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GeometryStrand: Mathematics 8, Number, page 33/34.

http://www.education.gov.sk.ca/adx/aspx/adxGetMedia.aspx?DocID=2391

Stage 1 – Desired ResultsEstablished Goal(s): GGoals: Number Sense, Spatial Sense, Logical Thinking, Mathematics as a Human EndeavourOutcome SS8.4 [C, CN, PS, T, V]Demonstrate an understanding of tessellation by:

Explaining the properties of shapes that make tessellating possible Creating tessellations Identifying tessellations in the environment.

Indicators: Id. Design and create (concretely or pictorially) a tessellation involving one or more 2-D shapes, and document the mathematics involved within the tessellation (e.g., types of transformations, measures of angles, or types of shapes).e. Identify different transformations (translations, reflections, rotations, and combinations of any of the three) present within a tessellation.Prerequisite Knowledge:

Measuring angles Identifications of shapes Creating and drawing precise shapes

Essential Question(s) EQ1. Brainstorm real life examples of tessellations.

(chain link fence, bee hive, brick wall)2. What do you know about triangles and

quadrilaterals? (they will always be able to tessellate)

3. If you were given a polygon that does not tessellate; how can we make it into one that can? (A shape that does not tessellate can be combined with other shapes to make a composite shape that does tessellate)

4. Can you draw any conclusions of the angles at a point? (At any given point where tessellations meet, the angles add up to 360°)

5. Discuss the Ideas (Pearson, 8, p. 467)

Understanding(s): UStudents will understand...

Tessellations occur when shapes can be organized in a manner where there are no gaps or overlaps

At any given point where tessellations meet, the angles add up to 360°

A shape that does not tessellate can be combined with other shapes to make a composite shape that does tessellate

Knowledge: KStudents will know…

What is meant by “a shape that tessellates” That a triangle and quadrilateral will always

tessellate Vertices will add to 360° A shape that does not tessellate can be

combined with another shape to create a

Skills: SStudents will be able to...

Draw and create a tessellation Measure angles of where vertices meet to

verify the sum of the angles is 360° Identify tessellations Adapt a non-tessellation into a composite

shape that can tessellate

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composite shape that tessellatesStage 2—Assessment Evidence

Performance Task(s): T Student’s examples of patterns in their

everyday world (pictures, clothing, etc.). They can bring in authentic items from their lives

Other Evidence: OE Ongoing assessment Exit slip

Stage 3—Learning PlanLearning Activities: LSet:

Discuss the definition of a plane as a class. Give and discuss what makes a tessellation. Look at the patterns and classify them according to the definition of a tessellation of the examples that students brought to class [T]. Now that they have real ideas, what are some other examples? [EQ 1] (7-10 minutes) [AD 1] [COM, C, V, MC]

Development:1. Distribute tracing paper to pairs of students to do Investigate [AD 2] (Math Makes Sense 8, Pearson,

p. 462). One partner draws a triangle and the other partner draws a quadrilateral. Trace your shape and cover the paper with copies of your shape, with no overlaps or gaps. [Teacher Notes] (See Pearson p. 462- Reflect and Share) and discuss these ideas. Ask students [I d] [EQ 2] [AD 3] [D, COM, IR, RT,V] (10 minutes)

2. Congruent copies of shapes that cover a plane with no gaps or overlaps are called tessellations. Have students look at Connect (Pearson, 8, p. 463) and discuss as a class. Ask students [EQ3]. How they could fix the hexagon on p. 463 to make a shape that does tessellate? [I e] [MAN, COM, C, V, MM & E, IR] (3 minutes)

3. Have students measure the angles at a point where the vertices meet of the tessellations they created and add them together. Ask students [EQ 4]. Look at the shapes on p. 464, ask: What do you notice about the angles that surround a point? (The sum is always 360°) [MM & E, IR, C] (3 minutes)

4. As a class, go through examples 1 and 2 together and discuss (Pearson, 8, p. 464-467). Use these examples to show that although some polygons do not tessellate, they may be combined with other shapes to create a new polygon that does tessellate. [C, V, ](4 minutes)

5. Discuss as a group, engaging every learner in answering the questions from Discuss the Ideas (Pearson, 8, p. 467). [EQ 5] [COM, C] (3 minutes)

6. Have the students complete questions 6 to 14 omit 12, 13. (See teacher notes ALL) [OE 1] Remind students to keep the tessellations they create for tomorrow’s lesson. [C, V, MM & E, IR] (15 minutes)

Extension:1. Create a regular octagon. Trace it. Does this regular octagon tessellate? Now use dot paper to

create an octagon that does tessellate. Explain why it tessellates. Show the other students your tessellation. [C, MM & E, PS, V, IR]

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Closure: Color in one of their tessellations where no two adjacent shapes can be the same color, these will

then be displayed in the classroom or hallway Have students fill in and complete exit slip (see teacher notes) [C, COM, MC] (5 minutes)

Adaptive Dimension: AD1. Have students walk around, touch and look to reach all learners that may need concrete

manipulatives2. Pairs will be pre-decided ahead of class to create varied skills pairs so that students can benefit

from the knowledge, experience and learning styles of each other.3. Hands on by creating and drawing the tessellations themselves (concrete manipulatives)

*Adapted from Tomlinson and McTighe, Integrating Differentiated Instruction + Understanding by Design, ASCD, 2006.

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Teacher NotesSet:For examples during the set, we will bring an example similar to these for students to classify and one non-example (all below). Have students walk around, touch and look to reach all learners that may need concrete manipulatives [AD 1]

http://3.bp.blogspot.com/_pg3Ul9H0z4s/SkqQ9caZIsI/AAAAAAAABx0/-QBsJ6uvlTs/s400/E110.jpg

http://filipspagnoli.files.wordpress.com/2009/05/mc-escher-humanity.jpg

Development:1. As students are drawing their shapes, create discussion using questions such as

those found in Pearson, ProGuide, Unit 8, p. 336. For questions 7 and 9, have copies available of the diagrams. (Pearson, 8, p.468), also have copies of the diagrams for question 11. Have pattern blocks for question 10 and tracing paper readily available for 7, 9, and 11.

ALL: As students are working keep close proximity and continually move around to reach all students (students are more likely to ask a question when the teacher is close to them). As they are working take notice of what they are doing, how they are doing it, their strengths and struggles as part of ongoing assessment [OE 1]

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Exit SlipWhat are three things you learn today about tessellations?

What are two things you found difficult?

List two tessellations you find in our everyday world.

In this box, create a tessellation using a triangle, quadrilateral or polygon or composite shape and tracing paper.

Did you enjoy what you learned today? (circle one)