C2 Two-Dimensional Geometry 9/18/14 Angle Relationships Time: 90 min block Standards: 7.G.B.5:Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure Objectives: SWBAT: define supplementary, complementary, vertical and adjacent angles, along with parallel and perpendicular lines use angle relationships to solve multi-step problems identify supplementary, complementary, vertical and adjacent angles, parallel and perpendicular lines Materials: Course 2 Composition Notebook Elmo/Whiteboard 5 Classroom computers 7 Textbooks 8-2 and 8-3 Exercises 8-2 Practice Worksheet Procedure: Students will take notes in their composition books. All vocab and examples should be written in it. As I give them notes, I will write in my composition book at the same time (which will be projected on the Elmo. 1. Vocab Students will look up the vocab either in their books or on the classroom computers. Vocab: ray: Part of line that has one endpoint and extends forever in one direction. Vertex: Where two rays meet to form an angle angle: Formed by two rays with a common endpoint, the vertex. Measured in degrees. Supplementary: The sum of two angles is 180 complementary: The sum of two angles is 90 vertical angles: Opposite angles formed by two intersecting lines. These angles are congruent. adjacent angles: Have a common vertex and a common side, but no common interior points. These angles are supplementary. Congruent: having the same size and shape. Parallel lines: two lines that will never intersect (show examples and symbols, and ask for examples in room) Perpendicular lines: two intersecting lines that form a right angle. (show example and symbols, and ask for examples in the room) 2. Go over vocab. Show examples of each vocab word.
3. Example 2 (8.2) in book - Go over angle notation. - Emphasize degree symbol 4. Example 4 (8.2) 5. Go back to Example 2 -Are these angles AXB (m=35º) and BXE (m=145º) adjacent to each other? Why? - Write in notebook that AXB and BXE are adjacent to each other. - Because they share a common side, BX, a common point, X, and their angle measurements add up to 180º. 35º + 145º = 180.
6. P R m 130 Q l S T Two lines l and m intersect. PQR = 130º. What is the angle measure of SQT? Why? - 130º because PQR and SQT are vertical angles which are congruent. HW 8-2 p. 450 13-21 odd 8-3 p. 454-55 18, 19, 21, 22 Identify 2 examples of parallel and perpendicular lines in your home. Day 2 Time: 45 minutes Checking for Understanding: Students correct homework from answer keys passed out to their tables. Answer any questions students were confused on. Reinforce teaching: Angle Exercise game Students over arms and hands in a series of formations. The leader will call angle measurements Acute angles: Touch elbows together in a V Obtuse: Touch tips of fingers together in a V Right: Touch finger tips of one hand to the elbow of the other arm in an L Parallel lines: Arms up vertically Perpendicular lines: Cross arms like a plus sign HW Practice 8-2 worksheet
Day 4 C2 Two-Dimensional Geometry Properties of Polygons Time: 90 minutes Standards: 5.G.B.4:Classify two-dimensional figures in a hierarchy based on properties 5.G.B.3:Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Objectives: SWBAT: - identify properties of polygons (triangles and quadrilaterals) - fit polygons into categories based on their properties Materials: 8 sets of Polygon Tiles Polygon note sheet Flow Chart Rulers Polygon capture sets Procedure: 1.Pass out Polygon Note Sheet, Flow Charts, and one Polygon Set to each table. 2.Start with the big picture, what is a polygon? 3.Ask students if they know what a polygon is. a. Define Polygon. b. Start sorting into more specific shapes. 1. Regular Polygons 2. Convex 3. Concave 4. Triangles 5. Quadilaterals. 6. Write in the properties and definitions as these terms are gone over. 4. After the polygon table is filled out, have students pull out all the triangles. Terms should be defined as terms are discussed. a. Notice that all these triangles are different. Each different kind of triangle can be classified based on their side lengths and their angle measurements. b. First, we will pick out triangles based on their angle measurements. 1. What is a right angle? Are there any triangles that appear to have any right angles? 2. What about a triangle with an obtuse angle? What do you notice about those triangles? 3. Lastly, what about triangles with acute angles? What do you notice about these triangles?
