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Lesson Plans Monday, April 8th Genece S. Porter Area of Instruction Fantastic Five/ Mental Math/Review Homework/ Teacher-Directed Math/Guided/ Independent Practice/Small Group/Closure/ Homework assigned 5-6.5 Represent the probability of a single-stage event in words and fractions. 5-1.1 Analyze information to solve increasingly more sophisticated problems. 5-1.2 Construct arguments that lead to conclusions about general mathematical properties and Lesson TSW unpack and complete their respective day’s Fantastic Five. At 7:45, TCW go over the Fantastic Five. Early finishers will complete their Enrichment Folders. Note that an experimental sample space includes outcomes from an experiment, while a theoretical sample space includes all possible equally likely outcomes. A fair experimental tool is designed to have equally likely outcomes. Have the class name some fair and unfair tools. Materials: equal-sized square tiles in three colors (30 for each group), paper bags Engage and Explore Give each group a prepared, closed bag of square tiles. Show students how to make a table to record tallies. Have group members take turns randomly picking one square at a time. Have them keep a tally of each color drawn (outcomes). Put each tile back in the bag after it is drawn. Shake the bag. Complete 15 draws (trials) and close the bag. Explain There are 30 square tiles in your bag. Study your tally table. How many tiles of each color are in the bag? Explain your reasoning. (Students should compare the numbers on their tally tables and show an informal, intuitive understanding of ratio and equivalent fractions (e.g. “Looking at 15 tiles, I see twice as many blue tiles as green tiles and only 1 red tile, so out of 30 tiles, I predict…”). Do you think the tally numbers would have been different if you had not replaced each tile after it was drawn? Explain. (Yes, because the probability of drawing a tile would change for each draw.) Elaborate and Evaluate Ask students to empty the contents of the bag. How did relationships. 5-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects. 5-1.5 Use correct, clear, and complete oral and written mathematical language to pose questions, communicate ideas, and extend problem situations. 5-1.6 Generalize connections between new mathematical ideas and related concepts and subjects that have been previously considered. Recess Activity Lunch your prediction compare to the colors of the actual tiles in the bag? Why? (Page 254) Have students read the Problem. Have students read Example 1. If the Problem had not mentioned that Cara spun the pointer of the spinner 20 times, how could you have known that the total number of trials was 20? (I could have added the number of spins in the table to find 20 total spins.) Is it important to know what Cara’s spinner looks like in order to find experimental probability? Explain. (You do not need to know what the spinner looks like. To find the experimental probability, you need to know the number of trials and the number of favorable outcomes that occur within those trials.) Have students read Example 2. Is Jenny guaranteed to spin a 4 in 3 of her next 10 spins? Explain. (No. You are not guaranteed anything in an experiment. The calculation is just a prediction.) (Page 255) Have students read Example 3. For which color are the experimental and theoretical probabilities closest in value? (yellow) Have students look at how the experimental and theoretical probabilities compare in Example 3 and in the Activity. Predict the change in the relationship between theoretical probability and experimental probability as the number of trials in an experiment increases. Lead students to see that experimental probability moves closer to theoretical probability as the number of trials increases.) Guided/Independent Practice pgs. 254-257 Homework-Worksheet on Finding the experimental probability of an event, and compare experimental and theoretical probabilities. Play and socialize unless it is raining, then TSW play Math Games and socialize in the classroom. Arts-TCW go to Activity, and the students will take turns going to the restroom TCW go to lunch, and the students will take turns going to the restroom Pack up/dismiss Lesson Plans Tuesday April 9th Lesson Area of Instruction Gym/Breakfast/Restroom Fantastic Five/ Mental Math/Review Homework/TeacherDirected Math/Guided/ Independent Practice/Small Group/Closure/ Homework assigned TSW unpack and complete their respective day’s Fantastic Five. At 7:45, TCW go over the Fantastic Five. Early finishers will complete their Enrichment Folders. Benchmark measurements of 45˚, 90˚, 135˚, and 180˚ can be used to estimate the measure of angles. To measure an angle, place the center point of the protractor over the vertex and its base 5-5.2 along one ray. That ray should point to 0. Use a protractor to (Page 310) Have students focus on the Examples. measure angles In Example A, explain how you would draw → from 0 to 180 MO degrees. To make an obtuse angle NMO. (You would have to draw and label