1. Can you tell from this frequency table how many students had 20 correct answers

Transcription

1 INVESTIGATION 1 Frequency Tables Histograms Surveys (page 54) A frequency table is a way of pairing selected data, in this case specified test scores, with the number of times the selected data occur. The frequency table below shows the scores from a math test in Mr. Lawson s class. Name Teacher Note: The extensions are optional. The scores in the table are grouped in intervals by the number correct. Refer to the frequency table to answer questions Can you tell from this frequency table how many students had 20 correct answers on the test? Why or why not? The frequency t shows the total number of s who scored or. 2. Mr. Lawson tallied the number of scores in each interval. How many scores wide is each interval? Why do you think Mr. Lawson arranged the scores in such intervals? The intervals are scores wide. One reason he might have arranged the scores in these intervals is to group the scores by the grades:,,, 3. Show how to make a tally for As a class activity, make a frequency table of the birth months of the students in the class. Make four intervals by grouping the months: Jan. Mar., Apr. Jun., Jul. Sep., Oct. Dec. If the teacher wishes, this activity may be optional. Saxon Math Course 1 I1-1 Adaptations Investigation 1

2 INVESTIGATION 1 (continued) (page 55) A histogram is a special type of bar graph with no space between the bars. The histogram below shows the same data as the frequency table. Refer to the histogram to answer questions Which interval had the lowest frequency of scores? 6. Which interval had the highest frequency of scores? 7. Which interval had exactly twice as many scores as the interval? 8. Make a frequency table and histogram for the following set of scores. (Use 50 59, 60 69, 70 79, 80 89, and for the intervals.) Test scores: 63, 75, 58, 89, 92, 84, 95, 63, 78, 88, 96, 67, 59, 70, 83, 89, 76, 85, 94, 80 A survey is a way of collecting data about a population. Rather than study every member of a population, a survey studies a small part of the population, called a sample. From the sample, conclusions are formed about the entire population. Saxon Math Course 1 I1-2 Adaptations Investigation 1

3 INVESTIGATION 1 (continued) (page 56) Mrs. Patterson s class gave 100 male and female students a choice of favorite sports. This survey was used to make the frequency table and bar graph below. Refer to the frequency table and bar graph for this survey to answer questions Which sport was the favorite sport of about 1_ of the students surveyed 4 (1 in 4 students)? 10. Which sport was the favorite sport of the girls who were surveyed? A softball B volleyball C basketball D cannot be determined from information provided 11. How might changing the sample group change the results of the survey? Instead of considering boys and girls together, they could have considered them. 12. How might changing the survey question the choice of sports change the results of the survey? If different were available to choose from, the results might be. extensions a. Complete the histogram based on the frequency table created in problem 4. Write two questions that can be answered by this histogram. How many students were b in? How many s are in the c? Saxon Math Course 1 I1-3 Adaptations Investigation 1

4 INVESTIGATION 1 (continued) (page 57) b. If you conducted a survey of favorite foods of class members, what would be the size of the sample? How will the data gathered by the survey be displayed? With a h. c. The table below uses negative integers to express the estimated greatest depth of each of the Great Lakes. U.S. Est. Greatest Depth (in meters) Lake Erie Huron Michigan Ontario Superior Depth 65 m 230 m 280 m 245 m 400 m Write the depths of the lakes in order from the deepest to the shallowest.,,, Are the data in the table displayed correctly on the bar graph below? Explain why or why not., the depths for Lakes and are switched. d. Use the table in extension c to answer the following questions: Lake Superior is how much deeper than Lake Erie? Is the depth of Lake Michigan closer to the depth of Lake Ontario or Lake Huron? Lake How much deeper is Lake Michigan than Lake Huron? Saxon Math Course 1 I1-4 Adaptations Investigation 1

5 INVESTIGATION 2 Investigating Fractions with Manipulatives (page 109) Use your fraction manipulatives to help you with these exercises: 1. What percent of a whole tower is 1_ of a tower? 2 2. What fraction is half of 1_ 2? 3. What fraction is half of 1_ 4? 4. Fit three 1_ pieces together to form 3_ of a whole tower. 4 4 Three fourths of a tower is what percent of a tower? 5. Fit four 1_ pieces together to form 4_ of a whole tower. 8 8 Four eighths of a tower is what percent of a tower? 6. Fit three 1_ pieces together to form 3_ of a tower. 6 6 Three sixths of a tower is what percent of a tower? 7. Compare 4_ 8, 3_, and 2_ to a 1_ tower cube. All of these fractions reduce to. 8. The fraction 2_ equals which single fraction piece? 8 9. The fraction 6_ equals how many 1_ 8 4 s? 10. The fraction 2_ equals which single fraction piece? 6 Name Teacher Notes: The mainstream Student Edition describes the use of pie-shaped fraction manipulatives. Because of visual acuity problems, it is recommended that Adaptations students use fraction, decimal, and percent tower manipulatives available in the Adaptations Manipulative Kit. If the manipulative kit is not available, Hint #31, Fraction Manipulatives, describes how to make paper fraction, decimal, and percent tower manipulatives. Introduce Hint #32, Percent, and Hint #33, Improper Fractions. Refer students to Fraction- Decimal-Percent Equivalents on page 13 in the Student Reference Guide. Post reference chart, Often Used Fractions. The extensions are optional. 11. The fraction 4_ equals how many 1_ 6 3 s? 12. If you add 1_ 8 + 1_ 8 + 1_, the sum is 3_. If you add 3_ and 2_ what is the sum? Form a whole tower using six of the 1_ pieces. Then remove (subtract) 1_ 6 6. What fraction of the tower is left? What equation represents your model? 1 1_ 6 = 14. Show how to subtract 1_ from 1 by forming a 3 tower of 3_ 3 and then removing 1_ 3. What fraction is left? 15. Use four 1_ s to show the subtraction 1 1_. Then write the answer Use eight 1_ s to show the subtraction 1 3_. Then write the answer What percent of a tower is 1_ of a tower? What percent of a tower is 1_ of a tower? 6 Saxon Math Course 1 I2-5 Adaptations Investigation 2

