Using Patterns to Solve Problems ^fsso^ Quick Review One box holds 15 books. Number of Boxes Number of Books >• How many books will 2 boxes 1 15 hold? 3 boxes? 4 boxes? Make a table. Two boxes hold 30 books. Three boxes hold 45 books. Four boxes hold 60 books. > Predict how many books 10 boxes will hold. 2 30 3 45 4 60 W\AAAAAAAAAAAAAAAAWNAAAAAAAAAAAAAAAA The pattern rule is: ^CiMultiply the number of boxes by 15. To predict the number of books 10 boxes will hold, multiply: 10 X 15 = 150 Ten boxes will hold 150 books. Try These 1. One concert ticket costs $11. a) Complete the table to find the cost of 7 tickets. b) Write a pattern rule for the cost. n i < !;¦ I & «• , us <s a '.i a Number of Tickets Cost ($) 1 2 3 4 c) Predict the cost of 10 tickets. d) Extend the pattern. How many tickets can you buy with $155? VVWWWXAAAAAAAAAAA \AAAAAAAA Copyright © 2005 Pearson Education Canada inc. Practice 1. Ivo practises the guitar 25 minutes every day. a) Make a table to show how many minutes Ivo practises in one week. b) How many minutes does Ivo practise in 10 days? c) How many minutes will Ivo practise in November? How many hours is that? d) How many days will it take Ivo to practise a total of 15 hours? 2. One minibus holds 18 students. a) Make a table to show how many students can ride in 6 minibuses. b) Write a pattern rule for the number of students. c) How many students can ride in 10 minibuses? Stretch Your Thinking ...... . ...... ¦ 1 . I 1 . > : • -j .. -5 . S .;i ?. O C ft' ft 't «; IS 1. Think about the minibuses in question 2 above. a) How many students can ride in 25 minibuses? b) How many minibuses are needed for 170 students? Copyright © 2005 Pearson Education Canada inc. 9 ^tNT Soqf_ J Modelling Patterns ^tssot1 Quick Review >• Here is a pattern of squares drawn Square Number of Dots on Perimeter on dot paper. 1 4 2 8 3 12 4 16 5 20 wwvwVAAAAAAAAAAAAAAA/^ One pattern rule for the number Another pattern rule for the of dots on the perimeter is: ^j^number of dots is: Start at 4. Add 4 each time. Multiply the square number by 4. The number of dots on any perimeter is a multiple of 4. The 10th square will have 10 X 4, or 40 dots on its perimeter. 57 is not a multiple of 4, so no square has 57 dots. 60 is a multiple of 4 because 15 X 4 = 60. So, the 15th square has 60 dots. Try These :> f > & ¦'} C 4> 1 o a) Complete the table for this pattern. Triangle Number of Dots on Perimeter 1 2 3 b) Which triangle will have 39 dots? 4 wwwwwwvsaaaaaaaaaaaaaaaaaa/^ 57 dots? c) Will any triangle have 46 dots? Why or why not? Copyright © 2005 Pearson Education Canada inc. Practice Complete the table for this pattern of Figure Perimeter 1 (units) 6 regular hexagons. 2 3 Write the pattern rule for the perimeters. 4 vwwwwwuVWWVWWWW Which figure will have a perimeter of 22 units? 34 units? Predict the perimeter of the 10th figure. Will any figure have a perimeter of 55 units? Explain. Complete the table for Figure this pattern. Perimeter Area (units) (square units) 1 2 3 4 vwwwww^AAAAAAAAAAAAAAIVWWWWWWVW Write the pattern rule for the areas. Stretch Your Thinking 1. a) Which figure in question 2 will have a perimeter of 120 units? _ What will its area be? b) Which figure in question 2 will have an area of 81 square units? _ What is its perimeter? ! Copyright © 2005 Pearson Education Canada inc.