Angle MO so that it extends from 5-1.3 point M to the left of the 90-degree angle.) Explain and justify Why do you line up one of the rays with 0 degrees answers based on on the protractor? (When you start measuring at mathematical zero, the measure of the angle is the number on the properties, protractor that the second ray passes through.) structures, and Why is the measure of <JKL not 120˚? (Because relationships. ray → 5-1.6 KL crosses zero on the right, which is the inside set Generalize of numbers so, you use the inside set of numbers to connections determine the measure.) between new (Page 311) Which scale of the protractor did you mathematical ideas use to measure 60˚? Explain. (→ and related concepts DE was pointing to and subjects that the right, so I started with the 0 at the right side of have been the protractor and used the inside scale.) previously Focus students’ attention on More Examples, A considered. 5-1.7 Use flexibility in mathematical representations. and B. What would happen if you used the inside scale to measure <ABC? (The measure of the angle would read 130˚ instead of 50˚.) What do you notice about each pair of measurements on the protractor? (Each pair makes a sum of 180˚.) Suppose you place the base of the protractor along → YX. How does this differ from using ray → YZ? (You would have to use the outside scale and start with the 0 on the left instead of the right; the measure of the angle is the same.) What strategies can you use to make sure that you are using the correct scale on the protractor? (Use estimation, benchmarks, and visual clues. If the angle looks like it is an acute angle, then it should be less than 90˚. If it looks like it is an obtuse angle, then it should be greater than 90˚.) Guided/Independent Practice-Pgs. 310-313 Homework-Worksheet on Estimating, Measuring, and Drawing Angles. Recess Activity Lunch Pack up/dismiss Play and socialize unless it is raining, then TSW play Math Games and socialize in the classroom. Library-TCW go to Activity and the students will take turns going to the restroom TCW go to lunch and the students will take turns going to the restroom Dismiss Lesson Plans Wednesday April 10th Area of Instruction Fantastic Five/ Mental Math/Review Homework/Teacher- Lesson Gym/Breakfast/Restroom TSW unpack and complete their respective day’s Fantastic Five. At 7:45, TCW go over the Fantastic Five. Early Finishers will complete their Enrichment Folders. Manipulatives such as pattern blocks can help students visualize the difference between regular polygons and those that are not regular. (Page 314) Have students read the Problem. Focus students’ attention on the definition of a regular 5-4.6 Analyze shapes to polygon. Explain whether or not you think the octagons that form Castel del Monte are regular. determine line symmetry and/or (Regular octagons have 8 equal sides and 8 equal angles; all of the octagons in Castel del Monte rotational appear to have sides of the same length and angles symmetry. of the same measure.) Discuss the polygons in the Example. Which is the 5-4.1 only kind of regular polygon that contains acute Apply the angles? (Only a regular triangle can have acute relationships of angles. Since the three angles have to be the same quadrilateral to measure, and the sum of the angles in a triangle make logical always totals 180˚, each angle has to be 60˚.) arguments about (Page 315) Focus students’ attention on the their properties. Activity. What does each labeled dot on the quadrilateral represent? (Each labeled dot 5-1.6 represents the vertex of an angle in the Generalize quadrilateral.) connections Explain whether you could have drawn a line between new mathematical ideas segment from B to D in Step 2 to form two triangles and related concepts in the quadrilateral. (Yes, the two triangles would have had different shapes, but the sum of their and subjects that angles would be 180˚.) have been Explain how you use the protractor to measure the previously angles. (To measure each angle, I placed the center considered. point of the protractor on the vertex of the angle and the base along one side of the triangle. I looked at where the next side crossed the scale of the protractor. I turned the triangles to measure all the angles.) Directed Math/Guided/ Independent Practice/Small Group/Closure/ Homework assigned Guided/Independent Practice pgs. 314-317 Homework-Worksheet on Identifying regular polygons; finding the sum of the angles in quadrilaterals. Recess Play and socialize unless it is raining, then TSW play Math Games and socialize in the classroom. Arts-TCW go to Activity and the students will take turns going to the restroom TCW go to lunch and the students will take turns going to the restroom Activity Lunch Pack up/Dismiss Lesson Plans Thursday April 11th Lesson Area of Instruction Gym/Breakfast/Restroom Fantastic Five/Mental Math/Review Homework/TeacherDirected Math/Guided/ Independent Practice/Small Group/Closure/ Homework assigned TSW unpack and complete their respective day’s Fantastic Five. At 7:45, TCW go over the Fantastic Five. Early finishers will complete their Enrichment Folders. bar (—) JK are used to show that segments are congruent. 