6 INVESTIGATION 2 (continued) (page 110) You can use fraction manipulatives to model comparisons. 19. Fit two 1_ pieces together and fit three 1_ pieces together. Use the models to complete the comparison Fit two 1_ pieces together and fit three 1_ pieces together. Use the models to complete the comparison Shade 1_ of the left-hand rectangle and shade 1_ 3 5 of the right-hand rectangle. Which fraction is larger? 22. Shade 3_ 5 3 of the left-hand rectangle and shade of the right-hand rectangle to model this comparison > 3 10 An improper (top-heavy) fraction is equal to or greater than 1. The numerator is equal to or greater than the denominator. 23. Fit together five 1_ pieces. Show that the improper fraction 5_ equals the mixed number 11_ by replacing four of the 1_ pieces with a whole tower The improper fraction 7_ equals what mixed number? The improper fraction 3_ equals what mixed number? Form 1 1_ 2 towers using only 1_ s. How many 1_ pieces are needed to make 11_ 4 4 2? 27. How many 1_ pieces are needed to make 2 whole towers? The improper fraction 4_ equals what mixed number? Convert (change) 11 into a mixed number How many twelfths equal these fractions of a tower? Saxon Math Course 1 I2-6 Adaptations Investigation 2

7 INVESTIGATION 2 (continued) (page 111) extensions a. Use fraction manipulatives to answer each problem = = = = Does the Commutative Property apply to addition of fractions? Does the Commutative Property apply to subtraction of fractions? b. Use fraction manipulatives to solve each problem. 1. One-fourth of a pizza was eaten. How much of the pizza was not eaten? = 2. Each of 3 students ate 1_ of a new box of cereal. What amount of cereal 8 in the box was eaten? = 3. More than half of the students in the class are girls. What fraction of the students in the class are boys? l than c. Estimate the placement of the following fractions on the number line. Use fraction manipulatives for help Saxon Math Course 1 I2-7 Adaptations Investigation 2

8

9 INVESTIGATION 3 Measuring and Drawing Angles with a Protractor (page 161) Angles are measured in degrees. Name Teacher Notes: Students will require a copy of Investigation Activity 10, a protractor, and an inch/ centimeter ruler to complete this Investigation. The extensions are optional. A protractor is used to measure the size of an angle. A protractor has two sets of numbers. If your angle is acute, use the smaller numbers. If your angle is obtuse, use the larger numbers. Type of Angle Acute angle Right angle Obtuse angle Straight angle Measure Greater than 0 but less than 90 Exactly 90 Greater than 90 but less than 180 Exactly 180 Practice reading a protractor by finding the measures of these angles. Then tell whether each is obtuse, acute, or right. 1. AOC 2. AOE 3. AOF 1. AOC 2. AOE 3. AOF 4. AOH 5. IOH 6. IOE 4. AOH 5. IOH 6. IOE Saxon Math Course 1 I3-9 Adaptations Investigation 3

10 INVESTIGATION 3 (continued) (page 162) Activity : Measuring Angles To measure an angle with a protractor: 1. Put the center point of the protractor on the vertex of the angle. 2. Put one of the zero marks on one ray of the angle. 3. Read the measure where the other ray of the angle passes through the protractor. Remember to write the degree symbol. Use a protractor to find the measures of the angles on Investigation Activity 10. To draw an angle with a protractor, begin with a horizontal ray like this: Now put the protractor with the center point of the protractor on the endpoint of the ray, and the ray on the zero degree mark of the protractor. Make a dot on the paper at the number on the protractor for the angle you want to draw. Remove the protractor and draw a ray from your endpoint of the first ray. It will go through the dot you made. Saxon Math Course 1 I3-10 Adaptations Investigation 3

11 INVESTIGATION 3 (continued) (page 162) Use your protractor to draw angles with these measures: Draw triangle ABC. Draw segment BC six inches long. Make a 60 angle at vertex B. Make a 60 angle at vertex C. Extend the segments to where they intersect at point A. B C Saxon Math Course 1 I3-11 Adaptations Investigation 3

12 INVESTIGATION 3 (continued) (page 163) 14. Use your inch ruler to find the length of segments AB and AC in triangle ABC. AB = AC = 15. Use your protractor to find the measure of angle A in triangle ABC. m A = 16. Draw triangle STU. Draw segment ST 10 centimeters long. Make a 90 angle at vertex S. Make segment SU 10 centimeters long. Complete the triangle by making segment TU. S 17. Use your protractor to find the measures of angle T and angle U. m T = m U = T 18. Use a centimeter ruler to find the length of segment TU to the nearest centimeter. TU = Saxon Math Course 1 I3-12 Adaptations Investigation 3

13 INVESTIGATION 3 (continued) (page 163) extensions a. The building code for this staircase requires that the inclination be between 30 and 35. Does this staircase meet the building code? Explain. I measured the angle of the staircase and found that it is. So the staircase meet the building code. b. Look at the two sets of polygons. Set 1 contains something not found in Set 2. What is it? The p in Set 1 have angles. Draw another figure that would fit into Set 1. Saxon Math Course 1 I3-13 Adaptations Investigation 3

