Answers Investigation ACE Assignment Choices Problem. Core Other Connections, Etensions Problem. Core Other Applications, Connections, Etensions ; unassigned choices from previous problems Problem. Core Other Applications ; Connections ; Etensions, ; unassigned choices from previous problems Adapted For suggestions about adapting ACE eercises, see the CMP Special Needs Handbook. Connecting to Prior Units Units,,, -, : Covering and Surrounding;, : Data About Us;, : Shapes and Designs;,, : Prime Time;, : Bits and Pieces II Applications. a. Basketball Road Trip Basketball Road Trip b. Estimates should be close to the following: mi, mi, mi, mi c. The data are represented in the table b corresponding and values and. The are represented b point (, ) on the graph. d. These values are not in the table. The would be the values of the wa between (, ) and (, ). If the plotted points on the graph are connected, then the values are represented b the point (., ) on the line. e. The distance (in miles) is multiplied b the time (in hours). f. hours g. about hours minutes; of mi is about mi h. hours, or hours minutes Investigation Rules and Equations ACE ANSWERS
. a. Bike Ride.......... c. d = miles d. t = hours e. Yes, in this case the information represented b a line connecting the points is accurate because the distance increases at a constant rate (so there would not be an jumps or curves between points).. a. L =.n b. L =. = $. c. We need to find n so that $. =.n. What number multiplied b. gives.? n = people. b. miles; miles; miles; miles. a. Traveling at mph.......... k m t d... a. $ after pament; $ after paments; $ after paments b. a = - n b. Traveling at mph Variables and Patterns
c. Sean s Loan Paments Number of Months Amount Owed $ $ $ $ $ $ $ $ $ $ $ $ $ $. A = lw, where A is the area, l is the length, and w is the width. h = s, where h is the number of hot dogs and s is the number of students. = w, where is the amount of material in ards and w is the number of windows. t = +.m, where t is the tai fare in dollars and m is the number of miles. t =.p. d = h. c =.p. b =.m +. is times ; =. t is minus s; t = - s. z is more than times n; z = n +. D Connections. a. Side (units) Perimeter (units ) Sean s Loan Paments The perimeter increases b as the length of the side increases b. Amount Owed $ $ $ $ Number of Months d. As n increases b, a decreases b $. As ou read down the columns of the table, the amount owed decreases b $ each time the number of months increases b. The points of the graph lie on a line that slants downward as ou read from left to right. More specificall, if we move unit to the right on the -ais, the line moves downward units on the -ais. e. Sean will pa off the loan in months. His last pament will be onl $. In the table, the amount owed drops below on month. In the graph, the point for = is below the -ais. b. Side (units) Area (units ) The area is the square of the length of the side. It grows at an increasing rate as side length increases. (..). =.. A = p = p cm <.. Triangle: ; parallelogram: ; pentagon: ; heagon:.. A = = cm.,. a. Kai will travel. in. in one turn because the circumference of his wheel is about. in., or about. in. b. Masako will travel about. in. for one turn because the circumference of her wheel is about. in., or. in. ACE ANSWERS Investigation Rules and Equations
c. Kai will travel about, in. for turns because. =,. Students ma convert this to,. ft or,. d. d. Masako will travel about, in. for turns because. =,. Students ma convert this to, ft or d. e.,. <. turns f.,. <. turns; mi is, ft or, in. So, it would take,. <,. turns to cover mi.. a.. ft b. The bike will travel about. =. ft in one turn, so in turns it will travel about, ft. c. Because mi =, ft, it will make,. <,. turns. d. The big wheel can go three times as far for the same number of turns because its diameter is three times the diameter of Masako s wheel.. A = lw. A = bh. P = b + h or P = (b + h) (p q). m =. A = pr. S = (n - ). O = n. A = bh... is equal to. is more than. is minus Etensions. a. Distance (mi) d b. s = t. club members. a. rides b. rides. seconds, seconds. seconds, seconds. a. (Figure ) Speed for a Car Trip Time (hr).... Average Speed (mi/h)..... b. t = + (b ), or t = b ; There are man possible eplanations. One wa to look at this pattern is that a bridge with toothpick on the bottom requires toothpicks, and each additional bottom toothpick requires additional toothpicks. c. The triangular design provides rigidit that the design made of squares doesn t. This is a principle that was developed in Shapes and Designs of Course.. Students need to subtract the cost of the amusement park from the tour profit with van found in Question D() of Problem.. A wa to approach this is to make a table using Figure Rod Bridges Rods Along Bottom Total Number of Rods Variables and Patterns
columns and from the table made for Question A of Problem. and add two new columns. (Figure ) Reasoning smbolicall: Cost of Amusement park = + n; Tour profit with van = n n ; Tour profit with amusement park = n n ( + n) = n This approach is more sophisticated and requires students to think about representing the subtraction of a quantit ( + n) from another quantit n n. Leaving the result as: Tour profit with amusement park = n n ( + n) is fine at this point. In Moving Straight Ahead and Sa It With Smbols, students will work more with writing and simplifing equations of this form. Possible Answers to Mathematical Reflections. First, identif the variables involved in the relationship. Then, choose letters to stand for those variables. Deciding which variable is Figure Number of Customers n Profit $ $ $ $ $ $, Tour Revenue and Epenses Tour Profit With Van $ $ $ $ $ $ n n Cost of Amusement Park $ $ $ $ $ $ n the dependent variable and which is the independent variable is helpful. Calculate some values of the dependent variable for specific values of the independent variable, and look for a pattern in those calculations. Describe the pattern in words. Finall, use the words as a guide to write an equation to represent the relationships.. Equations give ou a short wa to represent a relationship. The make calculating specific values more precise and efficient.. Tables allow ou to see pairs of values. However, the number of pairs ou can show in a table is limited. Also, it can be difficult to see the overall pattern in a table. Graphs make it eas to see the overall pattern visuall. However, it is harder to find eact values from a graph. Equations provide a brief summar of the relationship and allow ou to find values of one variable for an value of the other variable. Although ou can tell some things about the overall pattern from an equation, it doesn t give a visual picture of the pattern. Profit With Van Minus Cost of Amusement Park $ $ $ $ $ $ n n n ( n) ACE ANSWERS Investigation Rules and Equations