Patterns & Algebra Workbook 6, Part 2

Transcription

1 Patterns & Algebra Workbook, Part page Worksheet PA- page. a) + b) c) + d) e) + f) + g) h) + i) j) + k) + l). a) b) c) d) e) + f) g) h) + i) + j) + k) l) +. a),, b) 9,, c),, d) 9,,. a) ;, b) ;, c) ;, d) ;,. a) ;, b) + ;, c) ;, d) ;, e) + ;, f) ;,. a) Start at, multiply by b) Start at, add c) Start at, subtract d) Start at, multiply by e) Start at, add f) Start at, multiply by Worksheet PA- page. a) Gap:,,,,.. Pattern:, b) Gap:,,,,, Pattern:, c) Gap:,,, 9, Pattern:, d) Gap:,,,,, Pattern:, e) Gap:,,,, Pattern:, f) Gap:,,,, Pattern:, g) Gap: 9,,,, Pattern:, h) Gap:,,,,, Pattern:, Fig # Tri # Added 9 9. a) +, +, +, + RULE: Start at. Add,, by.) b) +,, +, RULE: Start at. Add, and then subtract. Repeat. c) +, +, +, + RULE: Start at. Add,, by.) d) +,, +, RULE: Start at. Add, and then subtract. Repeat. e),,, RULE: Start at. Subtract,,,, (The step increases by.). a) Start at. Add,,, (The step increases by.) b) Start at. Multiply by. c) Start at. Multiply by. d) Start at. Add,,, (The step increases by.). a) Figure : Figure : Figure : Figure : RULE: Start at. Add,,, by.) So Figure : b) Figure : Figure : Figure : 9 Figure : RULE: Start at. Multiply by. So Figure :. Answers will vary. Worksheet PA- page. a) Tables Chairs 9 b) Start at. Add, then add. Repeat. c) people. a) i) th : ; th : ii) Start at. Add,,, (The step increases by.) iii) b) i) th : ; th : ii) Option : Start at.,,,, iii) Option : Start at, add,,, (The step increases by.). a) Gap:,,,,,,,, Pattern:,,,,,,,,, b) Odd, odd, even. Repeat. c) = ; + = The sum of the first odd Fibonacci numbers equals the first even numbers. d) = ; + + = The sum of the first odd Fibonacci numbers three even numbers. Workbook Part ( rd Edition) ISBN Selected Answer Key Workbook

2 Patterns & Algebra Workbook, Part (continued) page Worksheet PA- page 9. a),, 9 RULE: Start at. Add each time. b) 9,, RULE: Start at. Add, and then subtract. Repeat. c),,. a) M, P b) W RULE: Start at. Subtract,,, by.) c) R, P d) S, T e) U f) P, K g) A, B, C, D. Answers will vary.. a), 9,,, b) 9,,,, c),,,, d),,,,. Answers will vary.. E =, Y = So E Y = = Worksheet PA- page. a) b) c) Years Weeks Years Days 9 Hours Seconds. Tank drains at a constant rate of L per minute. Tank drains at a variable rate per minute: L, L, L, (the step increases by L each time). After min, sec (or approximately min), Tank will be empty.. a) After minutes, the airplane will have 9 litres of fuel. b) After minutes, the plan will be km from the airport. c) When the plane reaches the airport, it will be carrying litres of fuel.. a) times b) 9. a) = = 9 = = = b) 9 = = = = = Teacher to check. Answers will vary. Worksheet PA- page. a) b) c) d) e) f). a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) ; or ;. Answers will vary.. Since addition is commutative, there are 9 possible answers: a) apples red = green b) children boys = girls c) cherries = d) = books Worksheet PA- page. a) x = b) A = c) n = d) x = e) y = f) n = g) b = h) x = i) z = j) m =. a) = b) = c) = d) = e) = f) n = 9 g) n = h) n = i) n =. a) x = b) x = c) x =. a) + = + = + = + = b) = = c) = = = = = = =. Teacher to check.. Answers will vary.. A = B = C = Worksheet PA-9 page. a) = b) = c) =. a) = b) = c) h = h. a) h = h b) t = t c) x = x d) n = n. a) A + = B b) A = B c) A + = B d) A + A = B e) A + A = B. Since the letter or symbol used as the variable is arbitrary, the equation gives the same solution. Workbook Part ( rd Edition) ISBN Selected Answer Key Workbook

