.
Extensions for Pre-AP
To meet the instructional needs of Pre-AP students, provide challenging problem-solving scenarios such as the one
below:
o The diagram below shows the top view of a solid figure created by stacking cubes.
3
3
4
3
2
1
1
2
4
If the center 2 is changed to a 4, how will this affect the front and side views? Justify your answer.
Resources
Adopted Instructional Materials
®
SpringBoard Mathematics with
Meaning: Middle School 2
4.2 “Sketching Solids”
Glencoe, Texas Mathematics, Course
3:
TWE/SE, 7-4, pp. 365 – 369
Geometry Lab: “Drawing 3-D
Figures”, p. 364
Ch. 7 Resource Masters, pp. 26 –
31
Teaching Math with Manipulatives,
p. 72
Supporting Resources
Spatial Visualization Tasks
Activity 8.7A 3D Models
Sketching Solids
Front, Top, and Side View
Recommendations for
Accommodating Special Needs
Students: Math 8, Cycle 4, Unit 12
Online Resources
Mathematics Toolkit – UT Dana
Center
Building Houses
Using Cubes and Isometric
Drawings
 - English Language Proficiency Standards (ELPS)
- Literacy Leads the Way Best Practices
- Aligned to Upcoming State Readiness Standard
- State Process Standard Ⓡ - State Readiness Standard Ⓢ - State Supporting Standard Ⓣ - TAKS Tested Objective (only 11th grade)
© Houston ISD Curriculum
2012 – 2013
Page 4 of 4