Practicum IV [February 20, 21] a.) Describe the relationship between the number of regular octagons and the number of sides in this pattern.

Transcription

1 Practicum IV [February 20, 21] [Chapter 61 (Representing Patterns)] Page 217 4) Please complete parts a), b), c), d), and e) a) Describe the relationship between the number of regular octagons and the number of sides in this pattern Table x y Figure 1: Question b) Make a table of values showing the numb roy dies for each figure in relation to the number of octagons Table 1: Question 4 Number of Octagons Number of Sides c) Write an equation to model the numb roy sides of each shape Explain what each variable represents f(x) = 2 + 6x d) How many sides would a shape made up of 17 octagons have? f(17) = 2 + 6(17) = 104 e) How many octagons are needed to make a figure with 722 sides? f(x) = 722 = 2 + 6x = 722 6x = 720 = x = = x = McAskill, Bruce MathLinks9 : teacher s resource Toronto: McGraw-Hill Ryerson, 2009 Print

2 5) Please complete parts a), b), c), d), and e) a) Make a table of values to show the number of circles in relation to the figure number Table 2: Question 5 Figure # Number of Circles b) Describe the relationship between the number of circles and the figure number Relation: Figure 2: Question 5 f(1) = 2 + 3(1) = 5 f(2) = 2 + 3(2) = 8 f(3) = 2 + 3(3) = 11 c) Develop an equation that can be used to determine the number of circles in each figure Explain what each variable represents d) How many circles are in figure 17? e) Which figure number has 110 circles? f(x) = 2 + 3x f(17) = 2 + 3(17) f(x) = 100 = x = 36 2 McAskill, Bruce MathLinks9 : teacher s resource Toronto: McGraw-Hill Ryerson, 2009 Print

3 6) Laura used grey and white tiles to crate a pattern Figure 1 Figure 2 Figure 3 Figure 3: Question 6 a) Make a table of values to show the number of grey tiles in relation to the figure number Table 3: Question 6 Figure # Number of Grey Tiles b) Describe the relationship between the number of grey tiles and the figure number There are the four in the corners that do not change, the edges increase by 1 spending on the figure number c) Develop an equation to model the number of grey tiles Explain what each variable represents f(x) = 4 + 4x d) How many great tiles are there in Figure 24? f(24) = 4 + 4(24) = 100 e) Which figure numbers has 176 grey tiles? Verify your answer f(x) = 176 = x = 43 3 McAskill, Bruce MathLinks9 : teacher s resource Toronto: McGraw-Hill Ryerson, 2009 Print

4 7) Matt created the following number pattern: a) Make a table of values for the first five terms {7, 16, 25, } The first thing to recognize is that this pattern has a linear relationship Table 4: Question 7 x f(x) = 7 + 9(x 1) b) Develop an equation that can be used to determine the value of each term in the number pattern c) What is the value of the 123 rd term? d) Which term has a value of 358? Page 218 f(x) = 7 + 9(x 1) f(123) = 7 + 9(123 1) = 1105 f(x) = 358 = x = 40 9) Jessica created a number pattern that starts with the term -5 Each subsequent number is 3 less than the previous number a) Make a table of values for the first five numbers in the pattern We are given that each subsequent number (Later in Sequence) is 3 less than the previous number Therefore the sequence is decreasing Table 5: Question 9 x f(x) 5 + ( 3)(x 1) ( 3)(1 1) 2-5+(-3) 5 + ( 3)(2 1) 3-5+(-3)+(-3) 5 + ( 3)(3 1) 4-5+(-3)+(-3)+(-3) 5 + ( 3)(4 1) 5-5+(-3)+(-3)+(-3)+(-3) 5 + ( 3)(5 1) b) What equation can be used to determine each number in the pattern? Verify you answer by substituting a known value into your equation f(x) = 5 3(x 1) And if you want to verify it you could use it to find the first term: c) What is the value of the 49 th term? d) Which term has a value of -119? Verify your answer f(1) = 5 3(1 1) = 5 f(49) = 5 3(49 1) = 149 f(x) = 119 = x = 39 4 McAskill, Bruce MathLinks9 : teacher s resource Toronto: McGraw-Hill Ryerson, 2009 Print

5 12) A school pays a company $125 to design gym T-shirts It costs an additional $15 to make each T-shirt a) Copy and complete the table of values Can you find a linear relation? Table 6: Question 12 Number of T-shirts Cost ($) The linear relationship can be found from the information in the question that reads A down payment of $125 following a cost of $15 per T-shirt : f(x) = 15x Table 7: Question 12 Number of T-shirts Cost ($) Here is how to find the missing value in the last row of the chart: 950 =15x =15x =x 55 =x b) Develop an equation to determine the cost of T-shirts Explain the meaning of the numerical coefficient 15 dollars just represents the cost to produce each T-shirt c) What would it cost to make 378 T-shirts? f(378) = 15(378) = 5795 d) If the school store has a budget of $2345 for T-shirts, how many T-shirts can be ordered? 2345 =15x =15x = 15x =x 5 McAskill, Bruce MathLinks9 : teacher s resource Toronto: McGraw-Hill Ryerson, 2009 Print

6 Page 219 Extend 15) Find the pattern that expresses all the numbers that are 1 more than a multiple of 3? Table 8: Question 15 Number x 3x (1) + 1 = 4 2 3(2) + 1 = 7 3 3(3) + 1 = (4) + 1 = (5) + 1 = (6) + 1 = 19 a) What is the 42 nd number? f(42) =3(42) + 1 f(42) =127 b) How can your patterns test to see if 45,678 is 1 more than a multiple of 3? =3x =3x Therefore this number is not 1 more than a multiple of = 3x 3 3 x = McAskill, Bruce MathLinks9 : teacher s resource Toronto: McGraw-Hill Ryerson, 2009 Print

7 of the height it was dropped from Each subse- 17) A ball is dropped from a height of 2 m The ball rebounds to 2 3 quent rebound Figure 4: Question 17 a) Make a table of values for the first five rebound heights in the pattern Table 9: Question 17 x f(x) = 2 ( ) 2 x b) What is the height of the 4 th rebound bounce? About 039 c) Is this a linear relation? Definitely Not, this is an exponential relation 7 McAskill, Bruce MathLinks9 : teacher s resource Toronto: McGraw-Hill Ryerson, 2009 Print