Reason with shapes and their attributes.

Grade 3 Geometry and Perimeter SDadfa;sdklfjas;Unit Overview Reason with shapes and their attributes. 1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Day 1: Investigations Unit 4 Session 3.1 Building Triangles Day 2: Investigations Unit 4 Session 3.3 Squares, Rectangles, and Other Quadrilaterals Although it is not required for students to name acute, obtuse, and right angles, this lesson will help students use appropriate language as they categorize quadrilaterals by attributes. During the introduction, hold up the triangles from yesterday with the right angle. Ask students what they notice about the angle in the triangle and the angles in the rectangle and square. Skip 2B LogoPaths Activity: Feed the Turtle as this is 4 th grade angle work. *Keep one or two examples of a triangle with a right angle to use Day 2. The discussion Squares and Rectangles is vital to this session. When discussing the shapes of the corners, use right or square angle as a reference. Day 3: Investigations Unit 4 Day 4 Day 5 Session 3.4 Right Angles and Not-Right Angles This lesson will help students begin to see different categories of quadrilaterals. More Quadrilateral work Not quadrilaterals Instead of Activity 2: Finding Angles Tell students today they will be creating quadrilaterals that are not rectangles or squares. As students work, look for some examples of a rhombus (you will want to use these during the discussion). Discussion: Hold up the examples of rhombuses. Ask, What is the same about these quadrilaterals? What is different? Next, put up an example of a rectangle and a rhombus, ask students to think, pair, share about how these quadrilaterals are the same and how they are different. Create an anchor chart as students share to compare rectangles and rhombus (how they are the same, how are they different see example on Investigations page 122). Create a second chart in the same manner comparing squares and rhombuses. See exit ticket (attached) Shapes culmination The Greedy Triangle Intro trapezoid. Then have students sort quadrilaterals Day 6 Day 7 Day 8 Day 9 Day 10 Measuring Around Ordering shapes by Mystery Perimeters shapes with square perimeter and intro logopaths tiles and centimeter Missing Measuring cubes LogoPaths Perimeters of building shapes sab p.17

Day 3 Exit Ticket Name: Like Me, Like Me Not Both of these shapes have 4 sides and 4 corners. 1. What is another attribute that they have in common? 2. Describe an attribute that is different between the two shapes above. Day 3 Exit Ticket Name: Like Me, Like Me Not Both of these shapes have 4 sides and 4 corners. 1. What is another attribute that they have in common? 2. Describe an attribute that is different between the two shapes above.

Reason with shapes and their attributes. 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Materials: Defining Quadrilaterals overhead or record on poster Venn Diagram (sorting circles) for each pair of studentsmake out of large construction paper or string quadrilateral set (attached) What s the Rule? Exit ticket Day 4: Sorting Quadrilaterals Emphasized Standards for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others 5. Use appropriate tools strategically. 6. Attend to precision. Words that you should hear students using in mathematical conversations: corner (angle) quadrilateral opposite sides equal (congruent) opposite sides won t meet (parallel) Ten Minute Math: Practicing Place Value: Write 538 on the board and have students practice saying it to a partner. Make sure all students can read, write, and say this number correctly. Ask students to find and sketch 5-6 different ways to make 538 using only strips of 10 and single stickers. Collect a few examples and ask students how they found their answers. Ask all students, Did anyone notice a pattern? Before: Defining Quadrilaterals. Have students look closely at the rhombuses and copy them in their math notebook. Then have students record observations about rhombuses. Repeat with squares. Next, ask students what would need to be done to this rhombus to make it a square? Why is there a square in the group of rhombuses? After students have had some time to think and write independently, have them get into groups of 4 and create a statement: For a rhombus to become a square During: Yesterday, we spent some time sorting quadrilaterals using different attributes (re-visit anchor chart). Today, we are going to use Venn Diagrams to sort quadrilaterals. In a Venn Diagram all of the shapes in a circle follow the same rule. Shapes in the part that overlap follow the rules in both circles. Today you are going to continue sorting quadrilaterals using more than one attribute. You will choose two attributes from our anchor chart. Place shapes in the circle that matches the attributes you selected. Remember to place shapes that have both attributes in the part of the circle that overlap so that it is in both circles. If you have time, try to repeat with two new attributes. Partner groups sort quadrilaterals using Venn Diagrams and attributes identified yesterday. After: One group had the attributes all opposite sides will not meet and at least 1 square corner Ask students, where should they put the parallelogram (k), the right trapezoid (m), and the square (a)? Ask students to explain how they decided to put it where they did in the Venn Diagram. Evaluation: What s the Rule

