n Chapter 1: Patterns in Mathematics

Transcription

1 Name: Date. n Chapter 1: Patterns in Mathematics Describe and extend patterns. Pattern rules describe how a pattern begins and how it continues. Pattern rules can be represented using words and operations. For example, a pattern rule for 3, 5, 7, 9,... is "start at 3 and add each time." 1. Daniel is on a bike trip. The table shows the distance Daniel travels each hour. a) Describe a pattern for the second column of the table. Distance Travelled Each Hour, -Time. - ' -Distane.(krr, b) If the pattern continues, how many kilometres will Daniel travel in 7 hours?. Write a pattern rule for each pattern. Is it an increasing pattern or a decreasing pattern? a) 4, 8, 1, 16, b) 50, 41, 3, 3, c) 3, 1, 48, 19, 3. Extend each pattern for four more terms. a) 1, 18, 8, 4, 35, 30, b) 35, 31, 7, 3, 19, c) 16, 19,, 5, 8, Copyright 010 Nelson Education Ltd. Review of Essential Skills: Chapter I I 1 I

2 Name: Date. Use patterns to solve a problem. 4. Nikesh and Hannah are travelling east to visit their relatives. Nikesh travels by train 105 km each hour. Hannah travels by car 90 km each hour. Hannah starts 1 h before Nikesh. How many hours will it take Nikesh to catch up to Hannah? Hannah's Trip, t, 4 Nikesh's Trip 0., 1-4, 'Ms s '..1:-.,.,, f -, z 1 1 Solve equations. 5. Solve each equation. a) x + = 5 x= e) 4 + n = 7 n= b) 6 = s s= f) 1 = 3 x d d= c) 3 + z = 7 z= g)y 5 = 13 y= d) 6 x c = 4 c= h) 1 = t 5 t = I I Review of Essential Skills: Chapter 1 Copyright 010 Nelson Education Ltd.

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4 Applying Rules 1 5. Rule: add 5 Rule: subtract 10 Rule: multiply by 3 6. Rule: multiply by add 4 In ut Out u Rule: multiply by 3 Rule: Multiply by subtract 4 add 1 4. Rule: subtract 5 8. Rule: divide by 6

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6 Grade 8 Patterns 1. Complete the fence up to the 5th post:.) Create a t-chart: # of posts # of boards 0 3.) Create a rule to describe the pattern: 4.) Create a graph: ei tilii m11,, ,, / i , S, 11.

7 Name: Date: Lesson: Qrapfts WI) Example: Rule: = ( x ) -1 Write the rule followed by each function table: Rule: Rule: , Rule: Rule: 5. _ _ Rule: Rule: _ Rule: Rule: For more worksheets, games and other learning tools, go to Copyright Asha Dinesh. All rights reserved.

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9 *** We can use an / machine to make a growing pattern. > This machine adds 8 to each input to get the output. The pattern rule that relates the input to the output is: Add 8 to the input. When each input increases by 1, the output increases by 1. The pattern rule for the input is: Start at 1. Add 1 each time. The pattern rule for the output is: Start at 9. Add 1 each time > This / machine doubles each input, then adds 6. -->, The pattern rule that relates the input to the output is: Multiply the input by, then add The pattern rule for the input is: Start at. Add each time. The pattern rule for the output is: Start at 10. Add 4 each time. When each input increases by, the output increases by Lf Unit 1 Lesson 1 7

10 0****000(9000 *(900000*( **** *0 0000( ** 0 1. For each / machine: Copy and complete the table. Write the pattern rule that relates the input to the output. Write the pattern rule for the input. Write the pattern rule for the output. a) b) ±. For each / machine: Copy and complete the table. Write the pattern rule that relates the input to the output. 4, Write the pattern rule for the input. 6 Write the pattern rule for the output. 8 a) -, > -- - b) 3. Look at question and your tables. a) How are the / machines the same? How are they different? b) How do the output numbers from the two machines compare? Explain. c) Is it possible to get more than one output number for each input? How do you know? 8 Unit 1 Lesson 1