14

15 INVESTIGATION 4 Collecting, Organizing, Displaying, and Interpreting Data (page 211) Statistics is gathering and organizing data so that we can draw conclusions from the data. Data can be quantitative or qualitative. Name Quantitative data comes in numbers like population, hours per week, etc. Qualitative data belongs to a category like the month in which a person was born or a favorite flavor of ice cream. In problems 1 5 below, decide whether the data are qualitative or quantitative. 1. Jagdish buys 50 bags of clothing for a clothing drive and counts the number of items in each bag. 2. For one hour Carlos notes the color of each car that drives past his house. 3. Sharon rides a school bus home after school. For two weeks she measures the time the bus trip takes. 4. Brigit asks each student in her class, Which is your favorite holiday New Year s, Thanksgiving, or Independence Day? Teacher Note: The extensions are optional. 5. Marcello asks each player on his little league team, Which major league baseball team is your favorite? Which team do you like the least? 6. Write a quantitative survey question about viewing TV: How many h per do you watch TV? Write a qualitative survey question about viewing TV: Which television programs are your f? (Collecting and recording the data is optional.) A line plot is a good way to organize quantitative data. The data shown here are responses to the question How many hours a week do you spend watching television? Saxon Math Course 1 I4-15 Adaptations Investigation 4

16 INVESTIGATION 4 (continued) (page 213) The data make the line plot below. Each dot is for one of the numbers. The plot shows that the number of hours watching TV ranges from 0 to 15, but most students watch either 2 4 or 7 8 hours each week. A bar graph is a good way to organize qualitative data. The frequency table and bar graph below display responses to the question, Which type of TV shows do you prefer to watch sports, news, animation, sit-coms, or movies? A survey asks questions to find out about a certain group of individuals. This group is called the population. For example, the population of a survey may be teenagers or senior citizens. The population of a survey often is not the same as the population of a city or a state. The population of a survey is often very large, so the survey is given to a small part of a population called a sample. But different samples give us different data. A sample that is very much like the population is called a representative sample. In problems 7 and 8 below, explain why each sample is NOT representative. How would you expect the sample s responses to differ from those of the general population? 7. To determine public opinion in the city of Dallas about a proposed leash law for dogs, Sally interviews shoppers in several Dallas pet stores. Pet store shoppers are more likely to own p than people from the general p. Support for a leash law might be among those surveyed than among the general population. Saxon Math Course 1 I4-16 Adaptations Investigation 4

17 INVESTIGATION 4 (continued) (page 214) 8. Tamika wants to know the movie preferences of students in her middle school. Since she is in the school orchestra, she chooses to survey orchestra members. O members are likely to have an interest in music than other s. So m preferred by orchestra members might be musically oriented than movies preferred by other s. The results of a survey can depend on the way the questions are worded or who asks the question. These factors can introduce bias into a survey. This means that people are encouraged to give certain answers and not others. Identify the source of the bias in each survey. Is the answer yes more likely or less likely because of the bias? 9. The researcher asked the group of adults, If you were lost in an unfamiliar town, would you be sensible and ask for directions? The word s would make people likely to answer yes. 10. Mrs. Wong baked oatmeal bars for her daughter s fundraising sale. She asked the students who attended the sale, Would you have preferred fruit salad to my oatmeal bars? Out of politeness, students might be likely to answer yes because Mrs. Wong baked the o for the sale. extensions a. One might guess that young people prefer different seasons than adults. The frequency tables below show the results when 24 people under the age of 15 and 24 people over the age of 20 were asked, Which season of the year do you like most fall, winter, spring, or summer? Under 15 Season Frequency fall 2 winter 0 spring 4 summer 18 Over 20 Season Frequency fall 6 winter 2 spring 8 summer 8 Saxon Math Course 1 I4-17 Adaptations Investigation 4

18 INVESTIGATION 4 (continued) (page 214) Display these results on the circle graphs below. Under 15 Over 20 Why do you think more people under the age of 15 chose summer than people over the age of 20? People the age of do not have school in the s. b. One might guess that young people drink different beverages for breakfast than adults. The frequency tables below show the results when 24 people under the age of 15 and 24 people over the age of 20 were asked, Which of the following beverages do you drink most often at breakfast juice, coffee, milk, or something else? Under 15 Beverage Frequency juice 8 coffee 2 milk 10 other 4 Over 20 Beverage Frequency juice 8 coffee 10 milk 2 other 4 Display these results on the circle graphs below. Under 15 Over 20 Use the Student Edition for extensions c and d. Saxon Math Course 1 I4-18 Adaptations Investigation 4

19 INVESTIGATION 4 (continued) (page 214) e. Use the menu to answer the questions below. Seafood Cafe Appetizers Shrimp Cocktail...$7.00 Zucchini Fingers... $5.00 Soup Seafood Gumbo... $4.50 Lobster Bisque... $4.50 Main Course Halibut... $15.75 Swordfish... $18.00 Flounder... $13.75 Crab Cakes... $12.50 Dessert Sorbet...$3.25 What is the most expensive item on the menu? The least expensive? What is the average price of the main course dinners? $15.75 $15.75 $15.75 $15.75 What is the range of prices on the menu? $15.75 $15.75 f. A number of bicyclists participated in a 25-mile bicycle race. The winner completed the race in 45 minutes and 27 seconds. The table below shows the times of the next four riders expressed in the number of minutes and seconds that they placed behind the winner. Rider Number 021 Time Behind Winner (minutes and seconds in hundredths) 1: : :13.45 The least time in the table represents the rider who finished second. The greatest time represents the rider who finished fifth. Write the four rider numbers in the order of their finish.,,, Saxon Math Course 1 I4-19 Adaptations Investigation 4

20 INVESTIGATION 4 (continued) (page 214) g. The average rate of speed for rider 008 was 33 miles per hour. At that rate, did this rider finish more than 1 mile or less than 1 mile behind the winner? Change the rate to miles per minute. 33 mi 1 hr 1 hr 60 min = mi 1 min 1:29.77 rounds to 1.5 minutes. Multiply. 1.5 min mi 1 min = mi mile is l than 1 mile. Saxon Math Course 1 I4-20 Adaptations Investigation 4