Day 4: Before Defining Quadrilaterals Directions: Look closely at the shapes in each group. What do all of the shapes in the group have in common? What do you notice about the length of the sides? What do you notice about the corners? Will the opposite sides ever meet each other? These are all rhombuses. Observations about rhombuses These are all squares. Observations about squares. When does a rhombus become a square? MATHEMATICS GRADE 3 UNIT 5: Geometry Georgia Department of Education Dr. John D. Barge, State School Superintendent May 2012 All Rights Reserved

Day 4: Exit Ticket What s the Rule? Name: Draw each shape where it belongs in the Venn Diagram. A B C D E Opposite Sides Equal No Square Corners All All opposite sides equal in length No square angles (corners)

Reason with shapes and their attributes. 3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Day 5: Properties of Quadrilaterals Emphasized Standards for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. Materials: Defining Quadrilaterals poster or overhead Triangle, dot or graph paper (students should choose which to use) to create polygons Quadrilateral Riddles Square Disguise Exit Ticket Words that you should hear students using in mathematical conversations: corner (angle) quadrilateral sides opposite sides equal (congruent) opposite sides won t meet (parallel) Ten Minute Math: Practicing Place Value: Say one hundred twenty-three and ask students to write the number. Make sure all students can read, write, and say this number correctly. Ask students to solve these problems mentally what is 123+20? 123+40? 123+60? 123+200? 123+400? 123+600? Write each answer on the board. Ask students to compare each sum or difference with 637 Which places have the same digits? Which do not? Why? If time remains, pose additional similar problems using 261 and 198. Before: Defining Quadrilaterals. Have students look closely at the rectangles and copy them in their math notebook. Then have students record observations about rectangles. Repeat with trapezoids. Next, ask students what would need to be done to a trapezoid to make it a rectangle? After students have had some time to think and write independently, have them get into groups of 4 and create a statement: For a trapezoid to become a rectangle During: Read the book the Greedy Triangle to introduce students to shapes that aren t quadrilaterals or rectangles. Ask students, What shapes did the triangle want to turn into? What did the triangle have to do to become a square A hexagon? (Students have had experiences with many of these shapes in 1 st and 2 nd grade so this lesson is just a review). The work in this lesson is designed to help students not only remember these shapes, but to also see different representations of each of these shapes. List all of the shapes in the Greedy triangle on a chart/poster and ask students what s different about each shape. Tell students that today they will be creating shapes using triangle, dot or graph paper. After: Have students bring their drawings to the discussion area. Ask students to quickly hold up their work and point to a pentagon. Ask, How do you know all of these shapes are pentagons? Draw a regular pentagon (all sides the same length and all angles equal) and a square on the board. Ask students, What attribute does the pentagon share with the square? Students may say, all straight lines, closed figure. Tell students to look closely at the length of the sides of the pentagon. Students should notice that all the sides are the same length. Say, find shapes on your paper that would match the attribute all sides the same length. Evaluation: Square Disguise Exit Ticket

Day 5: Before - Defining Quadrilaterals These are all rectangles. Observations about rectangles. These are all trapezoids. Observations about trapezoids. What would need to be done to a trapezoid to make it a rectangle? MATHEMATICS GRADE 3 UNIT 5: Geometry Georgia Department of Education Dr. John D. Barge, State School Superintendent May 2012 All Rights Reserved

Day 5: Shapes that aren t Triangles or quadrilaterals Name: Creating Polygons Directions: Use the triangle paper below to create 2-3 different examples of each of the following: triangles, quadrilaterals, pentagons, hexagons, octagons, decagons. Label each shape.

