Grade 4: 2D Geometry Unit, December 2013
CHRISTMAS GEOMETRY DAY: Wednesday DECEMBER 11
Learning Goal: Grade 4 students are learning to make connections as they explore and identify
two-dimensional shapes using concrete materials and drawings, as well as describe the
attributes of those shapes using effective mathematical language so that they can create
decorations for our Christmas themed bulletin board.
Success Criteria:
I will:
 make connections between math and literature, math, art, technology, home,
community, and my faith.
 understand the meanings conveyed by definitions of quadrilaterals.
 Identify and use the action words (e.g., model, draw, label, use, list, name, etc.) to
respond appropriately to questions.
 Describe how similar and congruent shapes are the same and how they are different.
 compare what the title tells me about a lesson with what the goal tells me.
 Describe what captions explain that is not clear from the pictures alone.
 will find the information I need to help solve problems and answer questions (e.g., read
the entire question or problem carefully, identify key words, look at diagrams, etc.).
 review the checklist before solving the problem to help me complete the problem.
Overall Expectations:
• solve problems using geometric models (refer to Lesson 2, 3, 6)
• investigate the attributes of two-dimensional shapes using concrete materials and drawings (2, 4, 5, 6, 7, 8)
• use language effectively to describe geometric concepts, reasoning, and investigations (1, 4, 8)
Specific Expectations: Two-Dimensional Geometry
• identify and sort quadrilaterals (1, 2, 8)
• sort and classify two-dimensional figures according to shape (1, 4, 8)
• identify similar and congruent figures using a variety of media (3, 4)
• construct congruent figures in a variety of ways (3)
• measure angles using a protractor (5)
• use mathematical language to describe geometric ideas (2)
• recognize and describe the occurrence and application of geometric properties and principles in the everyday world (6)
• discuss geometric concepts with peers and explain their understanding of the concepts (2, 7)
• discuss ideas, make connections, and articulate hypotheses about geometric properties and relationships (2)
Transformational Geometry
• draw lines of symmetry on two-dimensional shapes (7)
Connections to Literature:
Introduce and display books related to 2-D geometry, such as the following:
 Janice VanCleave’s Geometry for Every Kid: Easy Activities
 That Make Learning Geometry Fun (Janice VanCleave;
 John Wiley & Sons, 1994)
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Shape Up! (David Adler; Holiday House, 1998)
The Greedy Triangle (Marilyn Burns; Scholastic, 1994)
Grandfather Tang’s Story (Ann Tompert; Crown, 1990)
Connections to Math: Measurement: Students can explore the areas of the various shapes they work with. In
particular, they can note that congruent shapes always have the same area, although the reverse is not necessarily true.
Data Management and Probability: In the course of the chapter, students practice the use of sorting templates, such as
Venn diagrams. With a probability element students can consider a group of shapes and determine the likelihood of
various attributes (e.g., that a 2-D shape has a square corner, parallel sides, etc.).
Connections to Art: Students might use their artistic skills in designing geometric Christmas ornaments and sacred rose
window patterns similar to those required in the Chapter Task. In addition, they might create pieces of geometric art
built around some of the shapes they are studying in this chapter.
Connections to Technology: Students can use graphics software to explore a number of aspects of this chapter. They
can create shapes and copy them to show congruence, change the shape sizes to show similarity, and put together and
dissect shapes to create other shapes. If they use pre-made shapes from a graphics package, they can explore which
variations of that shape can be created with the original template and which cannot.
Connections to Home and Community:
At Home suggestions will be sent in the December class newsletter.
Connections to our Faith:
Students will investigate the history of and geometry used in sacred stained glass rose window patterns used in churches
and cathedrals.
* Instruction (see attached pdf document with lesson plan overview for Nelson text, Chapter
7, 2-D Geometry
Ongoing Activities:
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Create a word wall to focus on geometric terms related to this chapter: line, line segment, attribute, congruent,
quadrilateral, parallelogram, parallel, equal, rectangle, rhombus, square, trapezoid, kite, angle, protractor,
degree, line of symmetry, polygon, similar, pentagon, hexagon, triangle, angle, acute, right, straight, obtuse.
Create a collage of magazine and newspaper pictures of 2-D geometry situations that connect to students’
experience.
Add to a chart showing the problem-solving strategies students have used.
Math centre with geometric puzzles, pattern blocks, transparent mirrors, attribute blocks, and puzzles that can
be solved with these materials.
Have geometry problems of the week available to students. 1. How many triangles can you find?, 2. Look at the
pattern. What is the colour of the 100th circle?, 3. When two triangles overlap, what are all the possible overlap
shapes?)
Use math journal writing prompts to encourage students to write about connections they make to the
mathematics they are learning.
Connections to Literature:
Introduce and display books related to 2-D geometry, such as the following:
Janice VanCleave’s Geometry for Every Kid: Easy Activities
That Make Learning Geometry Fun (Janice VanCleave;
John Wiley & Sons, 1994)
Shape Up! (David Adler; Holiday House, 1998)
The Greedy Triangle (Marilyn Burns; Scholastic, 1994)
Grandfather Tang’s Story (Ann Tompert; Crown, 1990)
Connections to Math: Measurement: Students can explore the areas of the various shapes they work with. In
particular, they can note that congruent shapes always have the same area, although the reverse is not necessarily true.