c. Now will we classify triangles by their side lengths. Use the rulers to measure the lengths of all the triangles. Students should measuring the side lengths of the triangles in cm and writing them down. They work as a team to measure all of them. What patterns do you notice? 1.Define isosceles, scalene, and equilateral. 5. Put the triangles back in the pile and get all the quadrilaterals. a. What is a parallelogram? b. So get all the squares. What properties do squares have? c. Rectangles. Properties? d. There are some slanted-like squares. These are called rhombuses. See if you can pick out all the rhombuses. What are properties of these? e. Trapezoids. Properties? f. Kites like like arrows. g. There are some left over. Even those these polygons have nothing special about them, they are still quadrilaterals because they have four sides and four angles. 6. Many quadrilaterals have similar properties. Based on what we know, can a square be a rectangle? But can a rectangle be a square? a. Fill out a flow chart to help see what how quadrilaterals are similar and how they are different. Reinforce Teaching: -Polygon Capture HW 8-6 p.473 #5-8,24 8-7 p.476 #6-17,19-24
Polygon Properties Polygon Description/Properties Drawing/Examples Polygon Closed figure Classified by sides and angles Triangles, pentagon, octagon, etc. Regular Polygons Sides and angles are congruent Convex No sides or angles point into the middle Concave Side and angles point into the middle Triangles Right Classified by three sides and three angles Interior angles add up to 180 Have one right angle Acute All angles are acute Obtuse Only one obtuse angle Isoceles Two sides are congruent Scalene No sides are congruent
Polygon Description/Properties Drawing/Examples Equilateral All sides are congruent Quadrilateral Classified by four angles and four sides Trapezoid Only one pair of parallel sides Kites Adjacent sides are congruent Parallelogram Two pairs of congruent sides Rectangle Squares Rhombuses Four right angles Opposite sides congruent Two pairs of parallel sides Four right angles All sides congruent two pairs of parallel sides All sides congruent Two pairs of parallel sides
C2 Two-Dimensional Geometry Time: Day 1 (9/25/14): 15 min Day 2 (9/26/14): 25 minutes Day 3 (9/30/14): 45 minutes Finding the Area of Polygons Standards: 7.G.B.6:Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 6.G.A.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems Objectives: SWBAT: - find the area of triangles, quadrilaterals and polygons. - find the area of irregular shapes by splitting the shape into triangles and other shapes that they the area formulas for. - apply area to real-world problems. 9/25/14 Day 1: Materials: grid paper Procedure: Use the last 15 minutes of class on 9/25 to get started on area. Hand out pieces of grid paper to students. Have them draw a rectangle ABCD that is 6 units by 10 units. Count the boxes inside. Confirm that the area is 60 units2. Draw a diagonal line from corner A to D. Count the boxes in one of the triangles. Estimate. Relate that a right triangle s area is half of a rectangle/square. Ask for rectangle area formula. Introduce triangle formula. HW 9-3 #9-11 9-4 #8-10 9/26/14 Day 2: Materials: grid paper rulers scissors quarter sheets of scrap paper Procedure: Together with the students, draw a parallelogram on the grid paper. Emphasize that the vertical height of the parallelogram is 6 units. Have the students draw in the vertical height. Height 6 units, length 10 units.