11 4. Copy and complete this table. The pattern rule that relates the input to the, output is: 36 Divide the input by 6. 4 a) Write the pattern rule for the input. b) Write the pattern rule for the output Copy and complete this table. The pattern rule that relates the input to the output is: 30, Divide the input by 3, then subtract. 60 a) Write the pattern rule for the input. b) Write the pattern rule for the output The pattern rule that relates the input to the output is: Add 4 to the input. Then divide by. 4, Check the data in the / table. 8 4 Identify any output numbers that are incorrect How do you know they are incorrect? Show your work. -, The pattern rule that relates the input to the output is:, Divide the input by 6, then add a) Check the data in the / table. Identify any output numbers that are incorrect. How do you know they are incorrect? b) Correct the table. _ c) Write.3 more input and output numbers for this pattern rule. Show your work. ASSESSMENT FOCUS Question 7 Unit 1 Lesson 1 9

12 8. The pattern rule that relates the input to the output is: Multiply the input by 4. Then subtract 3. Find the missing numbers in the table. How can you check your answers? 3 9 6? 9? 1 45, _ 15? 9. The pattern rule that relates the input to the output is: Add 5 to the input. Then multiply by 3. Find the missing numbers in the table. What strategies did you use? 1 5?? 39 11?? 57 -.? a) Draw an / machine with two operations. Choose two numbers and:twooperati_olb for your machine. b) Choose 5 input numbers. Find the output numbers. c) Erase input numbers and output numbers. Each row must have at least one number. Trade tables with a classmate. Trade pattern rules that relate the input to the output. Find your classmate's missing numbers. Suppose you want to make an / machine to convert millimetres to metres. Describe what your machine would look like. 10 Unit 1 Lesson 1

13 0 0 C >- We can draw pictures to show the relationship in a table of values. In this table: The input increases by 1 each time. The output increases by 3 each time. We could draw a pattern of triangles on _ triangular dot paper. The figure number is the input. The number of triangles in each figure is the output Figure 1 FigLire Figure.3 Figure 4. Figure 5 We can use a pattern rule to describe the relationship between the columns in a table of values. This pattern rule tells us the numbers and operations in the corresponding / machine. The table shows the input and output for this two-operation machine., f 7., To identify the numbers and operations in the machine: The pattern rule for the output is: When the output increases by 4, that is a clue about what to do. Start at 1. Add 4 each time. 1 Unit 1 Lesson

14 ogootts0000tpos Each table shows the input and output from a machine with one operation. For each table: Identify the number and the operation in the machine. Continue the patterns. Write the next 4 input and output numbers. Write the pattern rule that relates the input to the output. a) ' b), , 4 8, d) ' Each table shows the input and output from a machine with two operations. For each table: Identify the numbers and the operations in the machine. Choose 4 different input numbers. Find the output for each input. Predict the output when the input is 10. Check your prediction. a) b) c), d) _ -, Unit 1 Lesson

15 Name Table of Values Draw straight lines to match each equation to its corresponding table. Complete the missing values in each table. The uncrossed words are another name for a function table, or table of values y x y=x+1 y=x 3 y= -x+ an input- -disastrous algebraic graphing mathematical x y x y y= 4x y= -x y=x+1 y=3x-4 y= -x+ 5 intergalactic turbo -powered output quadratic chair expression table Milliken Publishing Company 37 MP3443

16 See-Saw Math Activity Copy the diagrams and use the clues to find out what is on the last see-saw in each case. 1. Given '.,,.. Given _ a. 3. Given then 4. Given then 5. Given

