Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Line (geometry) wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
Trigonometric functions wikipedia , lookup
Name: ________________________________________ Date:________________ Soccer Goalies Prediction: In soccer, when a team shoots a penalty shot, the goalie must stand on the goal line to defend. But, during other times, the goalie can come out as far as he or she wants. Why do you think soccer rules require a goalie to stand ON the goal line for penalty kicks? Do you think there is an advantage if a goalie moves closer to the ball? __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Data Collection: Each member of your team will shoot the ball from the marked spot 5 times for each distance the goalie is standing. Record the fraction of shots made for each person from each distance. Note: a “shot made” means it does not hit the “goalie” and is between or touching the “goal” posts. See below for a diagram of what you will be doing outside. Name Fraction of shots made with goalie on goal line Fraction of shots made with goalie 12 feet out from goal line Fraction of shots made with goalie 24 feet out from goal line Group Totals Goal Line Goalie Goalie Goalie Shooting Location . Goalie on Goal Line . Goalie 12 ft. out from Goal Line IMP Activity: Soccer Goalies . Goalie 24 ft. out from Goal Line 1 AP S1 Analysis Questions 1. From which distance the goalie was from the goal line did your team score the least fraction of goals? Write an inequality to show which fraction was the smallest. 2. From which distance the goalie was from the goal line did your team score the greatest fraction of goals? Write an inequality to show which fraction was the largest. 3. Why do you think your team had a higher fraction of the goals go “in” from that distance? Use the pictures from the page before to SHOW what path the ball could have followed to make a goal in EACH of the three scenarios. __________________________________________________________________ __________________________________________________________________ 4. Describe what is different about the path a ball could have followed to score a goal in each of the three scenarios. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ In math terms, we call the representation of the difference between the paths a ball could take to score an Angle. What do you think the term angle means? Explain in words and with a picture. Words: _______________________________________________________________________ _______________________________________________________________________ Picture: IMP Activity: Soccer Goalies 2 AP S2 Name:________________________________________________Date:____________________ Lines and Line Segments Reference Set #1: Parallel Lines vs. Intersecting Lines Examples of Pairs of Parallel Lines/Segments Non-Examples of Pairs of Parallel Lines/Segments (Examples of Intersecting Lines) Draw two more examples of parallel lines or line Draw two more examples of Intersecting Lines or segments. segments. List three places in the real world where you see a pair of parallel lines. Use your own words to describe what a pair of parallel lines is. 1) 2) 3) Draw a picture of a figure with parallel lines. ! IMP Activity: Lines & Segments AP S3 Reference Set #2: Perpendicular Lines Examples of Pairs of Perpendicular Lines/segments Non-Examples of Pairs of Perpendicular Lines/segments Draw two more examples of perpendicular lines/segments. Draw two more examples of non-perpendicular lines/segments. List three places in the real world where you see a pair of perpendicular lines. Use your own words to describe what a pair of perpendicular lines is. 1) 2) 3) Draw a picture of a figure with perpendicular lines. ! IMP Activity: Lines & Segments 2 AP S4 Reference Set #3: Lines, Rays and Line Segments Examples of Lines Examples of Rays Examples of Line Segments Draw two more examples of Lines. Draw two more examples of Rays. Draw two more examples of Line Segments. Use your own words to describe what a line is. Use your own words to describe what a ray is. Use your own words to describe what a line segment is. How are lines, line segments and rays the same? How are lines, line segments and rays different? ! IMP Activity: Lines & Segments 3 AP S5 C B A ! IMP Activity: Lines & Segments 6 AP S6 D E F ! IMP Activity: Lines & Segments 7 AP S7 G H I ! IMP Activity: Lines & Segments 8 AP S8 M L K J ! IMP Activity: Lines & Segments 9 AP S9 O N P ! IMP Activity: Lines & Segments 10 AP S10 Name: ________________________________________ Date:________________ How Does That Spaghetti Intersect? Part 1: Intersecting Lines: Find all the ways two pieces of spaghetti (lines or line segments) can be glued down to the same piece of paper. After experimenting, glue down 5 of the ways you found that you think represent most of the options. Describe what each one represents in words (e.g., they make a narrow opening at the top). IMP Activity: How Does That Spaghetti Intersect? 