Have students cut the vertical height line to make a triangle and bring it over to the other side. this will show the relationship between a parallelogram and rectangle. Reiterate the formula to find the area of a rectangle and connect it to the formula to parallelogram. have a student find this connection Do example One more area to learn: Trapezoids. Introduce formula. Do example. Make a chart on the area formulas Polygon Rectangle/Square Triangle Parallelogram Trapezoid Formula A= lw A=1/2 bh A=bh A=1/2 h (b1+b2) Check for understanding: Favorite No Each student grabs a quarter-sheet of paper. I will give an area problem on doc cam of any of the above polygons. Give students 3-5 minutes to do the problem and collect the sheets. Find a common mistake or error file the pile and show it to class (keeping students anonymous!) Ask what went right, then what went wrong. Do another if time permits HW 9-4 #8-13, 24 9-3 #16, 24, 22, Day 3:
Materials: Area Worksheet Procedure: Part 1: Irregular shapes Think-pair-share 1. Students will get into pairs at their table. 2. Each student will get an Area Worksheet. For five minutes, students will individually look at the first two problems and start brainstorming and developing a plan to attack the problem. 3. After 5 minutes, students will share their plans with their partner and work together on the problems. 10 minutes. 4. Go over the problems with the whole class. 5. Favorite No Ans: 156 m2 Part 2: Real-life problems Think-pair-share 1. Students have same partners. 2. Each student will look at last two problems for five minutes to brainstorm and develop a plan to attack the problem. 3. After 5 minutes, students will share plans with partner and work together to solve problems. 10 minutes 4. Go over the problems with the whole class. 5. Favorite No Ari is going to use fabric to cover one of her walls. The wall is 60 ft long and 12 ft tall. The fabric is measured in square yards. How many square yards of fabric will be required to cover the wall? Answer: 80 HW: 9-6 #9-10, 13, 14, 1, 9-3 and 9-4 Problem Solving Odds.
C2 Two-Dimensional Geometry 10/2/2014 Time: 70 min Students: 22. Mix of 6th, 7th and 8th graders. Plotting Polygons on a Coordinate Plane Standards: 6.G.A.3.-Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Objectives: SWBAT: - draw polygons in a coordinate plane using coordinates for the vertices. - use coordinates to find the length of a side - can apply polygons on the coordinate plane in solving real-world and mathematical problems I can statements written on board: - I can draw polygons in a coordinate plane using coordinates for the vertices. - I can use coordinates to find the length of a side - I can apply polygons on the coordinate plane in solving real-world and mathematical problems Materials: -Notebook -22 copy of coordinate plane sheet #1-22 copies of coordinate sheet #2 -scissors -tape Procedure: For the first 20 min of class, students are checking in the homework assigned from the last class period on Tuesday. Each table has an answer key. One student from each table should be reading the answers out loud to their table while the other students correct their work. They should be discussing answers they got wrong and how to fix them. They should also be redoing (corrections) any problems they got wrong on the margins of their paper. Lauren, the instructional assistant, or Cindy will be stamping or circling planners for completed homework. As the students are correcting, I will walking around making sure students are on task and ask for any clarifications or problems to do on the board. Ask for problems to do on the board and go through them. Each student will get a coordinate plane sheet and will asked to get out their notebooks. Previous Knowledge: Review Plotting on a Coordinate Plane 1. A coordinate plane will be projected onto the screen.
