Use words and symbols to describe division by sharing. b) Write a division sentence. 4
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1 1 Sharing to Divide Use words and symbols to describe division by sharing You will need buttons, bread tags, toothpicks, or other small items to use as counters 1 1 tickets are shared equally by winners 10 is a division sentence The quotient is is a picture of the division model for sharing 10 counters equally in groups a) Model the problem with counters Draw a picture of your finished model b) Write a division sentence 1 Read the sentence as 1 shared equally by is for each c) Write a multiplication fact for your model 1 Model each situation Draw a picture of your model Write a division sentence for each a) tickets shared equally by winners b) 1 tickets shared equally by winners c) divided by 1 = = 1 Calculate each quotient Use counters to help you a) b) 1 c) 0 Copyright 00 Nelson Answers Chapter 10: Division 77
2 Grouping to Divide Divide by counting equal groups You will need buttons, bread tags, toothpicks, or other small items to use as counters 1 1 students work in groups of a) How many groups are there? Model your solution with counters and skip counting on the number line at the bottom of the page groups To model 8 on a number line, start at 8 and jump back by s to There are jumps So 8 b) Write a division sentence What is the quotient? 1 = How many groups of are there? Model your solution with counters or the number line at the bottom of the page groups Write the division sentence 18 = Divide a) 1 c) e) 1 g) 1 b) 1 7 d) 1 f) 7 h) 1 a) How many people can have tickets each? people b) How many people can have tickets each? people with tickets left over 1 a) Answers Chapter 10: Division Copyright 00 Nelson
3 Communicate About Division Use a model to explain how to divide Communication Checklist Did you show enough detail? Did you explain your thinking? Did you include a diagram? 1 Solve this problem and explain your steps Use the Communication Checklist Ian has 0 plums and baskets He puts an equal number of plums in each basket How many plums go in each basket? For example: Fariba gives out 1 cookies, cookies to each person How many people will get cookies? 1 So people get cookies Here is an explanation of the solution There are 1 cookies Each person gets cookies I want to find out how many people will get cookies before the 1 cookies are gone I can group 1 counters at a time I used 0 counters because there were 0 plums I folded a piece of paper into parts because there are baskets I put 1 counter in each part I can make groups of So people will get cookies to start Then I kept on taking out counters at a time and putting 1 in each part I did that as many times as I could Finally, I had 1 counter left over Then I found that there were 1 counters in each part So that means Ian could put 1 plums in each basket, but he would have 1 left over Maybe he would eat it or maybe he could find more plums and put 1 more in each basket, then there would be 1 in each basket Copyright 00 Nelson Answers Chapter 10: Division 79
4 Exploring Division Patterns Identify, describe, and extend division patterns You will need pencils of different colours 1 This chart shows the first 0 numbers of a 100 chart Use a different coloured pencil to answer each of parts a) to c) a) If a number is divisible by, print in its square b) If a number is divisible by, print in its square c) If a number is divisible by 10, print 10 in its square The numbers for the first row are done Add the colour a) What numbers in the chart are divisible by both and? 10, 0, 0, 0, 0 b) What else do you know about the numbers from part a)? 1 counters can be put into groups of with no counters left over So 1 can be divided by with nothing left over This means that 1 is divisible by They end in 0 They are the numbers divisible by 10 Write the next numbers after 0 that are divisible a) by 10 0 and 70 b) by and 0 c) by and Answers Chapter 10: Division Copyright 00 Nelson
5 Estimating Quotients Solve division problems using estimation Estimates will vary Examples are given 1 a) students are buying a gift for $1 About how much does each student have to pay? your work About $, because x = 0, so 1 is about b) With tax and gift wrap, the cost of the gift is $ About how much does each student have to pay? your work Estimated quotients are answers that are close to the actual quotient Use facts you know to estimate For example, 1 is about because 1 1 is about because 10 or because 1 About $ because x =, so is about Or about $7 because x 7 = 8, so = about 7 Estimate Write the number sentence you used for each a) 1 is about x = 1 b) is about x = c) 1 is about x = 10 d) 19 is about x = 18 e) 17 is about x = 1 $1 buys 7 markers About how much does each marker cost? about $ students share 1 markers About how many markers does each student get? about markers Copyright 00 Nelson Answers Chapter 10: Division 81
6 Division Strategies Use estimation and multiplication to solve division problems with greater numbers You will need a calculator 1 An office tower is 0 m high A -storey house is 8 m high About how many can be stacked to be as high as the office tower? To find out, complete the following I need to divide 0 by 8 If 0 8, then 8 0 If you use guessing and testing with multiplying, you can avoid having to divide with a calculator, which can give an answer with a decimal part For example, 0 8 is 7 Estimates will vary For example: Guess Test by using a calculator to multiply is way too high too low 8 00 pretty close About 8 8 can be stacked to be as high as the tower Use guess and test and multiplying a) Mary s birthday is 7 days away About how many weeks away is her birthday? about 10 weeks, or about 11 weeks b) Tennis ball containers hold balls each How many containers would be needed to hold balls? about containers 8 Answers Chapter 10: Division Copyright 00 Nelson
7 Test Yourself Circle the correct answer 1 In the division 1, which number is the quotient? A 1 B C D Which division sentence matches the picture? E 1 G 1 F 1 H 1 Which division fact is shown? A 10 B 10 C 1 D 1 Which question is not part of the Communication Checklist? E Did you show enough detail? G Did you explain your thinking? F Did you include a diagram? H Did you divide? Which number is divisible by? A B C D 9 Which number is divisible by? E F G H 9 7 Which number is divisible by 10? A 1 B C 90 D 8 Which is the best estimate for 1? E about 1 F about G about H about 7 9 Which is the best estimate for? A about B about C about D about 8 10 muffins will be put in packages of About how many packages are needed? Use guessing and testing and a calculator to multiply E 0 F 0 G 80 H 0 Copyright 00 Nelson Answers Chapter 10: Division 8
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