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Tasks

Activating Prior knowledge

Work On It

Consolidation

Questions

Diagnostic

Tell students that the class is starting a new unit on Geometry. In order to better meet their needs you are going to have a quick quiz. Calm their fears that this is not a test but rather information for you to see where they are in their understanding.

Have students answer various questions on angles, and 2-D & 3-D figures.

Teacher looks at the diagnostic and decides where to begin with the students.

How do you know an angle is acute?

How are a square and rectangle different?

How are a prism and a pyramid different?

Sub Task # 1

Create the anchor Chart for 2D shapes

(Subtask 1 & 2 are not necessary if the students have a good understanding of the geometric properties)

What are Geometric Properties?

What are the geometric properties of a triangle?

Students work in pairs to list the properties of different two dimensional polygons.

Have the students share the properties about the 2-D polygons. Create an anchor chart for students to refer to throughout the unit.

How are the polygons similar? How are they different? What are parallel lines? How many vertices does each shape have?

What are regular and irregular polygons?

Sub Task # 2

Create the anchor chart for 3D figures

Classify and construct polygons and angles

Yesterday we discussed the geometric properties of 2-D polygons. Today we are discussing the Geometric Properties of 3D figures. What are the properties of a cube?

Students work in pairs to list the properties of different 3-D figures.

Square based pyramid, triangular pyramid, rec. prism, cone, cylinder, etc.

Have the students share the properties about the 3-D figures. Create an anchor chart for students to refer to throughout the unit

What is the difference between a pyramid and a prism? (faces, edges, vertices, parallel lines)

Sub Task # 3


Math Makes Sense page 86 of textbook. Teachers Guide for figures

Draw 2-D polygons on the board. Ask: How are they alike and different? What is a regular figure? What is an irregular figure?

Which figures are regular? How do you know?

Students are to classify the figures by angles, parallel sides.

How might you identify the properties of a polygon? Which figures are regular and irregular? How did you classify?

Which figure has the most properties from the list? Which figure had the least properties from the list? Which properties describe the most figures?

Why are trapezoids also quadrilaterals? Why are trapezoids not parallelograms? (has only one side of parallel lines)

Sub Task # 4

Polygon Capture

Game

(Illuminations)


Polygon Capture:

Go over the rules of the game with the students

Students play the game. Object of the games: sort and classify polygons based on their properties.

Discuss the object of the game. What were some the some of the 2-D polygons you could choose for a specific card?

What are the properties of a square? Other polygons you could ask about include: rectangle, rhombus, triangle, parallelogram, trapezoid, and pentagon.

Sub Task # 5

Measure Angles


Review of angle names.

Model the use of the protractor for the students.

Construct angles, acute, obtuse, right, and straight. Construct a parallelogram and a rhombus, measure the angles and sides. What connections are made?

Choose several students to talk about the rhombus and parallelogram and the connections they made to sides and angles.

How do you know what kind of angle this is?

What is the exact degree of this angle?

How is a square a rhombus?

Sub Task # 6

Constructing Figures

Classify and construct polygons and angles.

Make the connection that a triangle has an interior of 180, quadrilateral 360.

Remind students how a figure can be decomposed into smaller figures

Draw a square: Draw a diagonal: Ask which two figures make up this figure.

Repeat with a kite, trapezoid, and pentagon.

Have students construct various triangles and quadrilaterals. Measure and name the angles and add the interior of the polygon. Construct a parallelogram with angle measure of 115 degrees and sides of 7cm and 6cm

Choose several students to share how they made the triangles and quadrilaterals.

How did you make the quadrilaterals and triangles? What was the sum of the angles?

What did you notice about the triangles? What did you notice about the quadrilaterals? What shapes make up quadrilaterals? What rule can we make?

Sub Task # 7

Geometers Sketch Pad

Lesson Plan in the book on page 96 & 97 of Math Makes Sense

Construct polygons using a variety of tools, given side and angle measurements

Students will use Geometers Sketch Pad to draw 2-D polygon and measure the sides and angles

Students will follow the instructions laid out in Math Makes Sense pg. 96 & 97. Have the students measure the perimeter and area of the polygons. They can observe the effect on area and perimeter by changing the size of the polygon.

Select several students to share their polygons with the class. Discuss the relationship between the interior of the figures and the generalization they made. Does this generalization still hold true? Why?

Journal Question:

How did GSP make it easier to draw the polygons?

(Change size and shape, easier to measure)

Task # 8

Geometers Sketch Pad


Students will use Geometers Sketch Pad to draw 2-D polygons

(parallelogram, rectangle, rhombus, square) and measure the sides and angles

Students will follow the instructions laid out in Math Makes Sense pg. 96 & 97. Today they will make a (parallelogram, rectangle, rhombus, square) and measure the sides and angles

Select students to share their polygons with the class. Discuss the connections they made between the polygons (angles interior, sides).

Task # 9

Isosceles and right trapezoids


Students will use Geometers Sketch Pad to draw 2-D polygons.

Draw three triangles on the board (equilateral, isosceles, right). Ask the students to name and defend the name of each triangle. Today they are going to explore quadrilaterals to find one that can be drawn as right and isosceles.

Students will follow the instructions laid out in Math Makes Sense pg. 96 & 97. Today they will make an isosceles and right trapezoid. Students will have time explore but will hand in one right and an isosceles trapezoid with a side measure of 5cm. They will measure all the sides and angles.

Have students share their discovery of what right and isosceles trapezoids are. How do you know it is a right trapezoid? How do you know it is an isosceles trapezoid? What are the angles and measurements in each trapezoid?

What do the interior angles add to? What shapes make up the trapezoid? Does this fit the rule that we discovered about the interior of polygons? Does the rule work with pentagons, hexagons and octagons?

Task # 10

Mid-Point Check in

Discuss the generalization/ rule that the students discussed in the Congress the day before about the interior of polygons. Ask them to think about other rules/generalizations that they have discovered throughout the unit.

Questions:

Compare a rhombus, square, rectangle and parallelogram. Tell how a square can be considered a parallelogram, rhombus and rectangle.

Construct a right trapezoid, tell the side and angles.

Discuss how a pyramid and prism are alike and different.

Collect and mark. Give the students descriptive feedback and look for any misconceptions that they might have.

What properties do a square and rectangle, rhombus and parallelogram share? Procedural: draw a parallelogram and trapezoid using a protractor. Measure sides and angles

Task # 11 Guide to Effective Instruction

Sketch 3-D figures and construct 3-D figures from drawings

3 cubes, grid paper

Tell students that they are going to learn about drawing different perspectives of 3-D figures. Use the lesson from Guides to Effect Instr. pg. 193 - 195

Sketch Climbing Structures. Work with a partner to combine cubes and then sketch the perspectives (top, back, front, sides).

What are the similarities in the views? What are the differences? Which was easiest to draw? Why? Which would be most helpful to help build the structure?

Where are isometric drawings used? How do the shape and number of faces of orthographic drawings relate to isometric drawings?

Sub Task # 12

Guide to Effective Instruction pg. 206-207

Sketch 3-D figures and construct 3-D figures from drawings using a variety of tools

6 interlocking cubes

Tell students they will work on GSP today to draw their structures. Remind them of the different perspectives (top, back, front, sides). Students begin by using 6 different coloured interlocking cubes to build the structure provided on pg. 206 from the Guide to Effective Instruction.

Students follow the instructions on pg. 206 & 207 to create the views in GSP. Those students that finish early can create other structures with the cubes and sketch the different perspectives. Print the views if possible.

How did GSP make it easier to draw the perspectives?

What was the easiest view to draw? Why?

What was the hardest view to draw? Why?

Why do we use these views?

Sub Task #13

Guide to Effective Instruction pg. 197

Sketch 3-D figures and construct 3-D figures from drawings

6 interlocking cubes

Tell the students you have built a 3-D figure from 6 cubes. You are going to describe the structure to the class. They are going to try and build the structure congruent to yours based on the instructions. They may not ask questions. Define congruent with the students.

Give students 6 interlocking cubes. Have them build the structure you describe. Have them share their structure with a partner. Have them sketch the different views.

Have students share their structures.

Discuss what language was useful in helping them to create the structure.

What was challenging about this task?

What is the hardest view to draw?

What do you notice about the left side view and the right side view?

What do you notice about the top view?

Sub Task #14

Guides to Effective Instruction

Build 3-D models using connecting cubes, isometric sketches of different views

Review what the word congruent means from the day before. Discuss some of the language choices that were used from the day before that were helpful to build the structure.

This activity comes from Marian Smalls book, Good Questions, Great Ways to Differentiate Math, on page 89.

Students will build a shape with interlocking cubes. They can choose to build the 3-D figure shown or they can build the structure from the orthographic views given.

Give the students 10 cubes to make the structure. They can build a structure using between 6-10 cubes. The creator describes the structure from the top, front and sides using mathematical language. The imitator may not ask questions. Students then compare their structures. They then switch roles.

Have students share their structures.

Discuss what language was useful in helping them to create the structure.

What was challenging about this task?

Sub Task # 15

Optional Task

Build 3-D models using connecting cubes, isometric sketches of different views

Marian Small pg. 89

Put students into groups of 4 and give students 40 interlocking cubes. Challenge them to build as many different four cube structures as possible.

Please see lesson on page 198-199 in the Guides to Effective Instruction

Have students share their structures. Have the students pull apart the structure to show how they manipulated the pieces to fit together.

What structures were hard to create?

How did you manipulate the structures to fit?

What made you successful?

Grade 6: Geometry and Spatial Sense (Geometric Properties, Geometric Relationships)

Overall Expectations:


Sketch three-dimensional figures, and construct three-dimensional figures from drawings

Specific Expectations:

Sort and classify quadrilaterals by geometric properties related to symmetry, angles and sides, through investigation using a variety of tools (e.g., geoboards, dynamic software) and strategies (charts, Venn Diagram)

Measure and construct angles up to 180 degrees using a protractor and classify them as acute, right, obtuse and straight

Construct polygons using a variety of tools, given angle and side measurements

Build three-dimensional models using connecting cubes, given isometric sketches or different views of the structure (top, front, side)

Sketch, using a variety of tools (isometric dot paper, dynamic geometry software), isometric perspectives and different views of three-dimensional figures built with interlocking cubes

Math Language

Propertiesprism, pyramidrhombus

Congruentpolygons, figures parallelogram

Orthographic sketches or views (top, front, side)triangles: isosceles, scalene

Verticesvertical line segmentangles: acute, right, straight, obtuse

Isometric dot paperhorizontal line segmenttrapezoids: right, isosceles

Isometric perspectiveedge

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