5-4.2 Compare the angles, (<C or <DCA) are used to show that angles side lengths, and are congruent. perimeters of An equal sign (=) is used for the length of a congruent shapes. line segment (MN = 2 inches). An equal sign (=) is used for the measure of 5-1.2 an angle (m<ABC = 56˚). Construct arguments that lead (Page 318) Have students read the paragraph. to conclusions about When a congruence symbol is used to show that line segments are congruent, what other symbol is general used? Explain. (A segment symbol (bar) is placed mathematical over each pair of capital letters that represent the properties and endpoints of the congruent line segments. For relationships. example, XY = NK.) Have students list sides that appear to be the same 5-1.7 length. Can you write congruence statements Use flexibility in relating the sides that appear to be the same mathematical length? (You must make sure that the sides are representation. congruent by measuring each side with a ruler. If two sides are congruent, you can write a congruence statement by using the symbol + between the two line segments, for example, KL = RS.) (Page 319) Can two angles be congruent even if the sides of the angles are not the same length? (A protractor measures the number of degrees when the endpoints of two rays join to form a vertex of an angle. Each ray extends to infinity, so it does not matter how long the rays are drawn; so, their length does not affect the measure of the angle.) Have students focus on Example 2. If you were asked to measure the angles of triangle ABC, how could you make sure that you measure accurately? (We could use a straightedge to trace and label the triangles on paper. Then, we could use the straightedge to carefully extend the sides of the protractor. Finally, we should look back at each angle to be sure we used the correct scale on the protractor.) Guided/Independent Practice pgs. 318-321 Homework-Worksheet on Identifying congruent line segments and congruent angles. Recess Play and socialize unless it is raining, then TSW play Math Games and socialize in the classroom. PE-TCW go to Activity and students will take turns going to the restroom TCW go to lunch and the students will take turns going to the restroom. Activity Lunch Pack up/dismiss Lesson Plans Friday April 12th Area of Instruction Lesson Fantastic Five/Mental Math/Review Homework/Teacher- Gym/Breakfast/Restroom TSW unpack and complete their respective day’s Fantastic Five. At 7:45, TCW go over the Fantastic Five. Early finishers will complete their Enrichment Folders. Directed Math/Guided/ Independent Practice/Small Group/Closure/ Homework Assigned 5-4.3 Classify shapes as congruent. 5-1.1 Analyze information to solve increasingly more sophisticated problems. 5-1.2 Construct arguments that lead to conclusions about general mathematical properties and relationships. 5-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects. Congruent figures have corresponding sides and corresponding angles. Congruent figures have the same shape and size. (Page 322) Have students read the paragraph. Discuss the corresponding sides and angles in Examples A and B. What if triangle DEF were facing the opposite direction? What could you do that would help determine which sides and angles correspond to triangle ABC? (Trace triangle DEF, cut it out, and then turn it to face the same direction as triangle ABC.) Have students focus on Example B. Since all the angles in both quadrilaterals have the same measure, I should use corresponding sides to find the corresponding angles. How does knowing the corresponding sides help you to find the corresponding angles? (I can see that an angle is the vertex between two sides, so I can look for the corresponding sides in the other rectangle. The angle that is formed by the vertices of these sides is the corresponding angle.) (Page 323) Direct students’ attention to the wallet-size photo on the page. How could you verify that two wallet-size photos are the same size? (Use a ruler to measure and compare the lengths of the sides.) How could you determine that two photos are congruent? (Identify the corresponding sides and angles, then measure the sides and angles. If the corresponding sides are congruent and the corresponding angles are congruent, then the photos are congruent.) Focus students’ attention on the Hands On Activity. How did you know how long the sides of each triangle should be? (I measured the lengths of each side in both triangles.) 5-1.6 Generalize connections between new mathematical ideas Guided/Independent Practice pgs. 322-325 and related concepts Homework-Worksheet on Identifying congruent and subjects that have been previously considered. Recess Activity Lunch Pack up/Dismiss figures. Play and socialize unless it is raining, then TSW play Math Games and socialize in the classroom. Library-TCW go to Activity and the students will take turns going to the restroom TCW go to lunch, and the students will take turns going to the restroom