Name: Creating Polygons Directions: Use the dot paper below to create 2-3 different examples of each of the following: triangles, quadrilaterals, pentagons, hexagons, octagons, decagons. Label each shape.

Day 5 Exit Ticket

Introduce Quadrilateral Riddles. Show the first part of the riddle: If I were a rhombus I would have 4 equal sides and 4 angles (corners). But I would not have 4 square corners, because that would be a and have students turn and talk with a partner to determine the missing shape. Re-read The Greedy Triangle. Explain to students that they will be creating their own Shape-Shifter book.. Provide the following list of shapes they must use in their book: Square, Pentagon, Rhombus, Octagon, Trapezoid, Rectangle Explain to students that they need to use all of the shapes above, but can use them in any order. They may also add more shapes if they choose. During: As students work, notice the explanations they use to change their shapes from one to another. Prompt students to use precise language. Students should mention the lengths of sides, size of angles and number of sides as they move from shape to shape. Students create their book with a partner or independently. If time permits, have some students create Quadrilateral riddles to use throughout the year. After: Choose a discussion topic based on the needs of your class. Evaluation: students complete 1 quadrilateral riddle. Name Date Quadrilateral Riddle Choose two quadrilaterals that are similar but have at least one difference. The first three lines of the riddle refer to one quadrilateral and its attributes. The last two lines of the riddle refer to the second quadrilateral and its attribute(s) that make it different from the first quadrilateral. Use specific math vocabulary to describe the attributes. If I were a I would have and I would have. But I would not have because that would be a! Optional: try another riddle using two new quadrilaterals. If I were a

I would have and I would have. But I would not have because that would be a! MATHEMATICS GRADE 3 UNIT 5: Geometry Georgia Department of Education Dr. John D. Barge, State School Superintendent May 2012 Page 56 of 56 All Rights Reserved Day 7: Measuring quadrilaterals Cluster: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Materials: centimeter cubes and square tiles electrical or painters tape (Create 8 shapes on the floor that have sides that are whole number amounts 4 to be measured with square tiles and 4 to be measured with centimeter cubes). What s the Perimeter? Recording sheet What s the Perimeter? Exit ticket Emphasized Standards for Mathematical Practice: 4. Model with mathematics 5. Use appropriate tools strategically. 6. Attend to precision. Words that you should hear students using in mathematical conversations: sides triangle, quadrilateral, pentagon, hexagon, octagon, sum perimeter length centimeter, inches, feet Ten Minute Math: Quick Images: 2D Show images 11 and 15 (one at a time from Quick Images T53-T54 and follow the procedure for the basic routine. For each image, students discuss how they drew their figures, including any revisions they made after each viewing. Ask students How did you remember the parts of the image? What did you notice about the relationship of the parts of the image? What helped you remember the whole image, so you could draw your design? For both shapes, make sure students are using precise language (smaller than square corners, opposite sides equal, etc).

Before: What are some of the attributes that we have been using to put polygons into groups? (equal sides, square corners, opposite sides never meet) Today, we are going to talk about another attribute of polygons. Sometimes mathematicians want to know how far it is the length.around the outside of a polygon. When mathematicians find the length around the outside of a polygon, they Shape Name of Polygon Equation Perimeter say they are finding the perimeter. Today, we are going to find the perimeter around a variety of shapes. How do you think a mathematician might find the length around the outside of a shape? Today, we are going to use centimeter cubes, 1 inch square tiles, and 1-foot rulers to measure the perimeter of shapes. Let s practice measuring the perimeter of a polygon using square tiles. (Model measuring and recording the perimeter of a polygon emphasizing finding the length of each side, no gaps or overlaps, and then finding the sum of the sides). Give directions for how students will visit each center 2 (centimeters, inches, feet) During: Students 3 measure and record the perimeter of polygons using centimeter cubes and inch tiles. (As students work, listen for strategies that students use. Some students might notice that they don t need to measure both of the opposite sides of a rectangle because they are congruent. Other students may notice that for a triangle it is the sum of 3 sides, a quadrilateral 4 sides, 4 etc. If students are noticing those strategies, have them share those strategies with class as part of the discussion). After: How is measuring perimeter like and different from measuring a line? (Also have students share interesting strategies that may emerge as they work-see During). Evaluation: What s the Perimeter? Exit Ticket What s the Perimeter? Recording Sheet Measuring in Inches (Use Square Tiles) Measuring in Centimeters (Use Centimeter Cubes) Shape Name of Polygon Equation Perimeter 5 6 7 8