1 AP S11 Part 2: Intersecting Rays: You will now use your spaghetti to investigate all the ways in which two rays can intersect when sharing a common endpoint. Use two pieces of spaghetti to represent your two rays and try to find all the ways the two rays can meet to share their endpoint. Glue down 5 examples you think illustrate most of the options and describe, in words, what each one represents (e.g., they make perpendicular lines). IMP Activity: How Does That Spaghetti Intersect? 2 AP S12 Part 3: Sorting Rays that share a common endpoint. Use the pairs of rays your teacher passes out and sort them into 2 groups: a group that has a common feature and a group that does not. Try to come up with at least 2-3 ways to sort the rays. Record the rule you used to sort below each one. Sort 1 Group 1: Feature/ Rule Group 2 (Does not have feature) ______________________________________ Sort 2 Group 1: Feature/ Rule Group 2 (Does not have feature) ______________________________________ Sort 3 Group 1: Feature/ Rule Group 2 (Does not have feature) ______________________________________ IMP Activity: How Does That Spaghetti Intersect? 3 AP S13 Angle: An angle is formed when two rays share a common endpoint. Describe what an angle is in your own words and draw a picture (or a few) to show this. Words: _______________________________________________________________________ _______________________________________________________________________ Picture: Part 4: Drawing all possible angles Begin by gluing down one ray (piece of spaghetti) so that the endpoint is on the point drawn below. Use your second ray to build and trace all possible angles you can form with this second piece of spaghetti and the ray (spaghetti) glued down. Ray 1- glued to paper Observation Time! What shape is made by all possible angles formed by the two rays? _______________________ Draw this shape onto the picture you made above. IMP Activity: How Does That Spaghetti Intersect? 4 AP S14 Part 5: Defining Fractions and Angles As you discovered above, all possible angles lie within a circle. Look at the circle below and use your definition of a fraction to determine what the angle representing ONE of the equal parts is called. Defining Fractions: Start with one whole (the circle) and divide it into ________ equal pieces. We’re talking about 1 of those _________ each pieces when we name the fraction _____________. Degrees (°): If the angle formed by the two rays represents 1 of the circle, we say this 360 angle measures 1 degree (1°). IMP Activity: How Does That Spaghetti Intersect? 5 AP S15 Practice Time 1 ths of the circle. Use fraction addition to show what this angle 360 represents. Use degrees to show how many total degrees (°) this angle would be. Recall that 1 = 1 degree (°). 360 1. An angle opens 3 Fractions: _________ + ____________ + ____________ = __________ Degrees: __________ + ____________ + ____________ = __________ 1 ths of the circle. Use fraction addition to show what this angle 360 represents. Use degrees to show how many total degrees (°) this angle would be. Recall that 1 = 1 degree (°). 360 2. An angle opens 5 Fractions: ______ + _________ + _________ + _______ + _______ = __________ Degrees: ______ + _________ + _________ + _______ + _______ = __________ 1 ths of the circle. Use fraction multiplication to show what this angle 360 represents. Use degrees to show how many total degrees (°) this angle would be. Recall that 1 = 1 degree (°). 360 3. An angle opens 15 Fractions: _________ • ____________ = __________ Degrees: __________ • ____________ = __________ 1 ths of the circle. Use fraction multiplication to show what this 360 angle represents. Use degrees to show how many total degrees (°) this angle would be. Recall 1 that = 1 degree (°). 360 4. 1. An angle opens 45 Fractions: _________ • ____________ = __________ Degrees: __________ • ____________ = __________ IMP Activity: How Does That Spaghetti Intersect? 6 AP S16 Shapes to Sort IMP Activity: How Does That Spaghetti Intersect? 10 AP S17 Name _________________________________________________________________ Date __________________________ Stacking & Labeling Angles Part 1:Stacking Predict: The largest angle below is Angle ______ because _____________________ ______________________________________________________________________________________ Angle A Angle C Angle B Task 1: Cut out Angles A, B, and C from the extra page by cutting carefully along the straight lines. Task 2: Line up a corner (vertex) of Angle A with the center of the circle. Glue Angle A in the circle. Task 3: Glue Angle B in the circle, stacking it on top of Angle A. Line up the corner (vertex) of Angle B with the corner (vertex) of Angle A. Then, glue Angle C in the circle, stacking it on top of Angle B. Line up the corner (vertex) of Angle C with the corner (vertex) of Angle B. Analysis: 1) What do you notice about angles A, B, and C? __________________________________________________________________________________________ 2) Was your prediction correct? Why or why not? __________________________________________________________________________________________ 3) What is the same about angles A, B, and C? __________________________________________________________________________________________ 4) What is different about angles A, B, and C? __________________________________________________________________________________________ Big Idea: Angles that are equal in measure can be represented by pictures with different length __________________. AP S18 Task 2: Sorting With your group, sort the angles in your envelope into different piles based upon angle measure.. I sorted my angles ___________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ What would happen if you stacked and glued the angles from the individual groups on top of one another?________________________________________________________________________ __________________________________________________________________________________________ Task 3: Circle Time How many degrees are in a circle? __________________ What fraction of the circle do angles A, B and C represent? _______________ How many degrees do angles A, B & C represent? _____________ Use fractions to show your calculation: Big Idea: We call an angle measuring 90° a right angle. We show angle is a right angle by drawing a small box in the corner of the angle as shown below. Task 4: Classifying the angles you sorted in Task 2 For each “group” of angles you sorted in task 2, describe them as being a right angle, less than a right angle or greater than a right angle. Glue one angle from each group below and record the name you gave that group. Big Idea: We call an angle measuring greater than 90°, an obtuse angle. We call an angle measuring less than 90°, an acute angle, Label each group glued above as right, obtuse or acute. AP S19 Angles for Task 1: Stacking Angle A Angle A Angle B Angle C Angles for Task 1: Stacking Angle B Angle C IMP Activity: Stacking & Labeling Angles 3 AP S20 center IMP Activity: Stacking & Labeling Angles 4 AP S21 Angles for Task 2: Sorting 33° 10° 120° IMP Activity: Stacking & Labeling Angles 8 AP S22 90° IMP Activity: Stacking & Labeling Angles 9 AP S23 IMP Activity: Stacking & Labeling Angles 10 AP S24 Name: ________________________________________ Date:________________ Doing a 180 Task 1: Your team will be assigned a starting ray (shown in the picture below)and a direction in which you must perform a turn. Use string or a meter stick to represent the starting ray, and then have a student model the turn with their body. Record what the angle formed by your body and the original ray looks like on your page below. 1: Open Counter Clockwise 1 turn 4 Team 2: Open Clockwise 1 turn 4 Team 3: Open Clockwise 1 turn 4 1 turn 2 1 turn 2 1 turn 2 3 turn 4 3 turn 4 3 turn 4 Full turn Full turn Full turn 4: Open Counter Clockwise 1 turn 4 Team 5: Open Clockwise 1 turn 4 Team 6: Open Clockwise 1 turn 4 1 turn 2 1 turn 2 1 turn 2 3 turn 4 3 turn 4 3 turn 4 Full turn Full turn Full turn Question: Does the direction in which the angle opens affect its measure? Why or why not? ___________________________________________________________________________ IMP Activity: Doing a 180 1 AP S25 Task 2: Labeling the Angles with Degrees Recall: How many degrees are in a circle? ________________ 1 1. How many degrees are there in a quarter ( ) turn of a circle? ____________ 4 1 Show your math below and label all the turns above with degrees. 4 1 2. How many degrees are there in a half ( ) turn of a circle? ____________ 2 1 Show your math below and label all the turns above with degrees. 2 3 3. How many degrees are there in a three-quarter ( ) turn of a circle? ____________ 4 3 Show your math below and label all the turns above with degrees. 4 4. How many degrees are there in a full turn in a circle? ____________ Show your math below and label all the full turns above with degrees. 5. What does it mean for someone to do a “180”? Explain in words and with a picture. Words: _______________________________________________________________ ____________________________________________________________________ Picture: 6. Professional snowboarders can do a trick called a “720”. What do you think this means? Explain in words and with a picture. Words: _______________________________________________________________ ____________________________________________________________________ Picture: IMP Activity: Doing a 180 2 AP S26 Task 3: Benchmark Angles In addition to a 90°, a 180°, and a 270° angle, there are other common angles we use in math. 1. Fold your 90° angle in half (2 equal parts). a) How many degrees is this angle? ________________ b) Show the math you used to determine this. c) What fraction of the circle does this angle represent? d) Show the math you used to determine this. e) Trace this new angle onto page 1 for each of the “teams” in the same box that shows the 90° turn and label this as a fraction and with degrees. 