Data Management and Probability: In the course of the chapter, students practice the use of sorting templates, such as
Venn diagrams. With a probability element students can consider a group of shapes and determine the
likelihood of various attributes (e.g., that a 2-D shape has a square corner, parallel sides, etc.).
Connections to Art: Students might use their artistic skills in designing geometric Christmas ornaments and sacred rose
window patterns similar to those required in the Chapter Task. In addition, they might create pieces of geometric art
built around some of the shapes they are studying in this chapter.
Connections to Technology: Students can use graphics software to explore a number of aspects of this chapter. They
can create shapes and copy them to show congruence, change the shape sizes to show similarity, and put together and
dissect shapes to create other shapes. If they use pre-made shapes from a graphics package, they can explore which
variations of that shape can be created with the original template and which cannot.
Connections to Home and Community:
At Home suggestions will be sent in the December class newsletter.
Connections to our Faith:
Students will investigate the history of and geometry used in sacred stained glass rose window patterns used in churches
and cathedrals.
Black and white rose window from church sanctuary
Geometry and Spatial Sense: identifying geometric properties of parallelograms; classifying two-dimensional
shapes by geometric properties (number of sides, angles, and symmetry); identifying a straight angle, a right angle,
and half a right angle; classifying prisms and pyramids by geometric properties; constructing three-dimensional
figures in a variety of ways; describing location using a grid system; performing and describing reflections
Grade 4: Mathematical Process Expectations (Ministry of Education)
The mathematical process expectations are to be integrated into student learning associated with all the strands.
Students will:
• PROBLEM SOLVING develop, select, and apply problem-solving strategies as they pose and solve problems and
conduct investigations, to help deepen their mathematical understanding;
• REASONING AND PROVING develop and apply reasoning skills (e.g., classification, recognition of relationships, use
of counter-examples) to make and investigate conjectures and construct and defend arguments;
• SELECTING TOOLS AND COMPUTATIONAL STRATEGIES demonstrate that they are reflecting on and monitoring their thinking
to help clarify their understanding as they complete an investigation or solve a problem (e.g., by comparing
and adjusting strategies used, by explaining why they think their results are reasonable, by recording their thinking
in a math journal);
• REFLECTING select and use a variety of concrete, visual, and electronic learning tools and appropriate
computational strategies to investigate mathematical ideas and to solve problems;
• CONNECTING make connections among mathematical concepts and procedures, and relate mathematical ideas to
situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, sports);
• REPRESENTING create a variety of representations of mathematical ideas (e.g., by using physical models,
pictures, numbers, variables, diagrams, graphs, onscreen dynamic representations), make connections among
them, and apply them to solve problems;
• COMMUNICATING communicate mathematical thinking orally, visually, and in writing, using everyday language,
a basic mathematical vocabulary, and a variety of representations, and observing basic mathematical conventions.
Grade 4: Geometry and Spatial Sense
Grade 4: Geometry and Spatial Sense
Overall Expectations
By the end of Grade 4, students will:
• identify quadrilaterals and three-dimensional figures and classify them by their geometric properties, and compare various angles
to benchmarks;
• construct three-dimensional figures, using two-dimensional shapes;
• identify and describe the location of an object, using a grid map, and reflect two-dimensional shapes.
Specific Expectations
Geometric Properties
By the end of Grade 4, students will:
– draw the lines of symmetry of two dimensional shapes, through investigation using a variety of tools (e.g., Mira, grid paper) and
strategies (e.g., paper folding) (Sample problem: Use paper folding to compare the symmetry of a rectangle with the symmetry of a
square.);
– identify and compare different types of quadrilaterals (i.e., rectangle, square, trapezoid, parallelogram, rhombus) and sort and
classify them by their geometric properties (e.g., sides of equal length; parallel sides; symmetry; number of right angles);
– identify benchmark angles (i.e., straight angle, right angle, half a right angle), using a reference tool (e.g., paper and fasteners,
pattern blocks, straws), and compare other angles to these benchmarks (e.g.,“The angle the door makes with the wall is smaller than
a right angle but greater than half a right angle.”) (Sample problem: Use paper folding to create benchmarks for a straight angle, a
right angle, and half a right angle, and use these benchmarks to describe angles found in pattern blocks.);
– relate the names of the benchmark angles to their measures in degrees (e.g., a right angle is 90º);
– identify and describe prisms and pyramids, and classify them by their geometric properties (i.e., shape of faces, number of
edges, number of vertices), using concrete materials.
Geometric Relationships
By the end of Grade 4, students will:
– construct a three-dimensional figure from a picture or model of the figure, using connecting cubes (e.g., use connecting cubes to
construct a rectangular prism);
– construct skeletons of three-dimensional figures, using a variety of tools (e.g., straws and modelling clay, toothpicks and
marshmallows, Polydrons), and sketch the skeletons;
– draw and describe nets of rectangular and triangular prisms (Sample problem: Create as many different nets for a cube as you can,
and share your results with a partner.);
– construct prisms and pyramids from given nets;
– construct three-dimensional figures (e.g., cube, tetrahedron), using only congruent shapes.
Location and Movement
By the end of Grade 4, students will:
– identify and describe the general location of an object using a grid system (e.g.,“The library is located at A3 on the map.”);
– identify, perform, and describe reflections using a variety of tools (e.g., Mira, dot paper, technology);
– create and analyse symmetrical designs by reflecting a shape, or shapes, using a variety of tools (e.g., pattern locks, Mira,
geoboard, drawings), and identify the congruent shapes in the designs.