21 INVESTIGATION 5 Displaying Data (page 264) Part 1: Qualitative Data We have studied bar graphs and circle graphs. Data can also be shown in pictographs. Each object in a pictograph represents a certain number, as shown in the key. Name Teacher Notes: Refer students to Statistics on page 23 in the Student Reference Guide. Students will need a protractor to complete this Investigation. In the pictograph above, how many cars and trucks are produced in Michigan? In the four named states? In the nation? 1. Display the car and truck production data on this horizontal bar graph. 2. What fraction of U.S. car and truck production took place in Michigan? Michigan total production = Saxon Math Course 1 I5-21 Adaptations Investigation 5

22 INVESTIGATION 5 (continued) (page 265) Another way to display qualitative data is a circle graph. It is sometimes called a pie graph. Each category is called a sector (pie piece) of the circle. We can calculate the angle of each sector if we know the fraction of the whole each part represents. A whole circle has 360, so each sector is a fraction of 360. We know that 12 million cars and trucks were produced. This table shows the fraction produced by each state. Category Count (millions) Fraction Michigan 3 Ohio 2 Kentucky 1 Missouri 1 Other States 5 Total Multiply each fraction by 360. The sector of the circle graph representing Michigan will cover = What is the central angle measure of the sector for each category? Michigan 90 Ohio Kentucky Missouri Other States 4. The circle graph below shows a 90 ( 1_ 4 ) sector for Michigan. Complete the circle graph with the data for each remaining category. Put the center of a protractor over the center of the circle and draw the angles for each category. Saxon Math Course 1 I5-22 Adaptations Investigation 5

23 INVESTIGATION 5 (continued) (page 265) 5. Compare the pictograph, bar graph, and circle graph. The pictograph shows the c between states using p. The bar graph also shows the c, but with b instead of pictures. The circle graph shows production by a p of the whole. Part 2: Quantitative Data Quantitative data comes in individual numbers, called data points. This data can be grouped in intervals and displayed in a histogram as in Investigation 1. When we group data in intervals, the individual data points disappear. If we want to see the individual data points, we can display them on a line plot. A line plot is a number line. Put an X over a number for each data point that matches that number. Suppose 18 students take a test that has 20 possible points. Their scores, listed in increasing order, are 5, 8, 8, 10, 10, 11, 12, 12, 12, 12, 13, 13, 14, 16, 17, 17, 18, 19 We represent these data in the line plot below. When describing numerical data, we often use terms such as mean, median, mode, and range. Here we define each of these terms: Mean: the average of the numbers (12.6) Median: the middle number when the data are arranged in numerical order (12) Mode: the most frequently occurring number (12) Range: the difference between the greatest and least of the numbers (14) Saxon Math Course 1 I5-23 Adaptations Investigation 5

24 INVESTIGATION 5 (continued) (page 266) 6. The daily high temperatures in degrees Fahrenheit for 20 days in a row are listed below. Write the temperatures in increasing order. Then display them on a line plot. 60, 52, 49, 51, 47, 53, 62, 60, 57, 56, 58, 56, 63, 58, 53, 50, 48, 60, 62, 53 47,,, 50,,,,,,,,, 58,,,,,,, What is the median of the temperatures? 8. The distribution of the temperatures is bimodal because there are two modes. What are the two modes? and 9. What is the range of the temperatures? degrees Quantitative data can also be displayed in stem-and-leaf plots. The stem is the number in the tens place. The leaves are the ones digits for all the data that begin with that stem. 10. We have plotted the data points for the temperatures in problem 6. Now show the stem-and-leaf plot for the measures in problem 6. Saxon Math Course 1 I5-24 Adaptations Investigation 5

25 INVESTIGATION 5 (continued) (page 267) 11. Compare the stem-and-leaf plot from problem 10 and the line plot of the same data in problem 6. In the line plot, it is easy to see which n has the most d p. In the stem-and-leaf plot, the d p are grouped together in intervals of t. The extension is optional. Saxon Math Course 1 I5-25 Adaptations Investigation 5

26 INVESTIGATION 6 Attributes of Geometric Solids (page 314) Polygons are two-dimensional shapes. Solids are three-dimensional shapes. The edges that are hidden from you can be shown with dotted lines. It helps to use manipulatives when answering questions about geometric solids. A polyhedron is a solid figure on which every face is a polygon. Polyhedrons do NOT have any curved surfaces. Geometric Solids Shape Name Description Triangular Prism Rectangular Prism Polyhedron Polyhedron Name Teacher Notes: Introduce Hint #49, Geometric Solids (Manipulatives), Hint #50, Faces on a Cube, and Hint #51, Surface Area of a Prism. Refer students to Geometric Solids on page 30 and Surface Area of a Prism on page 31 in the Student Reference Guide. Geometric Solids manipulatives can be found in the Adaptations Manipulative Kit. The extensions are optional. (Students will need Investigation Activities 12 and 13 for extension c.) Cube Polyhedron Pyramid Polyhedron Cylinder Not Polyhedron Cone Not Polyhedron Sphere Not Polyhedron Name each shape and a real object of the same shape r p c t p 4. c 5. s 6. p Saxon Math Course 1 I6-26 Adaptations Investigation 6

27 INVESTIGATION 6 (continued) (page 315) Solids can have faces, edges, and vertices. 7. A cube has how many faces? 8. A cube has how many edges? 9. A cube has how many vertices? Activity : Comparing Geometric Solids Using geometric solids, try to identify the following shapes by touch rather than by sight: cone pyramid cube cylinder The questions given in the Student Edition are optional. Here is a pyramid with a square base. One face is a square, the rest are triangles. 10. How many faces does this pyramid have? 11. How many edges does this pyramid have? 12. How many vertices does this pyramid have? To draw a cube start with two squares. The connect the vertices. 13. Draw a rectangular prism. Begin by drawing two rectangles like this. 14. Draw a triangular prism. Begin by drawing two triangles like this. 15. Draw a cylinder. Begin by drawing two flattened circles for the top and the bottom like this. Saxon Math Course 1 I6-27 Adaptations Investigation 6