2. Fold your 90° angle into thirds (3 equal parts). a) How many degrees is this angle? ________________ b) Show the math you used to determine this. c) What fraction of the circle does this angle represent? d) Show the math you used to determine this. e) Trace this new angle onto page 1 for each of the “teams” in the same box that shows the 90° turn and label this as a fraction and with degrees. Benchmark Angles: Common angles we use to estimate or compare angles. Draw a sketch of each benchmark angle below. 90° 45° IMP Activity: Doing a 180 30° 180° 270° 3 AP S27 Name: ________________________________________ Date:________________ Building a Protractor Task 1: Starting with each ray below and your 90° angle, draw a sketch (and label near the end of the ray) of the following angles: 30°, 45°, 90°, 180°, 270°. Be precise in your drawing. Opening up from a ray pointing to the right 0° or _____° Opening up from a ray pointing to the left. 0° or _____° IMP Activity: Building a Protractor 1 AP S28 Task 2: Using your pictures above, estimate the measure (in degrees) of each angle shown below. Record the estimate in the Estimate 1 column and also list if the angle is acute, right or obtuse. Angle Estimate 1 Estimate 2 Actual 1. 2. 3. 4. 5. 6. IMP Activity: Building a Protractor 2 AP S29 7. 8. 9. 10. Task 3: Predict: How can we be more precise in our estimates? _________________________________ _____________________________________________________________________________ Your teacher will now give you a 10° angle. What fraction of the circle is a 10° angle? _______ Use your ten degree angle to add more detail to your drawings on page 1. Beginning at 0°, sketch a ray to represent each 10° angle and label the angles at the end of the ray in increments of 10. When you are done, you should have a picture labeled from 0° to 360° counting by 10’s. Repeat the same process for the picture opening up from a ray pointing to the left (you will have to begin with your angle by the 0°!) IMP Activity: Building a Protractor 3 AP S30 Task 4: Estimation #2 Using what you have built on page 1 to be more precise in measuring angles, estimate the measure of each of the 10 angles from task 2 and record your new (or the same if you have not modified your original estimate) estimate. Task 5: Building the rest of the protractor Predict: How can we be more precise in our estimates? _________________________________ _____________________________________________________________________________ Go back to each of the pictures you were drawing on page 1. Draw a circle to represent the path the opening ray will follow as it slowly turns. This circle should be marked and show every 10°. Label every 5° with a dash and a number and then use small tick marks to divide each 10° into 1° increments. Do this for both models on page 1. You have now built a protractor. What do you think a protractor is? __________________________________________________ ______________________________________________________________________________ What is a protractor used for? _____________________________________________________ _____________________________________________________________________________ Task 6: Your teacher will now give you a protractor built to be precise to the nearest 1°. Try to use this protractor to measure the 10 angles from pages 2-3 and record what you think the exact measurement is in the final column (note: your final measurement should be CLOSE to your estimates; if not, look at how you are using the protractor!). IMP Activity: Building a Protractor 4 AP S31 Name: ________________________________________ Date:________________ Navigating in the Dark Navigating Outside Your group will go outside with a piece of chalk, a protractor and a meter stick. You will mark a starting point on the ground and then follow a series of directions to end up at another point. Your team then must determine what steps to take to get back “home” (to the starting location). These steps should be detailed enough that someone could follow them in the pitch dark (assuming they could read the protractor and meter stick!) Assign the following roles in your group: walker, distance measurer, angle measurer, recorder. The recorder will take a sheet of blank paper to draw a sketch of the path you took from start until end. Note: it is up to you to decide what path you would like to take to get back to the start! Task 1 Step What to Do 1 From your starting point, walk forward 3 meters. 2 Turn 45° left. 3 Walk forward 1 meter. 4 Turn 45° left. 5 Walk forward 2 meters. 6 Turn 100° left. 7 Walk forward 2 meters 8 9 10 11 12 Task 2 Step What to Do 1 Walk right 2 meters. 2 Turn 360° 3 Walk forward 2 meters. 