Name: Use square tiles to find the perimeter of these shapes. What s the Perimeter? Exit Ticket Name: Use square tiles to find the perimeter of these shapes. What s the Perimeter? Exit Ticket

Day 8: Ordering Shapes by Perimeter Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Materials: Ordering Shapes by Perimeter; Student activity book pages 12-13 string Centimeter cubes Inch tiles Emphasized Standards for Mathematical Practice: 4. Model with mathematics 5. Use appropriate tools strategically. 6. Attend to precision. Words that you should hear students using in mathematical conversations: Sides length triangle, quadrilateral, pentagon, hexagon, octagon, sum perimeter Ten Minute Math: Practicing Place Value: Say six hundred thirty-seven and ask students to write the number. Make sure all students can read, write, and say this number correctly. Ask students to solve these problems mentally what is 637+40? 637-30? 637+60? 637+100? 637+300? 637-200? Write each answer on the board. Ask students to compare each sum or difference with 637 Which places have the same digits? Which do not? Why? If time remains, pose additional similar problems using 673 and 525. Before: Yesterday, we measured the perimeter of some shapes in the room. What is the perimeter of a shape? Today, we ll be looking at the perimeter of some more shapes. Have students take out SAB pages 12-13. Ask students to predict the order of their perimeters from shortest to longest and record it on their sheets. Tell students they may choose an appropriate math tool to use to measure each shape (centimeter cubes, color tiles, paper clips, string, etc.) to determine the perimeter of each shape and complete the directions on the pages. See Investigations page 47 for more details on this work. During: As students work, watch how they approach finding the perimeter of the circle. If they struggle, suggest using string to find the perimeter, then measuring with centimeter cubes or inch tiles. Ask students, How do your predications match with your actual measurements? We re there any suprises? After: Ask students, What happened when you compared your predicted order to the order of the perimeters after you measurement? Did anything surprise you about the perimeters of these shapes? (See teacher/math notes page 51-52) Say, Let s Stretch out the perimeters of these shapes into straight lines so that we can have another way to compare them. Using a string, measure each shape. Then, tape each string to the board and label (perimeter of the star, perimeter of the circle, etc). Evaluation: Finding Perimeter Exit Ticket

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Day 9: Mystery Perimeters Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Emphasized Standards for Mathematical Practice: 4. Model with mathematics 5. Use appropriate tools strategically. 6. Attend to precision. Materials: Copies of Mystery Perimeter Warm-Up (1 per pair of students) Words that you should hear students using in mathematical conversations: sides triangle, quadrilateral, pentagon, hexagon, octagon, sum perimeter length Ten Minute Math: Go to www.discoveryeducation.com and log in (ALL CMS teachers have a discovery education log-in. See your math/literacy facilitator if you have trouble). Click the following link http://app.discoveryeducation.com/player/view/assetguid/e3755740-277a-4b96-bd61-3f58ca647274 (click introduction video). This video shows perimeter as a fence and references the shape. After watching the video, ask students Do you have to measure every side of a rectangle to find the perimeter? Turn and talk with a partner. Ask for a few student responses. Finally, click the NEXT arrow on the video to play the video Warm Up. This video shows why it s not necessary to measure all sides of a rectangle. Ask students, Can you think of another shape where you wouldn t need to measure all of the sides to find the perimeter? Before: http://app.discoveryeducation.com/player/view/assetguid/e3755740-277a-4b96-bd61-3f58ca647274 Click video Rectangles and Perimeter this video shows an irregular shape and gives students a strategy for finding unknown side lengths. Click the NEXT arrow to show the FIRST 15 SECONDS ONLY of the video The Test. Give each pair of students the Mystery Perimeter Warm-Up (this is the same perimeter that is shown on the video The Test. Tell students you are going to give them some time to determine the missing side lengths and the perimeter of the shape. Remind students they may use tools that will help them (graph paper, square tiles, centimeter cubes, or any other appropriate math tool). During: Give students about 15-20 minutes to complete this task. If students struggle, suggest they re-create the shape using a math tool and/or divide the shape into rectangles. Once most students have gotten a good start on the task, interrupt them to ask several students to share their strategy by asking, How are you starting to solve this task? The focus here is on entry strategies, not the answer. If students finish early, ask them to create a mystery perimeter for their partner to solve. They may use paper or another math tool. After: Ask students to share how they determined the missing lengths in the shapes. Then have them share how they determined the perimeter of the entire shape. Be sure to have students who share write their equations on the board for all students to discuss. Evaluation: Teachers choice based on student needs.