28 INVESTIGATION 6 (continued) (page 316) To find the surface area of a polyhedron, we add the area of its faces. Since a rectangular solid has six faces, you find the area of each face and then add the areas together. To find the surface area of a cube, find the area of one face. All six faces are the same, so just multiply the area of one face by six. 16. What is the area of each face of the cube? 17. What is the total surface area of the cube? It is more work to find the surface area of a rectangular solid that is not a cube. 18. What is the area of the front of the box? 19. What is the area of the bottom of the box? 20. What is the area of the right panel of the box? 21. Combine the areas of all six panels to find the total surface area of the box. Saxon Math Course 1 I6-28 Adaptations Investigation 6

29 INVESTIGATION 6 (continued) (page 317) 22. Here we show three ways to cut apart a box shaped like a cube. We have also shown another arrangement of six squares that does not fold back into a cube. Which pattern does not make a cube? A B C D We can also find the volume of a solid. The volume of a shape is the amount of space it occupies. When we measure volume, we label the answer with cubic centimeters, cubic inches, or cubic feet. In this Investigation we will count the number of cubes in a rectangular prism to find the volume. Count each layer of cubes. 23. How many cubes are used to make this rectangular solid? 24. How many small cubes are used to make this larger cube? 25. How many cubes are used to build this figure? Saxon Math Course 1 I6-29 Adaptations Investigation 6

30 INVESTIGATION 6 (continued) (page 318) extensions a. Look at the figures in problems 24 and 25. Draw the front view, top view, side view, and bottom view of each figure. b. Bring an empty cereal container from home. Open the glue joints and unfold the box until it is flat. On the unprinted side of the box, label the front, back, side, top, and bottom faces. Identify the glue tabs or any overlapping areas. (See the illustration in problem 21 for help.) Estimate the area of each of the six faces of the unfolded box. Do not include any glue tabs or overlapping areas in your estimate. Then estimate the total amount of cardboard that was used to make the box. Did you find the volume or the surface area of the cereal box? c. In problem 22, we show three nets that will form a cube. Investigation Activities 12 and 13 show nets for a triangular prism and a square pyramid. Cut out and fold these nets to form solids. Use tape to hold the shapes together. Use the Student Edition for extensions d f. d. How many blocks are in the tenth term of this pattern? Count the number of blocks in each figure. Continue the pattern to the tenth term. 1, 4,,,,,,,, Saxon Math Course 1 I6-30 Adaptations Investigation 6

31 INVESTIGATION 6 (continued) (page 318) e. Sketch the front, top, and bottom of each 3-dimensional figure. f. Figures A, B, and C were sorted into a group based on one common attribute. Figures D and E do not belong in the group above. What is the same about figures A, B, and C but not figures D and E? Figures A, B, and C each have two b. Sketch a figure that would belong in the group with figures A, B, and C. Saxon Math Course 1 I6-31 Adaptations Investigation 6

32

33 INVESTIGATION 7 The Coordinate Plane (page 363) Name A coordinate plane is a graph of perpendicular number lines. Origin: point where the number lines cross x-axis: horizontal number line (always the first number given) y-axis: vertical number line (always the second number given) Coordinates: the two numbers that tell the location of a point To graph a point: 1. Always begin at the origin. 2. Next move on the x-axis. If sign is positive, move right. If sign is negative, move left. 3. Last, move on the y-axis. If sign is positive, move up. If sign is negative, move down. Refer to the coordinate plane below to answer questions 1 6. Teacher Notes: Introduce Hint #55, Rectangular Coordinates, and Hint #56, Coordinate Geometry. Refer students to Rectangular Coordinates on page 18 in the Student Reference Guide. Space is provided on the investigation worksheet to work the activity, so no copies of Investigation Activity 15 need be made. The extensions are optional. 1. What are the coordinates of point A? (, ) 2. Which point has the coordinates ( 1, 3)? point 3. What are the coordinates of point E? (, ) 4. Which point has the coordinates (1, 3)? point 5. What are the coordinates of point D? (, ) 6. Which point has the coordinates (3, 1)? point Saxon Math Course 1 I7-33 Adaptations Investigation 7

34 INVESTIGATION 7 (continued) (page 365) We can name points on the plane as vertices of rectangles. Then we can find the perimeter and area of the rectangles. Suppose we are told that the vertices of a rectangle are (3, 2), ( 1, 2), ( 1, 1), and (3, 1). We graph the points and then draw segments between the points to draw the rectangle. We can see from the graph that the rectangle is four units long and three units wide. Adding the lengths of the four sides, we find that the perimeter of the rectangle is 14 units. To find the area, we can count the unit squares within the rectangle or multiply the side lengths. Either way, the area of the rectangle is 12 square units (units 2 ). 7. The vertices of a rectangle are located at ( 2, 1), (2, 1), (2, 3), and ( 2, 3). a. Graph the rectangle. What do we call this special type of rectangle? s b. What is the perimeter of the rectangle? c. What is the area of the rectangle? Saxon Math Course 1 I7-34 Adaptations Investigation 7

35 INVESTIGATION 7 (continued) (page 365) 8. The vertices of a rectangle are located at ( 4, 2), (0, 2), (0, 0), and ( 4, 0). a. Graph the rectangle. Notice that one vertex is located at (0, 0). What is the name for this point on the coordinate plane? o b. What is the perimeter of the rectangle? c. What is the area of the rectangle? 9. Three vertices of a rectangle are located at (3, 1), ( 2, 1), and ( 2, 3). a. Graph the rectangle. What are the coordinates of the fourth vertex? (, ) b. What is the perimeter of the rectangle? c. What is the area of the rectangle? Saxon Math Course 1 I7-35 Adaptations Investigation 7

