20762_Problem_solving_Year_5_Number_and_place_value_2

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KEEPING RECORDS 1. Kellie is a keen netball player. She notices that when the players in her club are being organised on the stand for the end of season photo, if 7 players are seated in each row, 4 players do not get a seat. When they squash up a bit to seat 8 players in each row, they have enough seats for the coach, the assistant coach and the first-aid person. How many netball players are there in Kellie’s club? 2. Kyle is uploading photos of his cricket team onto his website. He knows that most of his friends would not be interest in it if he only put one photo on each screen, so he decides to scale them down to be smaller so that they can see several photos on screen at the same time. When he places 8 photos per screen, he still has 4 photos left. When he puts 12 photos on screen, he needs 3 less webpages. How many photos does he have to upload and how many webpages does he need? 3. Kellie decides to upload the photos of the players in her club taken at last season’s games onto a website like Kyle’s. Some photos show a lot of action and need to be quite large, while others are of only one or two players and could be smaller. At first, she decides to put 5 pictures on each webpage, but this takes up a lot of pages and the last page only has two small photos. When she changes the arrangement to 8 pictures on a page, the last page has three larger photos. How many photos does Kellie have? 4. Kellie wants to have the same number of photos on each webpage. How many pages would she need to make to do this? R.I.C. Publications ® www.ricpublications.com.au Problem-solving in mathematics 25
TEACHER NOTES Problem-solving To analyse and calculate information in written numerical problems Materials materials, calculator Focus These pages explore word problems that require a number of operations, including division. The wording has been kept fairly simple to help with the problem-solving process. Students need to determine what the problem is asking and, in many cases, carry out more than one operation in order to find solutions. If necessary, materials can be used to assist with the calculations as these problems are about reading for information and determining what the problems are asking rather than computation or basic facts. Discussion Page 33 These problems have more than one step of calculating operations. The questions are centred around the discount and sale prices. The wording has been kept fairly simple to assist with the problem-solving process. Students need to have an understanding of the concept of how marked price goods can be discounted. Some problems involve calculating the price after the discount has been applied, while others involve calculating the full price of a product as compared to its sale price. A table can be used to assist with the problems that have a variety of possible answers. A calculator can be used assist if necessary— key in the full amount, press the ‘subtraction’ key, enter in the discount, press the ‘per cent’ key and the sale price will displayed. Page 35 The ‘sugar mill’ problems involve the concept of tonnes. In most cases more than one step is needed to find a solution. The first investigation about tonnes of cane over a season results in a calculation of 815.8 bins. This is an example of where the answer does not make sense in light of the problem and would need to be thought of as 815 full bins and one bin which is not full, or 816 bins. Similar thinking is required for most of the problems. The problem about the two farms results in approximately 2123 tonnes per month, which would be about 1061.5 tonnes per farm. The numbers are not exact and can be used to discuss how totals such as these are calculated and in most cases would not be exact, but rather an approximation. The last problem sees 353 truck loads, so, if 4 trucks are used then there would be 88 trips using 4 trucks and 1 trip using 1 truck. Possible difficulties • Confusion over the need to carry out more than one step to arrive at a solution • Using all the numbers listed in the problem, rather than just the numbers needed • Not thinking in terms of the problem and writing solutions such as 6.04 trains • Difficulty with the concepts of tonnes, discount, percent and profit Extension • Students could write their own problems and give them to other students to solve. Page 34 These investigations involve more than one step and involve concepts of grams and kilograms. The concepts of profit and repackaging are also explored in many of the problems. Students may find it helpful to draw diagrams to visualise what is happening in order to find solutions. A table can be used in the first investigation to help manage the data, while a diagram may be helpful for Problem 2 in order to visualise the actual process of repackaging and the cost involved in buying the large bottles and selling the smaller tubs. The second part of Problem 3 requires the students to first determine not only the summer and winter months but also the number of weeks per month, which can vary from year to year. 32 Problem-solving in mathematics www.ricpublications.com.au R.I.C. Publications ®
Page 1 and 2: Your partner in education YEAR 5 PR
Page 3 and 4: FOREWORD Books A-G of Problem-solvi
Page 5 and 6: FOREWORD diminished or left out of
Page 7 and 8: TEACHER NOTES Problem-solving To an
Page 9 and 10: THE TROPICAL FRUIT ORCHARD The trop
Page 11 and 12: TEACHER NOTES Problem-solving To or
Page 13: THE TOWN’S CENTENARY While Kellie
Page 17 and 18: AT THE DELICATESSEN 1. The delicate
Page 19 and 20: SOLUTIONS Note: Many solutions are
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