4 Turn 90° right 5 Walk forward 1 meter. 6 Turn 45° right. 7 Walk backwards 3 meters. 8 9 10 11 12 Question: Will every group’s picture of the path they took look the same? Why or why not? ___________________________________________________________________________ IMP Activity: Navigating in the Dark 1 AP S32 Navigating a Ship Scenario: You have been given the all-important task of creating the path for a ship to take so that it can navigate in the dark safely through many islands. Navigating a Ship Task: For the map you’ve been given, determine the path the boat should take to get safely from the point labeled “here” to the point labeled “there”. Use a protractor and a ruler (measure to the nearest mm) to determine the path the boat should take to avoid crashing into land. Number and record the steps on the page provided. Testing Your Path: Once your directions are written, trade them with another person at your table (give only the directions, not the map). With the directions you have been given, draw out the path on a piece of blank paper. When you think you’ve successfully “navigated” your ship, ask your partner for the original map. Then overlay your path onto the map to see if you’ve made it safely! Step What to Do (include direction, angle, distance, etc) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Summary Questions 1. Did your ship make it safely? ____________ 2. If not, what wentwrong? ___________________________________________________________________________ 3. When is it important to be precise in our measurements? ___________________________________________________________________________ IMP Activity: Navigating in the Dark 2 AP S33 Map 1 **Start** • **End** • IMP Activity: Navigating in the Dark 4 AP S34 Map 2 **End** • • **Start** IMP Activity: Navigating in the Dark 5 AP S35 Map 3 **Start** • • **End** IMP Activity: Navigating in the Dark 6 AP S36 Name: ________________________________________ Date:________________ Revisiting Soccer Goalies: Cutting Angles Opening Question: In soccer, what do you think it means for the goalie to “cut down the shooter’s angle?” Record your idea with words and a picture below. __________________________________________________________________ __________________________________________________________________ Picture: Opening Scenario: While you were at school, your little brother found a 90° from your school work and decided to cut it as shown by the dotted line below (thankfully he cut through the vertex). Is the angle still 90°? _______ Why or why not? _____________________________________ ___________________________________________________________________________ Investigation: Each member of your team will begin with a 90° angle. Each of you will choose to make 1, 2, or 3 cuts through the vertex of your angle. Once cut, measure each “new” angle with the protractor and record the measure of each angle. Glue the angles back together at the vertex to show what the sum of the angles should be and then use math to show that the angles are or are not still equal to 90°. Angles Glued Together: Math to show angles still form or no longer form a 90° angle. (Bonus: Use a number bond to show this!) _____________________________________________________________________ IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles 1 AP S37 Big Idea Questions 1. How is decomposing an angle (cutting it into smaller angles) similar to decomposing a number (such a 10 or 90)? _____________________________________________________________________ _____________________________________________________________________ 2. How is it different? _____________________________________________________________________ _____________________________________________________________________ A Lost Piece I Your brother thought it was fun to continue cutting your angles when you were gone at school, but he usually taped them back together so that you never knew. One day, he cut a right angle into 3 angles (through the vertex of course), but he lost one of the angles. Below are the two angles he has. 1. What is the measure of the angle he lost? _________ 2. Explain how you determined this. _____________________________________________________________________ _____________________________________________________________________ A Lost Piece II Your brother is back at his cutting. This time, he cut a 180° into 4 angles (through the vertex of course), but he again lost one of the angles. Below are the three angles he has. 1. What is the measure of the angle he lost? _________ 2. Explain how you determined this. _____________________________________________________________________ _____________________________________________________________________ IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles 2 AP S38 Angle Puzzles Your brother got out of control with his angle cutting one day while you and two friends were outside