MYSTERY PERIMETER WARM-UP 20 m 10 m 5m 30 m 10 m MYSTERY PERIMETER WARM-UP 20 m 10 m 5m 30 m 10 m

Day 10: Geometry Assessment and Perimeter Problems Cluster: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Emphasized Standards for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 6. Attend to precision. 7. Look for and make use of structure. Mathematical Goal: Students will solve real-world and complex geometric perimeter problems by applying geometric and measurement concepts. Materials: Perimeter Problems- 1 copy of each for each partner pair. (Remember, these lessons are an introduction into perimeter - More work with perimeter will come later in the year.) Words that you should hear students using in mathematical conversations: Polygons perimeter a ttribute sides sum length triangle, quadrilateral, pentagon, hexagon, octagon, Ten Minute Math: None today Before: Have students get into pairs and solve the 4 perimeter puzzler problems. Remember, more work with perimeter will come later in the year. During: Students solve Perimeter Challenge Problems with a partner (find missing sides and the perimeter when it is not given). Give students time to complete the geometry assessment independently (approximately 25 minutes). After: Have students share strategies for solving some of the Perimeter Challenge Problems. Focus on how students used understanding of measuring perimeter and knowledge about shapes to solve each of the problems. Evaluation: Geometry-Assessment

3 rd Grade Geometry Mini-Assessment Name:. 1. Complete the table below Which shapes above belong to the group all sides are the same length? Which shapes above belongs to the group all sides are different lengths? Which shapes above have OPPOSITE sides that are the same length? 2. Find a shape in the table above that appears in more than 2 categories. Justify why that shape belongs in both of the categories. 3. Complete this sentence; the shapes above are all because

4. Draw 2 examples for each category in the table below. Square Rhombus Rectangle A quadrilateral that is NOT a square, rhombus, or rectangle. 5. Gwen says that ALL rectangles belong in the group some square corners. Lea says that all rectangles belong in the group all square corners. Who is correct AND WHY? 6. Which attributes do rhombuses and squares have in common (Use the list of attributes in the Attribute bank) Attribute Bank All sides that are the same length (congruent) 2 sides the same length 4 square corners 4 sides and 4 angles All angles are congruent (the same) 2 angles are the same

PERIMETER PUZZLERS #1 Adam walked across the front of a square-shaped yard. He walked 36 feet. If Adam were to walk the perimeter of the yard, how far would he walk? Explain how you know.

PERIMETER PUZZLERS #2 All of the short sides on this figure are the same length. What is the perimeter of this figure? 25 cm

PERIMETER PUZZLERS #3 The perimeter of this rectangle is 68 units. What is the length of the unlabeled sides? 50 units Units units 50 units PERIMETER PUZZLERS #4 25 cm I am a quadrilateral with four square corners (right angles). All of my sides are 8 units long. Draw the shape and label the length of each side. What s my shape called: What s my perimeter?

ADDITIONAL RESOURCES YOU MAY WANT TO INCORPORATE INTO THIS UNIT: Name: Square Disguise Exit Ticket This shape thinks she looks just like a parallelogram. What are the attributes of a parallelogram? Do you agree that this shape is a parallelogram? Name: Square Disguise Exit Ticket This shape thinks she looks just like a parallelogram. What are the attributes of a parallelogram? Do you agree that this shape is a parallelogram? Name: