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Name Master 3.1 Date Unit Rubric: Geometry Not Yet Adequate Adequate Proficient Excellent Reasoning; Applying concepts shows understanding of shows little understanding; may be figures and solids by: unable to: – describing and making generalizations – comparing and sorting – explaining or demonstrating relationships – describing examples – describe properties – compare and sort figures and solids – explain or demonstrate relationships – describe geometric properties in everyday experiences in everyday experiences shows some understanding (may be vague or incomplete); partially able to: – describe properties – compare and sort figures and solids – explain or demonstrate relationships – describe geometric properties in everyday experiences shows understanding; able to clearly and appropriately: – describe properties – compare and sort figures and solids – explain or demonstrate relationships – describe geometric properties in everyday experiences shows thorough understanding; in various contexts, able to precisely and effectively: – describe properties – compare and sort figures and solids – explain or demonstrate relationships – describe geometric properties in everyday experiences Accuracy of procedures identifies and classifies lines, angles, figures, and solids according to their attributes makes frequent minor errors in: – identifying and classifying lines, angles, figures, and solids – constructing and relating nets makes few errors in: makes no errors in: – identifying and classifying lines, angles, figures, and solids – identifying and classifying lines, angles, figures, and solids – constructing and relating nets – constructing and relating nets may be unable to use appropriate strategies to investigate and create geometric problems with limited help, uses some appropriate strategies to investigate and create geometric problems; partially successful uses appropriate strategies to investigate and create geometric problems successfully uses appropriate, often innovative strategies to investigate and create geometric problems successfully explains reasoning and procedures clearly unable to explain reasoning and procedures clearly partially explains reasoning and procedures explains reasoning and procedures clearly explains reasoning and procedures clearly, precisely, and confidently uses appropriate geometric terms and symbols (e.g., names of lines, figures, and solids) uses few appropriate mathematical terms or symbols appropriately uses some appropriate mathematical terms and symbols uses appropriate mathematical terms and symbols uses a range of appropriate mathematical terms and symbols with precision constructs and relates nets to 3-D solids makes major errors in: – identifying and classifying lines, angles, figures, and solids – constructing and relating nets Problem-solving strategies uses a range of appropriate strategies to investigate and create geometric problems Communication Copyright © 2004 Pearson Education Canada Inc. 53 Name Master 3.2 Date Ongoing Observations: Geometry The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning. STUDENT ACHIEVEMENT: Geometry Student Reasoning; Applying concepts Accuracy of procedures Problem solving Communication Describes properties Explains relationships Offers reasoned predictions, and generalizations Identifies and classifies lines, angles, figures, and solids Constructs and relates nets to solids Solves/creates problems involving figures and solids (including constructions) Uses mathematcial language and symbols (e.g., attributes) Explains procedures and solutions Use locally or provincially approved levels, symbols, or numeric ratings. 54 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.3 Date Performance Assessment Rubric: Under Construction Not Yet Adequate Adequate Proficient Excellent unable to explain or apply: – attributes of figures, including angles – congruence – relationships between figures and solids partially explains, and applies: – attributes of figures, including angles – congruence – relationships between figures and solids explains and applies: – attributes of figures, including angles – congruence – relationships between figures and solids thoroughly and effectively explains and applies: – attributes of figures, including angles – congruence – relationships between figures and solids makes major errors in: – naming objects and figures – sketching figures – describing angles and lines – constructing nets makes frequent minor errors in: – naming objects and figures – sketching figures – describing angles and lines – constructing nets makes few errors in: – identifying objects and figures – sketching figures – describing angles and lines – constructing nets rarely makes errors in: – identifying objects and figures – sketching figures – describing angles and lines – constructing nets uses few effective strategies to: – design the castle and build its model; may be unworkable – incorporate the required figures into window design uses some appropriate strategies, with partial success, to: – design the castle and build its model; may have major flaws – incorporate the required figures into window design uses appropriate and successful strategies to: – design the castle and build its model; may have some flaws – incorporate the required figures into window design uses innovative and effective strategies to: – design the castle and build its model; may have minor flaws – incorporate the required figures into window design explains design clearly unable to explain design clearly partially explains design explains design clearly explains design clearly, precisely, and confidently uses appropriate terms and symbols related to geometric properties and relationships (e.g., names of figures and solids, congruent, degrees) uses few appropriate mathematical terms or symbols uses some appropriate mathematical terms and symbols uses appropriate mathematical terms and symbols uses a range of appropriate mathematical terms and symbols with precision Reasoning; Applying concepts shows understanding by demonstrating, explaining and applying concepts in geometry, including: – attributes of figures, including angles – congruence – relationships between figures and solids (e.g., castle, wall, and sketch) Accuracy of procedures accurately: – identifies objects and figures – sketches a variety of figures (windows), including congruent figures, on graph paper – describes angles – constructs nets Problem-solving strategies uses appropriate strategies to design: – a castle model that can be built from materials – windows that include congruent figures, and examples of the figures studied Communication Copyright © 2004 Pearson Education Canada Inc. 55 Name Master 3.4 Date Unit Summary: Geometry Review assessment records to determine the most consistent achievement levels for the assessments conducted. Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying levels for each achievement category. Most Consistent Level of Achievement* Strand: Shape and Space: Geometry Reasoning; Applying concepts Accuracy of procedures Problem solving Communication Ongoing Observations Strategies Toolkit (Lesson 11) Work samples or portfolios; conferences Show What You Know Unit Test Unit Problem: Under Construction Achievement Level for reporting *Use locally or provincially approved levels, symbols, or numeric ratings. Self-Assessment: Comments: (Strengths, Needs, Next Steps) 56 Copyright © 2004 Pearson Education Canada Inc. OVERALL Name Master 3.5 Date To Parents and Adults at Home … During the next three weeks, your child’s class will be exploring geometry. Through daily activities, your child will explore the relationship between flat, two-dimensional figures and solid, three-dimensional objects in the world around them. In this unit, your child will: Construct congruent figures. Explore angles. Recognize and identify horizontal, vertical, perpendicular, intersecting, and parallel lines. Sort and classify figures. Explore solids. Build nets. Geometry is an important part of a student’s mathematical experience. Geometry provides students with a strong link between the mathematics they learn in the classroom and the real world. Here are some suggestions for activities to do at home. Look around the kitchen for different objects that have the same shape as a solid. For example, a can of soup is a cylinder, a cereal box is a rectangular prism, and an orange is a sphere. Find objects that have the same shape, but have different sizes. For example, drinking glasses often have the same shape, but come in different sizes. Copyright © 2004 Pearson Education Canada Inc. 57 Name Master 3.6 Figures 1 58 Copyright © 2004 Pearson Education Canada Inc. Date Name Master 3.7 Date 6-Division Protractor Copyright © 2004 Pearson Education Canada Inc. 59 Name Master 3.8 Quadrilaterals 1 60 Copyright © 2004 Pearson Education Canada Inc. Date Name Master 3.9 Date Quadrilaterals 2 Copyright © 2004 Pearson Education Canada Inc. 61 Name Master 3.10 Quadrilaterals Venn Diagram 62 Copyright © 2004 Pearson Education Canada Inc. Date Name Master 3.11 Date Figures 2 Copyright © 2004 Pearson Education Canada Inc. 63 Name Master 3.11b Figures 2 64 Copyright © 2004 Pearson Education Canada Inc. Date Name Master 3.12 Date Face-Off Game Cards Copyright © 2004 Pearson Education Canada Inc. 65 Name Master 3.13a Date LESSON 8A: Exploring Nets of Solids EXPLORE You will need a cereal box or a Toblerone box and a pair of scissors. Cut along the edges of the box until you can lay it flat. Place the flattened box on a large piece of paper. Trace the box and cut out the tracing. Use a ruler to draw the fold lines on the tracing. Write about the figures you see. Fold the tracing along the fold lines. Show and Share Share your tracing with another pair of students. How are your tracings the same? How are they different? CONNECT A cutout that we can fold to form a model of a solid is called a net. We can make a net for a solid from its faces. The faces must be arranged so that they can be folded to make the solid. There are different ways to arrange the faces to make a net. This rectangular prism has 2 congruent square faces and 4 congruent rectangular faces. Here are the steps to make a net for this prism. Trace around a square face 2 times. 66 Copyright © 2004 Pearson Education Canada Inc. Name Date Master 3.13b Trace around a rectangular face 4 times. Place the rectangles as shown. Tape the longer sides together. Tape a square to each end of one rectangle. To check that this is a net, fold it to make a rectangular prism. Here is another net for the same rectangular prism. One of the congruent squares is in a different position. Copyright © 2004 Pearson Education Canada Inc. 67 Name Date Master 3.13c PRACTICE 1. Which of these pictures are nets of a cube? How do you know? a) b) c) 2. How many different nets can you make for a cube? Draw each net on grid paper. How do you know all of them are different? 3. Design and draw a net for: a) a square pyramid b) a triangular pyramid c) a triangular prism 4. The net for a solid has 3 pairs of congruent rectangles. a) What kind of solid is it? How do you know? b) Draw a net for the solid. 5. This is part of a net for a rectangular prism. Copy this figure on grid paper. Draw the other faces to complete the net. How many different ways can you do this? Show your work. Reflect Draw a net that you could use to make a box to hold chocolates. What kind of solid will your net make? Explain how you made your net. 68 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.14 Date Additional Activity 1: Look Out for Angles Work with a partner. You will need old magazines, scissors, glue, a card with a square corner, and heavy paper. Look for angles in the magazines. Cut out each angle. Use the card to measure the angles as less than, equal to, or greater than a right angle. Sort the angles by these attributes: • Has all angles less than a right angle. • Has all right angles. • Has all angles greater than a right angle. Glue the angles on heavy paper to make an angle collage. Take It Further: Draw a picture. Include items with right angles, angles less than a right angle, and angles greater than a right angle. Copyright © 2004 Pearson Education Canada Inc. 69 Name Master 3.15 Date Additional Activity 2: Congruent Figures Work with a partner. You will need a ruler, triangular or square grid paper, scissors, glue, and heavy paper. Draw 10 four-sided figures each. Write your initials on each figure. Cut out each figure. Place your figures and your partner’s figures on a table. Look for congruent figures. If you find no congruent figures, choose one figure and draw a figure congruent to it on grid paper. Glue each pair of congruent figures on heavy paper. Write how you know the figures in each pair are congruent. Take It Further: Repeat the activity. Draw figures that are not four-sided figures. 70 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.16 Date Additional Activity 3: Go Fish for Faces Play with a partner. You will need 36 Face-Off game cards (Master 3.12) and models of solids. Each card shows the face of a solid. The goal is to use all your cards to make solids. How to play: 1. Decide who will be the dealer. The dealer deals 6 cards to each player. Players do not show their cards. The deck of remaining cards is placed face down. 2. Players take turns. Player A looks at his cards. If the cards show the faces of a solid, he places the cards face up and says the name of the solid. 3. If Player A cannot make a solid with his cards, he asks Player B for a card he needs to complete a solid. If Player B has this card, she gives it to Player A. If Player B does not have this card, she tells Player A to “go fish.” Player A takes a card from the deck. 4. Player B has a turn. 5. Play continues until one player has no cards left or until all the cards have been used. The first player to use all his cards, or the player with the fewer cards left when all the cards have been used, is the winner. Take It Further: Play the game again. Add cards that show different faces, such as hexagons and pentagons. Copyright © 2004 Pearson Education Canada Inc. 71 Name Master 3.17 Date Additional Activity 4: Prisms and Pyramids Work with a partner. You will need models of various prisms and pyramids, and 4-column charts. Select 2 different prisms. Name them. Work together. Look at one of the prisms. Count the number of faces, edges, and vertices. Record your findings in a table. Count the number of faces, edges, and vertices on the other prism. Record your findings. Tell how the prisms are similar. Tell how the prisms are different. Select 2 different pyramids. Name them. Look at one of the pyramids. Count the number of faces, edges, and vertices. Record your findings in a chart. Count the number of faces, edges, and vertices on the other pyramid. Record your findings. Tell how the pyramids are similar. Tell how the pyramids are different. Take It Further: Choose 1 prism and 1 pyramid. Tell how the models are alike and how they are different. 72 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.18 Date Step-by-Step 1 Lesson 1, Question 4 Use a geoboard or square dot paper. Make each figure. Join the dots to divide each figure. Check that you understand the meaning of “congruent.” Step 1 Divide this figure into 3 congruent triangles. Hint: Make each triangle 2 units long at the bottom. Step 2 Divide this figure into 3 congruent rectangles. Hint: Make 1 side of each rectangle 2 units long. Step 3 Divide this figure into 4 congruent shapes. Hint: Make 4 rectangles. Which figure can you divide in different ways? _______________________________________________________ Why can you not divide the other figures in different ways? _______________________________________________________ Copyright © 2004 Pearson Education Canada Inc. 73 Name Master 3.19 Date Step-by-Step 2 Lesson 2, Question 6 Step 1 Use a ruler and draw a line. Mark one end of the line with a dot. Step 2 Use a ruler to draw another line that starts at the dot. Step 3 Use a 6-division protractor transparency to measure your angle. Place the baseline of the protractor on one line. Place the centre mark of the protractor on the dot. Count from 0 along the protractor until you reach the other line. Read and record the angle’s measure. _______________________________________________________ Step 4 Use the words baseline, arm, vertex, and degrees to explain what you did. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ 74 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.20 Date Step-by-Step 3 Lesson 3, Question 4 Step 1 Look at the 90º mark on a protractor. What kind of angle measures 90º? _______________________________________________________ Step 2 Use a ruler to draw an angle you think is less than 90º. Step 3 Use a ruler to draw an angle you think measures 90º. Step 4 Use a ruler to draw an angle you think is greater than 90º. Step 5 Use a protractor to check that each angle is the correct size. Copyright © 2004 Pearson Education Canada Inc. 75 Name Master 3.21 Date Step-by-Step 4 Lesson 4, Question 6 Step 1 List 3 attributes of parallelograms. _______________________________________________________ _______________________________________________________ _______________________________________________________ Step 2 Use a ruler and draw a parallelogram on the dots. Step 3 Write something about a parallelogram that is never true. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ Step 4 Write something about a parallelogram that is sometimes true. _______________________________________________________ _______________________________________________________ _______________________________________________________ Step 5 Write something about a parallelogram that is always true. _______________________________________________________ _______________________________________________________ _______________________________________________________ 76 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.22 Date Step-by-Step 5 Lesson 5, Question 4 Step 1 List some attributes of a square. Hint: Think about angles and sides. _______________________________________________________ _______________________________________________________ Why is this quadrilateral not a square? Step 2 List some attributes of a rectangle. Hint: Think about angles and sides. _______________________________________________________ _______________________________________________________ Why is this quadrilateral not a rectangle? Step 3 List some attributes of a rhombus. _______________________________________________________ _______________________________________________________ Why is this quadrilateral not a rhombus? Step 4 List some attributes of a kite. _______________________________________________________ _______________________________________________________ Why is this quadrilateral not a kite? Copyright © 2004 Pearson Education Canada Inc. 77 Name Master 3.23 Date Step-by-Step 6 Lesson 6, Question 4 Use the “Attributes of Quadrilaterals” chart in your book to solve these riddles. All the figures are quadrilaterals. Write down all the different figures you find for each riddle. a) I do not have any right angles. All my sides are the same length. What am I? _____________________________________________________ b) All 4 of my angles are right angles. I have 2 pairs of equal sides. What am I? _____________________________________________________ c) I have 2 parallel sides. I have 2 right angles. What am I? _____________________________________________________ d) Make up your own riddle by filling in two or more of these phrases: I have _____ parallel sides. I have _____ right angles. I have _____ opposite sides equal. I have _____ adjacent sides equal. Trade riddles with a classmate. Solve your classmate’s riddle. 78 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.24 Date Step-by-Step 7 Lesson 7, Question 3 Step 1 What makes 2 figures similar? Hint: Think about the lengths of sides and the sizes of angles. _______________________________________________________ _______________________________________________________ Use words and pictures to show your answer for each of these questions. Step 2 Are all squares similar? ________________________________ ________________________________ ________________________________ Step 3 Are all rectangles similar? ________________________________ ________________________________ ________________________________ Step 4 Are all triangles similar? ________________________________ ________________________________ ________________________________ Copyright © 2004 Pearson Education Canada Inc. 79 Name Master 3.25 Date Step-by-Step 8 Lesson 8, Question 4 Step 1 Use words and pictures. Explain the difference between a pyramid and a prism. ______________________________ ______________________________ ______________________________ Step 2 Are these the faces of a pyramid or a prism? ____________________ What is the name of the solid? _______________________________ How do you know? ________________________________________ _______________________________________________________ _______________________________________________________ Step 3 Are these the faces of a pyramid or a prism? ____________________ What is the name of the solid? _______________________________ How do you know? ________________________________________ _______________________________________________________ _______________________________________________________ 80 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.26 Date Step-by-Step 8A Lesson 8A, Question 5 This is part of a net for a rectangular prism. Step 1 How many faces make up a rectangular prism? _________________ How many faces do you need to add to this figure to make a rectangular prism? ________________________________________ Step 2 Copy the figure on grid paper. Use the same paper and sketch the faces you need to add. Step 3 Cut out the figure and the faces. Place the cutouts together to make a net for a rectangular prism. Use tape to join the cutouts. Can you fold your creation to make a rectangular prism? _____________________________________________________________ Step 4 Sketch the net you made. Cut apart your net, and re-arrange the pieces to make another net. Sketch this net. Copyright © 2004 Pearson Education Canada Inc. 81 Name Master 3.27 Date Step-by-Step 9 Lesson 9, Question 4 Think about how to sort solids using faces, edges, and vertices. Think about how to sort solids using the shapes of their bases. Complete each sentence. Use “all,” “some,” or “no” to make each sentence true. Explain how you know the sentence is true. Step 1 _________________ rectangular prisms have 6 vertices. This is true because _______________________________________________________ Step 2 _________________ cubes are rectangular prisms. This is true because _______________________________________________________ Step 3 _________________ rectangular prisms are cubes. This is true because _______________________________________________________ Step 4 _________________ triangular prisms have 5 congruent faces. This is true because _______________________________________________________ 82 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.28 Date Step-by-Step 10 Lesson 10, Question 3 Step 1 Make a list of the solids you know. Solid Edges Vertices Step 2 Record the number of edges and the number of vertices in each solid. Step 3 Use Plasticine and drinking straws to make skeletons for some of these solids. Look for patterns. Step 4 Underline the solids in your list that have skeletons with 20 or fewer edges, and 6 or fewer vertices. Copyright © 2004 Pearson Education Canada Inc. 83 Name Master 3.29 Date Unit Test: Unit 3 Geometry Part A Use one tan Pattern Block. 