© Rex Boggs, April 2004

Mathematics Unit Plan

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Grade: 7

/ Unit: Geometry in 3 Dimensions / Time: 11 to 20 periods
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Textbook(s)

/ Impact Math, Course 2, Chapter 2

Visit rex.boggs.tripod.com/middleschoolmath.htm for resources for this unit.

Unit Overview

Hands on!

This is very much a hands-on chapter. Where possible, the students should start with the concrete (e.g. colored cubes) and gradually move to the pictorial (e.g. drawings) and the symbolic (e.g. formulas).
Section 2.1
Section 2.1 is not in the Grade 7 Scope & Sequence. If you are behind the pacing calendar, you might consider skipping this section (but discuss this with your Math Coach or Principal first).
Section 2.2
The Explore, Problem Set A and Problem Set B on pages 91-93 are not in the Grade 7 Scope and Sequence, so they can be skipped to save time (again, discuss with Math Coach or Principal first). However, we suggest you do them if you have the time. Problem Set F is foundational for Section 2.3, so should be done. The two-period investigation LP – Designing a Moon Station I is a hands-on activity that consolidates previous work. Recommended, if you can spare the time.
Time
Because there are a number of optional topics and activities, the time for this chapter ranges from 11 to 20 periods.
Surface Area and Volume of Prisms
When studying surface area, students benefit from actually holding the 3-D shapes in their hands, and seeing all of the surfaces. They also benefit from constructing some 3-D shapes from their nets.
Students should start their study of volume by constructing rectangular prisms using 1” cubes to discover the formula for the volume of the rectangular prism: Volume = Area of the base x thickness. I prefer the term ‘thickness’ rather than ‘height’ because the term ‘height’ is a misnomer if the prism is lying on its side. Also, the term ‘height’ is ambiguous when finding the volume of a triangular prism – does ‘height’ refer to the perpendicular height of the triangular face, or the height of the prism?
I prefer to include cylinders in the definition of a prism, as the formula for the volume is exactly the same.
There is only one volume formula needed for prisms (including cylinders):
V = A x t
where V = volume of the shape, A = Area of congruent faces and t = thickness (i.e. distance between the parallel congruent faces). Special formulas (e.g. Volume = Side3 for a cube) should be used only after the more general formula is understood and mastered.
Problem Set D and Problem Set E in Section 2.3 are optional.
Nets and Solids
The activity LP – Nets of a Cube supports the Explore on page 129 and is a nice group activity. The activity LP – Nets of Polyhedra is optional, but recommended. It could be done as a project, for assessment. See the Topic Planner below for details.

Learning Objectives By the end of this unit I want my students to be able to…

·  (optional) By building block structures, identify patterns and express them algebraically
·  (optional) Draw front, top and side views of block structures.
·  Find the volume and surface area of any block structure by counting cubes and exposed faces.
·  Identify a variety of types of 3-D shapes
·  Know the names of common polyhedrons
·  Find the volume of any prism (including a cylinder) by using
Volume = Area of base x perpendicular height.
·  Create nets, and from them, the associated 3-D shape.
·  Use nets to find the surface area of a 3-D shape.
·  Apply knowledge of surface area and volume to practical situations.

Vocabulary

The student should be able to spell, know the definition of, give an example of and (where appropriate) draw a diagram of:
cube prism rectangular prism
triangular prism cylinder face
vertex edge polyhedron
tetrahedron octohedron dodecahedron
icosahedron net (of a prism) dimensions
top view front view side view
volume area surface area

Additional Resources

1” cubes / These are supplied with both the Grade 6 and Grade 7 Impact Math kits.
Lesson plans / Lesson plans that directly support this unit include:
LP – Visualizing Block Structures
LP – Designing a Moon Station I
LP – Volume of a Rectangular Prism
LP - Nets of a Cube (plus the accompanying handout)
LP – Nets of Polyhedra (plus the accompanying handout)
There are also some additional lesson plans that you might prefer to use in place of (or in addition to) those above. They include:
LP – Grade 7 Chapter 2 from Bruce Williams
LP – Grade 7 Chapter 2 from Cath O’Hara
LP – Designing a Moon Station II
LP – Maximizing Volume
LP – The Popcorn Box Problem
Volume OHT / This OHT helps your students discover the formula for the volume of a prism.
Teaching Tips (TT) / TT – Distributing and collecting materials in 15 seconds
TT – The only area formula you will ever need


Topic Planner

Topic

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Lessons
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Page

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Suggested Activities

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Comments

Section 2.1
*Building block patterns / *2 periods / 78
80
81 / Explore
Read Investigation 2
Problem Set B, Q1-9 / *Section 2.1 is optional. It is not in the Scope and Sequence.
Group size: pairs. 36 cubes per pair.
Section 2.2
*Visualizing block structures / *2 periods / 91
92
93 / Lesson plan LP – Visualizing Block Structures / *Optional. Not in the Scope and Sequence. This lesson plan
includes Explore, Problem Set A and Problem Set B.
Measuring block structures / 1 period / 98
99
99 / Think & Discuss
Problem Set F, Q1-4
Share and Summarize / Group size: pairs. 8 cubes per pair.
*2 periods / - / LP – Designing a Moon Station I / *Optional, but recommended. This investigation consolidates previous topics.
Section 2.3
Review of Area / 1 or 2 periods, as needed / - / Revise area formulas for a square, rectangle, parallelogram, triangle, circle. See Teaching Tip – The Only Area Formula You Will Ever Need for a simple (but radical) approach to this topic.
Surface Area and Volume / 1 period / 109
110 / Think & Discuss
Problem Set A, Q1-2 / Alternatively, replace these lessons with the lesson plan LP – Volume of a Rectangular Prism.
1 period / 111
112 / Problem Set B, Q1-2
Share & Summarize
Volume of prisms / 2 periods / 112
114 / Problem Set C, Q1-5
Think and Discuss / You may also wish to use the overhead transparency Volume of a Prism OHT.
*1 period / 115
116 / Problem Set D, Q 1-3
Share & Summarize / *Optional. Do this section only if you have time.
Modeling with block structures / 1 period / 116
117 / Investigation 3
Think & Discuss / Read aloud and discuss.
*3 periods / 117
118 / Problem Set E.
Problem Set F / *Optional. Only do these Problem Sets with an advanced group, and if time.
Section 2.4
Nets and Solids / 2 periods / 129 / The lesson plan LP - Nets of a Cube and the accompanying Nets of a Cube activity sheet support the Explore activity on page 129.
1 period / 130 / Problem Set A
Share & Summarize / Group size: 4 (to share the work). One copy of Master 12 per group is needed.
1 period / 132
134 / Problem Set B, Q1 – 2
Share & Summarize / Have copies of Master 13 available if students need to make the solid first.
*Nets of polyhedra / *2 periods / - / LP – Nets of Polyhedra / *Optional, but recommended if time. This can be used as an assessment piece for this unit

Assessment

Instrument

/ Details
Chapter Test / TBD
Project / Use the lesson plan LP - Nets of Polyhedra and the accompanying nets.

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