36 INVESTIGATION 7 (continued) (page 365) Activity : Drawing on the Coordinate Plane 10. Christy made the following drawing on a coordinate plane. Then she wrote directions for making the drawing. Follow Christy s directions to make a similar drawing. The coordinates of the vertices are listed in order, as in a dot-to-dot drawing. Draw segments to connect the following points in order: a. ( 1, 2) b. ( 1, 3) c. ( 1 1 2, 5 ) d. ( 1 1 e. ( 1, 8) f. ( 1, ) g. ( 2, 9 1 i. (2, 10) j. ( 2, ) k. ( 1, 8 1 m. ( 1 1 2, 6 ) n. ( 1 1 2, 5 ) 2 ) 2 ) 2, 6 ) h. ( 2, 10) l. (1, 8) o. (1, 3) p. (1, 2) Lift your pencil and restart: a. ( 2 1 2, 4 ) b. ( 2 1 2, 4 ) d. ( 5, 2) e. ( 2 1 2, 4 ) c. (5, 2) Saxon Math Course 1 I7-36 Adaptations Investigation 7

37 INVESTIGATION 7 (continued) (page 366) 11. Carlos wrote the following directions for a drawing. Follow his directions to make the drawing on your own grid paper. Draw segments to connect the following points in order: a. ( 9, 0) b. (6, 1) c. (8, 0) d. (7, 1) e. ( 6, 1 2 ) f. (6, 1) g. ( 9, ) i. (7, 1) j. ( 6, ) k. ( , 3 ) h. (10, 2) l. ( 11, 2) m. ( , 0 ) n. ( 10, ) o. ( 9, ) p. ( 3, 3 1 q. ( 7, 8) r. ( 10, 8) s. ( 9, ) 2 ) Lift your pencil and restart: a. ( , 0 ) b. ( 11, 1 2 ) c. ( 12, 1 2 ) d. ( , 1 ) e. ( 12, ) f. ( , 2 ) g. ( 12, ) h. ( 11, ) i. ( , 3 ) j. ( , 8 ) k. ( 9 1 2, 8 ) l. ( 7, 3) m. ( 6, ) q. ( 1, 2) n. ( 7, 3) o. ( 6, 5) p. ( 4, 5) Saxon Math Course 1 I7-37 Adaptations Investigation 7

38 INVESTIGATION 7 (continued) (page 367) 12. On the coordinate plane, make a straight segment drawing using at least ten different points. Then write directions for making the drawing by listing the coordinates of the vertices in dot-to-dot order. Saxon Math Course 1 I7-38 Adaptations Investigation 7

39 INVESTIGATION 7 (continued) (page 367) extensions a. Use whole numbers, fractions and mixed numbers to write the coordinates for each point. A (, ) B (, ) C (, ) D (, ) E (, ) F (, ) b. Use the given coordinates to identify the point at each location. (6, 6) (4.5, 3) (2.5, 1.5) (3.5, 0) (3, 4.5) (0.5, 5.5) Saxon Math Course 1 I7-39 Adaptations Investigation 7

40

41 INVESTIGATION 8 Geometric Construction of Bisectors (page 417) Bisect means to cut into two equal parts. Activity 1 : Perpendicular Bisector Follow the instructions to bisect segment AB. Name Teacher Notes: Students will require a compass and a ruler to complete this investigation. Activity 3 is optional for selfpaced students. Inclusion students may use the textbook to complete Activity 3. The extensions are optional. Set the compass so that it is more than half of the length of segment AB. Set the pointed end of the compass on an endpoint. Swing an arc on both sides of the segment. Be careful not to reset the radius of the compass. Set the pointed end of the compass on the other endpoint. Swing another arc so that both arcs intersect. Saxon Math Course 1 I8-41 Adaptations Investigation 8

42 INVESTIGATION 8 (continued) (page 418) Draw a line through the two points where the arcs intersect. This line will bisect the segment. This line is perpendicular to segment AB. It is called a perpendicular bisector of the segment. Activity 2 : Angle Bisector Follow the instructions to bisect this angle. Set the point of the compass on the vertex of the angle. Sweep an arc across both sides of the angle. Label the two points that the arc intersects A and B. Now set the compass so that it is more than half of the distance between A and B. Set the pointed end on point A. Sweep an arc between the two rays of the angle. Be careful not to reset the radius of the compass. Saxon Math Course 1 I8-42 Adaptations Investigation 8

43 INVESTIGATION 8 (continued) (page 419) Set the pointed end on point B. Sweep an arc to cross the first arc. Draw a ray from the vertex of the angle through the intersection of the arcs. This ray is the angle bisector of the angle. Saxon Math Course 1 I8-43 Adaptations Investigation 8

44 INVESTIGATION 8 (continued) (page 420) extensions Use the figure and your protractor to answer questions a c. a. Does OB bisect AOE? Measure AOE. Measure AOB. b. Does Is m AOE two times m AOB? OD bisect BOE? Measure BOE. Measure BOD. Is m BOE two times m BOD? c. Use angle measures to classify these angles in the figure as acute, obtuse, or right. See the Student Reference Guide. Angle Measure Type Angle Measure Type AOE AOB BOD EOF AOC BOF Saxon Math Course 1 I8-44 Adaptations Investigation 8