17 Table of Values Find the expression for each table of values. Remember: once you figure out what the pattern goes up by, you have figured out what you multiply your variable by. Then check your first pair of numbers to see if your expression works. Day # (d) Total allowance $ Example: I notice that in column two (total allowance $), my pattern starts at 5 and increases by 4 each time. Because I know what it goes up by, I know that I must multiply my variable d (which stands for the day number), by 4. I will try my expression 4d to see if I get the correct answer of 5, since that is the first number in my pattern. I insert 1 into my expression 4d -> 4(1)=4 pairs of numbers to see if my expression is correct. Since 4 does not equal 5, I have to figure out what to add to my expression. In order to get from the number 4 to number 5, I must add 1. So I will change my expression to 4d+1 and check the next I plug the next day number () into my new expression. 4d+1 -> 4()+1=9... It works! Now I check one more to make sure my expression is correct. 4d+1 -> 4(3)4-1=13... It works! I now know that 4d+1 is my expression for this table! Week # Total yoga (w) classes 1 Shape # Total # of (s) blocks 1 10 Term # Total # of (t) circles Expression:. Expression: 3. Expression:

18 # Hours Total km hiked travelled (h) # of Total # guitar cost lessons (I) # of Total cost bowling games (g) Expression: 5. Expression: 6. Expression: Try creating your own table of values and matching expression. 1..

19 Growing Patterns Tables & Chairs Investigation o o 00 o 0 00 Figure 1 Figure Figure 3 PROBLEM: Restaurants often use small square tables to seat customers. One chair is placed on each side of the table. Four chairs fit around one square table [Figure 1]. Restaurants handle larger groups of customers by pushing together tables. Two tables pushed together [Figure ] will seat six customers. Draw a diagram showing how many customers would be seated at three square tables pushed together [Figure 3]. Number of Complete the table for reference: Number of Tables. Customers Find a pattern you can use to predict the number of customers that may be seated at any size table. Describe the pattern in words CHALLENGE: Use your pattern to complete this table without drawing a picture or using manipulatives. Write an algebraic rule for the number of customers (c) in terms of the number of tables (t). Number of Tables C = Number of Customers Tables & Chairs Investigation 1 KawaseMathwire.corrr -

20 Name: Date: Fir Tree Students in Mrs. Como's class are making up their own growing patterns. Angela uses triangle pattern blocks to make a growing fir tree. Use pattern blocks to build and draw the next two fir trees in this pattern. Complete the table of values. Predict what the tenth fir tree will look like and tell how many blocks you would need to build it. Explain any pattern you used to find this answer. Tree # Number of blocks added TOTAL ber of blocks Fir Tree- 1 Kawas@Methwire.conr -

21 Row of houses 56 Double row of squaresn ffi -->. N umber N uxnber II of houses" dots 8 N umber Number N umber of f smaj. of Grosses(i) squares matchs 1 -> 1 > > >. Ex.pLaAn the two patiteims lin/ words. 3. Write/ the mappings iheu cagebraik motattork. EXpiktA411 theee two pattyrnsn/ words. 3. WriLte. till& two rmappings ca,geibrccto nota,ttork

22 Joined hexagons 7 Wall with spikes, 1. Number Number Number of of of hexagons dots matches Number Leingth Nuim,be s e Pnatzku >. EXpLabfl the, two patty( nas Lr words.. Bop Label, the, two p attarls Words. 3. Writ& the, two maipp ing s 'tin/ alge1bralo. 3. Write, the, two map p ings Ln1 ai&brcuc mutat n, TWiXLtWV.

23 RE CT ANGLES DIAMOND DOTS Le7th. rectangle 1 PvLitt,ete x (clistcuacei rou,n,dy) --> IF 1. N uirnibeir NuxnAer ) of cf diamort,ots clots utwaọ.er 0c0t ExpLaAn in words h,ow to get the, second, nkum43e4from, the, jiirst.. ExpliaLn, in words how to get the second& win-doer from, tkle 3. Me, Whi01, miappurt,g s gimen by

24 Building a fence 3 Lt. Row of squares 1, N tamb w Nwm,beir N wm,beir N wm,beir of of posts ret,iits squxu-es.-l I I I r I I 1 r Li > 6 po 5-1s 1 --> nuo Abeir rad5 s M crt),ot re.5. ExpLain/ words h,ow to gel the, secort,d). Emlictin 1,n, words hdow to gel tklei second/ ruurnkeir from, theji,rst. rt,tvm,be,r from, tikefixst. 3. The, wktolo mapping Ls gineini by r -= 3. Tftwkwl&rnppixig i,s 9e/by