2. Ask student to label one coordinate plane on their notes a review 3. I will ask a student to come up to the screen and point to where (2, 3) is and have them explain why. 4. Ask another student to point to (-3, 5). 5. Ask for questions. New Material: As I write on my notebook, students should be writing in theirs. Title: Plotting Polygons 10/2 Students should plot points on one coordinate plane. 1. Plot points A (1,3), B (1, - 5), C (-4, 3) and D (-4, -5). 2. Connect the dots (A to B, B to C, C to D and D to A) 3. What polygon was made by these vertices? Rectangle. 4. How do you know? a. Lengths of the sides determine that this polygon is a rectangle. Sides AB and CD are 8 units and sides BC and AD are 5 units. 5. Farmer John s land is rectangle we just plotted above. How much land does he have in square acres? 40 acres 2. Turn page to leave room for grid. Suggest students should do the same. Think-Pair-Share 2. On their own for 5 min, each student will plot H (1, 3), I (4, 3), J (-3, -2) and K (6, -2) and find the area of that polygon (Trapezoid). 3. After the 5 minutes, students will share their answers with their table. Tablemates should explain if a student got it wrong. 4. I will call on a table and they will share their answer. 30 units 2 Group Work: 11-3 from Bennet et al. (2007) Mathematics: Course 1.Austin, TX: Holt, Rinehart, and Winston. 1. Give students 10 minutes to work on 11-3.Use this worksheet to explain how they should create their own picture and include a detailed instruction so that a classmate could do it. 2. With the extra time in class, I will give students time to tape their notes in their notebooks. These notes will include those taken on previous days. When they are finished taping, they can start on the homework. HW. 1. Create-a-Picture 1. Students will design their own picture using the coordinate grid. They must list the points they used, and have similar directions like those on 11-3. Must have at least 5
points but no more than 30. The next day in class they will exchange papers with a student at their table who will plot the points. 2. Problems from textbook: Bennet et al. (2007) Mathematics: Course 2. Austin, TX: Holt, Rinehart, and Winston. 1. 9-3 #19, 20, 9-4 #18-21, 9-6 #14
Coordinate # 1
Coordinate #2
C2 Unit 1 Two Dimensional Geometry 10/07/14 Time: 70 minutes Area and Circumference of Circles and Pi Standards: 7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 5.G.B.4:Classify two-dimensional figures in a hierarchy based on properties. Objectives: SWBAT: - know the formulas for area and circumference of a circle. - solve area and circumference problems. - know properties of circles - conclude that the ratio between circumference and diameter is pi from measuring several circular objects Materials: -Notebooks -rulers -Tape measures - 22 copies What is Pi worksheet -22 copies of 9-5 Procedure: Part 1: Area and Circumference Student have their notebook out for notes. While they are getting out their notebooks, calculators can be passed out. Review/Go over radius and diameter. r= 2d or d=r/2 If the diameter of the circle is 6 in, what is the radius? 6. Circumference of a circle 1. Special name for the perimeter of the circle 2. Formula C=2πr or dπ 3. Pi can be approximated to 3.14 Radius of the circle is 4 cm. What is the circumference of the circle?
6. Also use radius to find the area of circle. a. Formula A=(pi)(r^2) b. Use previous example, radius of 4 cm. What is the area? 7. Example 2: Use diameter to find circumference and area. a. d=7m Checking for Understanding: 5. Favorite No Part 2: Pi 3. Students receive What is Pi worksheet and 9-5. 4. The circular objects (Lysol tubs, wooden cylinders, cans, etc.) will also be passed out. 2 or 3 per table. 5. What is Pi worksheet will be projected on the screen. Directions: With your teammates at your table, you determine what is so special about pi and where it came from. Each person will measure the diameter and circumference of an object, in centimeters. Name the object here 3. Demonstrate how diameter and circumference are measured. Write down the measurement. Since there are only two or three objects at your table, when you are done measuring, pass that object on to a table on the right. 1. Explain how that should be done. You also need to write down your group s measurements. This needs to get done before you leave. Fill out the table Answer the following questions at the end Work with your able well. If you don t finish by the end of class, it will be homework. HW 9-4 13-19, 27 Finish What is Pi
Name What is Pi? So, we have learned that Pi can help us find the circumference and area of a circle. Where did that number come from? This activity is designed to explore the origins of this magical number. Directions: List the object you are measuring. Measure, in centimeters, the diameter and the circumference of one object, then pass it on to the table on your right. Write down all of your group s measurements. Object I measured Diameter: Circumference: Group member #1 measured a Diameter: Circumference: Group member #2 measured a Diameter: Circumference: Group member #3 measured a Diameter: Circumference: Group member #4 measured a Diameter: Circumference:
Name of Object Diameter Circumference Use the information above to answer the following questions: 1. What do you notice about the number in the ratio column? 1. Does the size of the circle change the ratio of the circumference and diameter? Why or why not? 3. From this activity, tell me what Pi is.