playing. He cut everyone’s and does not know how to put them back together. Below are all of the pieces he has. Before he began cutting (through the vertex of each angle), there was one 90° angle, one 180° angle and one 140° angle. Put the three original angles back together. Glue the angles and use a math sentence to show that each set of smaller angles really add up to the sum of the angle from which they were cut. IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles 3 AP S39 Revisiting the Soccer Goalie 1. What do you think it means for a goalie to “cut down the shooter’s angle?” __________________________________________________________________ __________________________________________________________________ 2. Using the pictures below, draw angles to represent the path the ball could take form the shooting location to score (the vertex should be on the shooting location). Scenario 1 Scenario 2 Scenario 3 Goal Line Goalie Goalie Goalie Shooting Location Goalie on Goal Line Goalie 12 ft. out from Goal Line Goalie 24 ft. out from Goal Line 3. Find the sum of the two angles representing the paths the ball could take to score in EACH of the three scenarios above. Use the table below to organize your information. Scenario 1 Measure Angle 1: Measure Angle 2: Sum: Measure Angle 1: Scenario 2 Measure Angle 2: Sum: Measure Angle 1: Scenario 3 Measure Angle 2: Sum: 4. Compare the total angle a shooter could use to make a goal (sum) for each of the three scenarios. Write a math sentence to show what you see. 5. What does it mean, mathematically, to cut down a shooter’s angle? __________________________________________________________________ __________________________________________________________________ IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles 4 AP S40 90° Angle for students to use in the Investigation 90° Angle for students to use in the Investigation 90° Angle for students to use in the Investigation 90° Angle for students to use in the Investigation IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles 7 AP S41 Name: ________________________________________ Date:________________ Sorting Shapes Sort 1: Sort your shapes into piles based on the number of sides of each polygon. As a group presents, write a definition for each category of the Polygons and list the letters of the shapes that meet this criteria. Triangle: ________________________________________________________________ _________________________________________________________________________ Quadrilateral: _____________________________________________________________ _________________________________________________________________________ Pentagon: ________________________________________________________________ _________________________________________________________________________ Hexagon: ________________________________________________________________ _________________________________________________________________________ Sort 2: Sort the pentagons into 2 piles. Then sort the hexagons into 2 piles. Record a rule for your sort below and be prepared to share. Rule for pentagon sort: ___________________________________________________________ _____________________________________________________________________________ Rule for hexagon sort: __________________________________________________________ _____________________________________________________________________________ Shape Q is a regular pentagon. Measure its sides and angles and define what it means for a pentagon to be regular: __________________________________________________________________________ Shape R is a regular hexagon. Measure its sides and angles and define what it means for a hexagon to be regular: __________________________________________________________________________ IMP Activity: Sorting Shapes 1 AP S42 Sort 3: Take all of your quadrilaterals and sort them into 2 groups: a group that has a key feature and a group that does not have that key feature. Record the letters of your sort as well as your rule below. Quadrilaterals that have this feature: _______________________________________________ Quadrilaterals that do not have this feature: __________________________________________ Feature/Rule: __________________________________________________________________ Sort 4: Find all the quadrilaterals that have NO parallel lines. Record the letters of these shapes. Note: The name we have for this group is simply the term, quadrilateral Quadrilaterals with NO parallel lines: _______________________________________________ Sort 5: Sort the quadrilaterals that have parallel lines into those with 1 set of parallel lines and those with 2 sets and record the letters of each group’s shapes below. Quadrilaterals with exactly 1 set of parallel lines are called trapezoids: ____________________ Quadrilaterals with 2 sets of parallel lines are called parallelograms: ______________________ Sort 6a: Sort the parallelograms into 2 groups, one group where all parallelograms have a right angle and a group of parallelograms that do not have a right angle. List the letters of the shapes below. Parallelograms with a right angle are called rectangles: ________________________________ Parallelograms without a right angle are simply called parallelograms: ___________________ Sort 6a: Sort the parallelograms into 2 groups, one group where all parallelograms have all four side lengths the same measure and one where the four side lengths are not all the same.. List the letters of the shapes below. Parallelograms with four equal side lengths are called rhombi (this is plural for rhombus): ___________________________ Parallelograms without four equal side lengths are simply called parallelograms: _____________ IMP Activity: Sorting Shapes 2 AP S43 Sort 7: Sort the rectangles into 2 groups based upon the lengths of the sides. List the letters of the shapes below. Rectangles with 4 equal sides are called squares: _____________________________________ Sort 8: Measure the side lengths (in cm) and angles of each triangle and record the information in the table below. Triangle Side Lengths (cm) Angle Measures Type A B C D E F G Triangles!! Right Triangles contain exactly one 90° angle. List which triangles are right triangles: ________ Acute Triangles have all three angle measures less than 90°. List which triangles are acute triangles: ________ Obtuse Triangles have exactly one angle measure greater than 90°. List which triangles are obtuse triangles: ________ Equilateral Triangles have all three congruent (equal in measure) side lengths. List which triangles are equilateral triangles: ________ Bonus: what do you notice about the angles of equilateral triangles? _________________ Isosceles Triangles have exactly two congruent (equal in measure) side lengths. List which triangles are isosceles: _______________________ Bonus: what do you notice about the angles of isosceles triangles? _________________ Scalene Triangles have no congruent (equal in measure) side lengths. List which triangles are scalene: _______________________ IMP Activity: Sorting Shapes 3 AP S44 A B C D E F IMP Activity: Sorting Shapes 6 AP S45 G H I J K L IMP Activity: Sorting Shapes 7 AP S46 M N O P IMP Activity: Sorting Shapes 8 AP S47 Q R S T U V IMP Activity: Sorting Shapes 9 AP S48 Name:_____________________________________ Date:____________ Period:__________ Cutting Corners Directions: Below each shape, write the name of the shape (be as specific as possible). 1) 2) Directions for making posters: Begin with your assigned shape. Make 1 straight cut through the shape to get two new shapes. Tape the 2 new shapes on the poster (so it looks like the original shape) and then label the two shapes with a noun and as many adjectives as you think apply. Continue doing this to the same original shape (beginning with a new copy each time) to get as many different shapes as possible. IMP Activity: Cutting Corners© 1 AP S49 Challenge Questions Directions: Answer each question BOTH in words and with a picture to explain your thinking. 1. Can a triangle have more than 1 obtuse angle? Why or why not? 2. Can a trapezoid be called “right”? Why or why not? 3. Can a triangle have two right angles? Why or why not? 4. Can a right triangle also be isosceles? Why or why not? 5. Can a trapezoid be isosceles? Why or why not? 6. Can an equilateral triangle be obtuse? Why or why not? IMP Activity: Cutting Corners© 2 AP S50 Ticket Out The Door Directions: Below each shape, write the name of the shape (be as specific as possible). 1) IMP Activity: Cutting Corners© 2) 6 AP S51 Starting Shape: Parallelogram IMP Activity: Cutting Corners© 7 AP S52 Starting Shape: Trapezoid IMP Activity: Cutting Corners© 8 AP S53 Starting Shape: Rectangle IMP Activity: Cutting Corners© 9 AP S54 Starting Shape: Triangle IMP Activity: Cutting Corners© 10 AP S55 Starting Shape: Square IMP Activity: Cutting Corners© 11 AP S56 Name:______________________________________________ Date:____________ Can You Make What I Have? In the space below, use your ruler and protractor to draw a single figure that has all of the following properties: • The figure is composed of between 4 and 6 lines, rays or segments. (Make sure to label points with letters) • The figure includes at least one right angle. • The figure includes at least one obtuse angle. • No part of the figure is disconnected from the rest. • The figure encloses some area. Below or on the reverse write directions that would tell someone how to draw your figure without having seen it. Consider using some of the sentence frames provided and the word bank to help you write your directions. Also make sure to label your vertices with letters! My Creation Sentence Frames: Draw a _____________ line ________ cm long. Label this point _________________. From ________________, draw ______________. Directions