45 INVESTIGATION 9 Experimental Probability (page 470) Name Theoretical probability is done by analyzing the structure of an experiment. Setting up a probability ratio to calculate the probability of rolling a certain number on a number cube is an example of theoretical probability. Experimental probability must be done by observation or by doing an experiment repeatedly. Many real-world situations need surveys for this. A pizza company wants to know what types of pizzas will be needed for a football game, so they ask 500 customers what type of pizza they would order: cheese, tomato, or mushroom. The number of customers who choose each type of pizza is the frequency for that type of pizza. Dividing the frequency by the total number of customers gives the relative frequency. The relative frequency is either a fraction or a decimal. Relative frequency can be used to estimate the probability that a type of pizza will be ordered. Showing the relative frequency as a percent gives the chance that a type of pizza will be ordered. Out of the 500 customers, 175 chose cheese, 225 chose tomato, and 100 chose mushroom. The chart shows the frequency, relative frequency, and percent chance for each type of pizza. Type Frequency Relative Frequency Chance Cheese = % Tomato Mushroom = % = % Teacher Notes: Students require 6 marbles (4 green and 2 white) and a small, opaque bag to complete the activity. (If marbles are not available, use small objects that cannot be distinguished by touch, such as different colored paper clips.) Students may complete the experiment without a partner if one is not available. The extensions are optional. The company plans to make 3000 pizzas for the football game. How many mushroom pizzas should they make? Multiply the relative frequency by the number of pizzas: = 600 About 600 pizzas should be mushroom. Saxon Math Course 1 I9-45 Adaptations Investigation 9

46 INVESTIGATION 9 (continued) (page 471) A town has 4 markets: Bob s Market The Corner Grocery Express Grocery Fine Foods A sample of 80 adults were surveyed for their favorite market: 30 chose Bob s Market 12 chose Corner Grocery 14 chose Express Grocery 24 chose Fine Foods 1. Present the data in a relative frequency table similar to the one for pizza. Store Frequency Relative Frequency Chance Bob s Market Corner Grocery 80 =. Express Grocery 80 =. Fine Foods 80 =. = % 2. Estimate the probability that an adult s favorite market is Express Grocery. Write your answer as a decimal. 3. Estimate the probability that an adult s favorite market is Bob s Market. Write your answer as a reduced fraction. 4. Estimate the chance that an adult s favorite market is Fine Foods. Write your answer as a percent. 5. Suppose the town has 4000 adult residents. The Corner Grocery is the favorite market of about how many adults in the town? Multiply 4000 by the relative frequency for Corner Grocery. Saxon Math Course 1 I9-46 Adaptations Investigation 9

47 INVESTIGATION 9 (continued) (page 471) Activity : Probability Experiment This experiment will determine the probability that 2 green marbles will be drawn out of a bag at the same time. 6. Repeat the steps below exactly 25 times and record your results. 1. Place 4 green marbles and 2 white marbles in a bag. 2. Shake the bag. 3. Without looking in the bag, take two marbles. 4. Tally the results in the table. Outcome Tally Both green Both white One of each 7. Use your tally table to make a relative frequency table. (The frequency is the number of tallies for each result. Divide each frequency by 25 to find the relative frequency.) Outcome Frequency Relative Frequency Both green 25 = Both white 25 = One of each 25 = 8. Estimate the probability that both marbles drawn will be green. Write your answer as a reduced fraction and as a decimal., Because 25 is really a small amount of times to try, this probability is only a guess. The more times an experiment is repeated, the more likely the estimate will be close to the theoretical probability. Saxon Math Course 1 I9-47 Adaptations Investigation 9

48 INVESTIGATION 9 (continued) (page 472) extensions a. Ask 10 students the following question: What is your favorite sport: baseball, football, soccer, or basketball? Record each response in the relative frequency table. Share the results of the survey with your class. Sport Frequency Relative Frequency Baseball 10 = Football 10 = Soccer 10 = Basketball 10 = b. In groups conduct an experiment by drawing two marbles out of a bag containing 3 green marbles and 3 white marbles. Each group should perform the experiment 30 times. Record each group s tallies in the frequency table shown below. Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Whole Class Both Green Both White One of Each Tally Rel. Freq. Tally Rel. Freq. Tally Rel. Freq. Calculate the relative frequency for each group by dividing the tallies by 30 (the number of times each group performed the experiment). Then combine the results from all the groups. To combine the results, add the tallies in each column and write the totals in the last row of the table. Then divide each of these totals by the total number of times the experiment was performed (equal to the number of groups times 30). The resulting quotients are the whole-class relative frequencies for each event. Discuss your findings. On the basis of their own data, which groups would guess that the probabilities were less than the whole class s data indicate? Which groups would guess that the probabilities were greater than the whole class s data indicate? Saxon Math Course 1 I9-48 Adaptations Investigation 9

49 INVESTIGATION 9 (continued) (page 473) extensions (continued) c. Roll two number cubes 100 times. Each time, record the sum of the upturned faces. When you are finished, fill out the relative frequency table. The sample space of the experiment has 11 outcomes. Sum Frequency Relative Frequency Are the outcomes equally likely? If not, which outcomes are more likely and which are less likely? more likely less likely Estimate the probability that the sum of a roll will be 8. Estimate the probability that the sum will be at least 10. Estimate the probability that the sum will be odd. Saxon Math Course 1 I9-49 Adaptations Investigation 9

50

51 INVESTIGATION 10 Compound Experiments (page 524) Name Compound experiments have two or more parts performed in order. Consider this compound experiment: A spinner with sectors A, B, and C is spun; then a marble is drawn from a bag that contains 4 gray marbles and 2 white marbles. Teacher Notes: Review Probability, Chance, Odds on page 25 in the Student Reference Guide. The extensions are optional. This experiment has two parts: spinning and drawing a marble. Use a tree diagram to show all the compound outcomes. There are three possible outcomes for the spinner: A, B, or C There are two possible outcomes for drawing a marble: gray or white Notice that the total number of compound outcomes is the product of the number of possible outcomes for the two parts. (3 2 = 6) The probability of a compound outcome is the product of the probabilities of each part of the outcome. To find the probability of A, gray : 1. Find the probability of spinning an A : Find the probability of drawing a gray: 4 6 ( reduces to 2 3 ) 3. Multiply the probabilities of each part = 1 3 The probability of A, gray is 1 3. Saxon Math Course 1 I10-51 Adaptations Investigation 10