1. Measure the side lengths of each figure. Label each angle as a right angle (R), less than a right angle (L), or greater than a right angle (G). Figure Side lengths A B C 2. Which figures in Question 1 are congruent? Explain your answer. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 3. Name the figure in Question 1. What are the attributes of this figure? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 84 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.29b Date Unit Test continued Part B 4. This hexagon is one face of a solid. a) Sketch the other faces if this solid was a hexagonal prism. b) Sketch the other faces if this solid was a hexagonal pyramid. c) Look at the figures you sketched in parts a and b. Which figures are congruent? How do you know? __________________________________________________________ __________________________________________________________ __________________________________________________________ Copyright © 2004 Pearson Education Canada Inc. 85 Name Master 3.29c Date Unit Test continued Part C 5. Use 1-cm grid paper. a) Draw a rectangle. b) Name all the solids you know that have a rectangular face. __________________________________________________________ __________________________________________________________ __________________________________________________________ c) Draw the faces of each solid you named. d) Give an example of an object that matches each solid you named in part b. __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ 6. Use triangular dot paper. a) Draw a net for a triangular pyramid and a net for a triangular prism. b) Describe how your nets are the same and how they are different. __________________________________________________________ __________________________________________________________ __________________________________________________________ 86 Copyright © 2004 Pearson Education Canada Inc. Name Master 3.30 Sample Answers Unit Test – Master 3.29 Part A 1. Figure Side lengths A 1 cm by 1 cm by 1 cm by 2 cm B 2 cm by 2 cm by 2 cm by 4 cm C 1 cm by 1 cm by 1 cm by 2 cm 2. Figures A and C are congruent. They have the same size and shape. 3. All of the figures are trapezoids. A trapezoid has one pair of parallel sides. Part B 4. a) Date b) Part C 5. a) Student should draw a rectangle on 1-cm grid paper. b) Triangular prism, rectangular prism, rectangular pyramid c) Student should draw the appropriate number of faces needed to form solids named in part b. (See page 101 in Student Edition.) d) Toblerone bar, cereal box, tent 6. a) Students should draw a net consisting of 4 congruent triangles that will fold into a triangular pyramid, and a net consisting of 3 congruent rectangles and 2 congruent triangles arranged so that it will fold into a triangular prism. b) The nets are the same because they both have triangular bases. They are different because the pyramid has 1 triangular base and the prism has 2. The pyramid has 4 faces, 6 edges, and 4 vertices. The prism has 5 faces, 9 edges, and 6 vertices. c) All of the rectangles are congruent; all of the triangles are congruent. The hexagon is regular. Copyright © 2004 Pearson Education Canada Inc. 87 Name Master 3.38 Date Curriculum Focus Activity: Exploring Lines A horizontal line goes left and right. A vertical line goes up and down. Two lines that cross at a point are intersecting lines. Two lines that intersect at right angles are perpendicular lines. Two lines that never meet are parallel lines. PRACTICE 1. Draw: a) a pair of parallel lines that are vertical b) a pair of intersecting lines that are not perpendicular 2. Look at these letters: A B D F H K L M N T V W X Y Z Which letters have: a) 2 pairs of parallel lines? b) just 1 pair of perpendicular lines? c) 1 pair of parallel lines? d) just 1 horizontal line? e) just 1 vertical line? f) 1 pair of intersecting lines? 3. Use dot paper. Draw a figure with: a) 2 pairs of parallel sides b) 1 pair of perpendicular sides 4. Find a black and white picture in a magazine or newspaper. a) Colour a horizontal line red. b) Colour a vertical line orange. c) Colour 2 other lines that are perpendicular blue. d) Colour 2 different lines that are intersecting green. e) Colour 2 different lines that are parallel yellow. 88 Copyright © 2004 Pearson Education Canada Inc. Extra Practice Masters 3.31–3.37 Go to the CD-ROM to access editable versions of these Extra Practice Masters. Copyright © 2004 Pearson Education Canada Inc. 89