3 Patterns & Algebra Workbook, Part (continued) page. a) = n, n represents the number of girls. b) = s, s represents the number of stamps that were given away. Worksheet PA- page. Two circles. Two circles. Two triangles. Three circles BONUS:. Three circles. Two circles. a) b) c) d) e) f) g) h) =. Teacher to check. Worksheet PA- page. a) O.P st nd (,) (,) (,) (,) b) O.P st nd (,) (,) (,) (,9) 9 c) O.P st nd (,) (,) (,) (,). Answers must list four of the following ordered pairs: a) O.P st nd (,) (,) (,) (,9) 9 (,) b) O.P st nd (,) (,) (,) (,) (,9) 9 c) O.P st nd (,) (,) (,) (,9) 9. Ordered pairs: (, ), (, ), (, ), (, ). a) b) BONUS: c) d). Graphs will vary. Sample answer:. NOTE: Sample T-tables are given but answers may vary. Teacher to check graphs.. A: a) b) 9 c) input of. To find the output, multiply the input number by, then subtract. number by ). B: input of. To find the output, add to the input number. number by ). Workbook Part ( rd Edition) ISBN Selected Answer Key Workbook

4 Patterns & Algebra Workbook, Part (continued) page C: input of. The output is equal to the input. number by ).. Answers may vary. Worksheet PA- page. a) $. b) $. c) $. d) minutes e) If billed by seconds, $.. a) km b) km c) Yes. The difference in distance from to hours is. Therefore, Kathy had not travelled during this time interval and likely rested. d) No. In the first h, Kathy travelled km/h at a speed of a km/h. Excluding her rest period, Kathy then travelled km over h at speed of km/h.. a) metres b) metres c) Tom won the race by metres. d) Ben had a metre head start. e) seconds. a) i) $. ii) $. c) For a -hour rental, Dave s store costs $. whereas Mike s store costs $9.. Mike s store is less expensive. Worksheet PA- page 9. a) increases by each time; Multiply input by and add to get the b) increases by Add to input gets the c) increases by each time; Multiply input by and add to get the d) increases by each time; Multiply input by e) increases by.,.,. (the step increases by. each time);,, (the step increases by each time); Multiply input by f) increases by,, (the step increases by ); Multiply input by the input to get the. g) increases by. Multiply input by. Dist Sec Min Hr. km 9. km.9 km Worksheet PA- page 9. a) b) c) d). Gaps:,, Sequence:,,,. Sequence:,,,,,. Teacher to check.. a) b) Worksheet PA- page 9. a) Tables Chairs b). $.. km RULE: Start at and add.. cups of water. The th and the th receive both a book and a calendar.. Counting by s and s, you see that is divisible by both numbers (and is less than ). So they each collected apples: Anna collected baskets of, and Emily collected baskets of.. a) There will be shaded squares on the perimeter, and we know this since # shaded pieces = figure # + (or, in this specific case, + ). b) There will be 9 white squares: = = (this gives us the figure # we need) And, in Figure, there are = 9 white squares.. As such, Method A will cost Gerome $ or hours ( $ + $ and Method B will cost him $ ( $). So Method A is cheaper. 9. The core pattern is shapes in length and the closest multiple of to without going over is ( ), with remainder. So, to find the nd shape, look at the nd shape of the core pattern: it is a pentagon.. Paul shovelled the following # of sidewalks each day: Day : Day : Day : 9 Day : iii) $9. b) $. Workbook Part ( rd Edition) ISBN Selected Answer Key Workbook

5 Patterns & Algebra Workbook, Part (continued) page. # E # T P 9 9 Patterns in columns # of edges increases by # of triangles increases by, then by, then by, etc (step increases by each time); Perimeter increases by each time. Relations in rows # of edges multiplied by itself gives # of triangles # of edges multiplied by gives perimeter. a) Decreases b) metres c) cm = m d) Yes (decreases by. each time) e) i). C ii). C. No, Marlene isn t right. She will need blocks to make Figure (since = ). Workbook Part ( rd Edition) ISBN Selected Answer Key Workbook