52 INVESTIGATION 10 (continued) (page 525) Calculate the probability of each compound outcome to complete the table. For the last row, find the sum of the probabilities of the six compound outcomes. Outcome Probability A, gray 1_ 2 2_ 3 = 1_ 3 A, white 1. B, gray 2. B, white 3. C, gray 4. C, white 5. sum of probabilities 6. Consider this experiment: A bag of marbles contains four gray marbles and two white marbles. One marble is drawn from the bag and not replaced; then a second marble is drawn from the bag. 7. Complete this tree diagram showing all four possible compound outcomes. Because the first marble drawn is not replaced, the probability changes for each part. To find the probability of G, G : 1. Find the probability of drawing a gray on the first draw: 4 6 ( reduces to 2 3 ) 2. Find the probability of drawing a gray on the second draw: Multiply the probabilities of each part = 2 5 The probability of G, G is 2 5. Saxon Math Course 1 I10-52 Adaptations Investigation 10

53 INVESTIGATION 10 (continued) (page 526) 8. Calculate the probability of each compound outcome to complete the table. For the last row, find the sum of the probabilities of the four compound outcomes. Outcome Probability gray, gray 2_ 3 3_ 5 = 2_ 5 gray, white white, gray white, white sum of probabilities 9. Suppose we draw three marbles from the bag, one at a time and without replacement. What is the probability of drawing three white marbles? What is the probability of drawing three gray marbles? white white white grey grey grey = = Consider this experiment: A nickel is flipped; then a quarter is flipped. 10. Complete this tree diagram to show all possible compound outcomes. 11. Complete this table to show the probability of each compound outcome. Outcome Probability H, T 1_ 2 1_ 2 = 1_ 4 Saxon Math Course 1 I10-53 Adaptations Investigation 10

54 INVESTIGATION 10 (continued) (page 527) Use the table you made in problem 11 to answer problems What is the probability that one of the coins shows heads and one of the coins shows tails? Two outcomes are like this, and. 13. What is the probability that at least one of the coins shows heads? There are outcomes like this. 14. What is the probability that the nickel shows heads and the quarter shows tails? There is outcome like this. extensions For a and b, refer back to the table you made in problem 8. a. Find the probability that the two marbles drawn from the bag are different colors. Add the probabilities of the two outcomes where the marbles are different colors. b. Find the probability that the two marbles drawn from the bag are the same color. Add the probabilities of the outcomes where the marbles are the same color. For c and d, refer back to the table you made in problems 1 6. c. The complement of A, gray is not A, gray. Find the probability that the compound outcome will not be A, gray. Subtract the A, gray probability from 1. d. Find the probability that the compound outcome will not include A and will not include gray. Add all the probabilities that do not contain A or gray. e. Explain why the probabilities in c and d are different. The o in c can include A and can include g, just not both. The outcomes in d cannot include either or. Saxon Math Course 1 I10-54 Adaptations Investigation 10

55 INVESTIGATION 10 (continued) (page 527) extensions (continued) For g and f, consider this experiment: A number cube is rolled; then a quarter is flipped. f. Complete the tree diagram to show the sample space for the experiment. g. Find the probability of each compound outcome. Saxon Math Course 1 I10-55 Adaptations Investigation 10

56

57 INVESTIGATION 11 Scale Factor: Scale Drawings and Models (page 578) Scale drawings are two-dimensional pictures of larger objects. A road map is an example of a scale drawing. Scale models are three-dimensional copies of three-dimensional objects. A scale model usually shows a small representation of a large object, but sometimes it will be a big model of a very small object. A legend tells how much a certain measure represents. Below is a scale drawing of Angela s apartment. The legend says that every 1_ inch on the drawing equals 5 feet in the real apartment. 2 Because 1_ inch = 5 ft 2 1 inch = 10 ft 1 1_ inches = 15 ft 2 2 inches = 20 ft The drawing of Angela s apartment is 2 inches long and 1 1_ inches wide. (The dashed grid lines are every 1_ 2 2 inch.) So the real apartment is 20 feet long and 15 feet wide. Name Teacher Notes: The extensions are optional. Students will require a copy of Activity 21 and 22 to complete extension b. 1. What are the actual length and width of the kitchen shown above?, 2. In the scale drawing each doorway measures 1_ inch. Since 4 1_ inch is half of a 1_ inch, what is the actual width of each doorway? A dollhouse was built as a scale model of an actual house so that 1 inch = 1.5 feet. What are the dimensions of a room in the actual house if the corresponding dollhouse room measures 8 in. by 10 in.? 4. A scale model of an airplane is built so that 1 inch = 2 feet. The wingspan of the model airplane is 24 inches. What is the wingspan of the actual airplane in feet? by Saxon Math Course 1 I11-57 Adaptations Investigation 11

58 INVESTIGATION 11 (continued) (page 579) A good way to solve these types of problems is with a ratio box. For problems 5 8, complete the ratio box, set up a proportion, and find the answer. 5. A scale model of a sports car is 7 inches long. The car itself is 14 feet long. If the model is 3 inches wide, how wide is the actual car? 6. For the sports car in problem 5, suppose the actual height is 4 feet. What is the height of the model? 7. The femur is the large bone that runs from the knee to the hip. In a scale drawing of a human skeleton the length of the femur is 3 cm, and the full skeleton measures 12 cm. If the drawing represents a 6-ft-tall person, what is the actual length of the person s femur? 8. The humerus is the bone that runs from the elbow to the shoulder. Suppose the humerus of a 6-ft-tall person is 1 ft long. How long should the humerus be on the scale drawing of the skeleton in problem 7? Saxon Math Course 1 I11-58 Adaptations Investigation 11