for making my figure. Word Bank Parallel Perpendicular Line Line Segment Ray Point Vertical Horizontal Acute Obtuse Right Intersecting Angle Degree CM/ Inch Vertex 1.) _________________________________________________________________________________ __ _________________________________________________________________________________ 2.) _________________________________________________________________________________ __ _________________________________________________________________________________ 3.) _________________________________________________________________________________ __ _________________________________________________________________________________ 4.) _________________________________________________________________________________ __ _________________________________________________________________________________ IMP Activity: Can You Make What I Have? 1 AP S57 5.) _________________________________________________________________________________ __ _________________________________________________________________________________ 6.) _________________________________________________________________________________ __ _________________________________________________________________________________ 7.) _________________________________________________________________________________ __ _________________________________________________________________________________ 8.) _________________________________________________________________________________ __ _________________________________________________________________________________ 9.) _________________________________________________________________________________ __ _________________________________________________________________________________ 10.) ________________________________________________________________________________ __ ________________________________________________________________________________ IMP Activity: Can You Make What I Have? 2 AP S58 Name: ________________________________________ Date:________________ Not All Designs Are Created Equal Task 1: Sort the pictures you have been given into two groups: in one group put all the pictures have a certain feature and in the other group put the pictures that do NOT share that feature. Record the letter of the pictures in each group as well as your rule for sorting. Come up with at least 3 different ways to sort the pictures. Sort 1: Rule ________________________________________________________________ __________________________________________________________________________ Pictures that fit this rule: _____________________________________ Pictures that do NOT fit this rule: _______________________________ Sort 2: Rule ________________________________________________________________ __________________________________________________________________________ Pictures that fit this rule: _____________________________________ Pictures that do NOT fit this rule: _______________________________ Sort 3: Rule ________________________________________________________________ __________________________________________________________________________ Pictures that fit this rule: _____________________________________ Pictures that do NOT fit this rule: _______________________________ Teacher’s Sort: Rule _________________________________________________________ __________________________________________________________________________ Pictures that fit this rule: _____________________________________ Pictures that do NOT fit this rule: _______________________________ IMP Activity: Not All Designs are Created Equal 1 AP S59 Line of Symmetry: A line that could be drawn through a 2-Dimensional picture or shape such that the figure can be folded on the line into matching parts. Task 2: Try to fold the designs in pictures A, C, E, G, I and K along the line of symmetry to show that the pictures are really symmetrical. Try to do the same thing for the other 6 pictures and be prepared to show that those pictures are NOT symmetrical. Task 3: Investigating Polygons for symmetry. Predict: Which polygons do you think will have a line of symmetry? _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ You will use the shapes you sorted for the Sorting Shapes lesson to investigate which polygons have a line of symmetry. After trying to fold the shape to find out if it does have a line of symmetry, draw a sketch below of the ones that do and show where the line of symmetry is. IMP Activity: Not All Designs are Created Equal 2 AP S60 Task 4: Drawing the other half For each shape below, only half of the shape is showing. Assume a line of symmetry was used to show you just half of the picture. Use this information to draw the other half of the picture. IMP Activity: Not All Designs are Created Equal 3 AP S61 C K A IMP Activity: Not All Designs are Created Equal F B L 6 AP S62 E I D H G IMP Activity: Not All Designs are Created Equal J 7 AP S63