Maths investigations. Year 1

Transcription

1 Maths investigations Year 1

2 Money- 5 coins Today we looked at coins and the total of them. Our teacher said that she had 5 coins in her pocket and they were between 1p and 10p. We had to try and work out how many different combinations of coins she could have in her pocket. We started by doing it with our teacher as a class. Have a look at the combinations! Year 1 We then went and tried this at our tables and worked with our partners.

3 We then came back and we used the 1p and 2p coins. We had to try and work out all the different combinations and their totals. We started by looking at 2p 2p 2p 2p 2p and 1p 1p 1p 1p 1p and then swapped one 2p with a 1p and so on. We came up with lots of different combinations! Year 1

4 We worked with our partners and came up with lots of different ways of making the 5 coins that were in Miss Malaponti s pocket. Year 1

5 Sticks Today we looked at a tricky investigation using sticks. We started by lining up two red sticks and one blue stick. We looked at the difference in size. We then tried to find away of lining up the red and the blue sticks to see how many red sticks and blue sticks we would need before they were both the same length. Year 1 We found that 2 blue sticks were the same length as 3 red sticks.

6 Year 1 After finding that 3 red sticks and 2 blues sticks were the same length we carried on trying to find how many red sticks and blue sticks we would need until they were both the same length again.

7 Here are our results! 3 lots of 2 2 lots of 3 4 lots of 3 6 groups of 2 Year 1 We found that the groups of 3 kept going up in 2s and the groups of 2s kept going up in 3s.

8 Dominos This week we looked at the patterns in the dominoes. We started off by looking at the number patterns we could see in the dominoes that were next to each other. We looked at some together with Miss Malaponti and worked out what the patterns were. Year 1

9 We then had a go at trying to work out what the missing domino would look like! The dominoes to our left had the same number on the top so the next domino in the sequence would also have a 2 on the top, however the bottom part of the dominoes were going up in 1s which means that the next domino in the sequence would have been 2 on top and 6 underneath. Year 1

10 Here is a completed missing domino sheet. As you can see the top domino part went up one way and the bottom went up in another. It was very hard working out what would go in the middle. This one was one of the trickiest as there was only one domino to show us the pattern. Some of us decided it was zero and others thought about making their own pattern. Year 1

11 Maths investigations Year 2

12 Lots of biscuits Yesterday some children in year 2 did some baking. Tony, Laaibah, Mushtaaq and Gustaf baked vanilla cookies. When they had finished they arranged them like this: Then, Tilda and Waleed came over to play too. How many biscuits could they all have now? We thought about 12 6 using the sharing strategy. We all used different strategies to count the biscuits. Some of us counted is 2s, 3s or 4s. Year 2 How many biscuits did they make? If they shared them out equally how many would they get each?

13 But then it got even trickier, because Katelyn came over and we had to try and share the biscuits between 7 children =? Some of us chose to cut up the biscuits into halves or quarters. Year 2 This struck a huge debate about what to do if you can t share equally (using whole numbers). One person said they thought it was impossible to share an even number equally between an odd number (e.g. 12 7) but we soon realised this wasn t true because you can do 10 5 equally.

14 Last week I went into the lunch hall to help Fiona and Mable. They were baking chocolate chip cookies. When they came out the oven they looked like this: How many biscuits were there? Fiona then turned her oven tray around and the biscuits looked like this! Now we have 10 rows and 6 columns! But the answer was still the same! 10 x 6 = 60! We finished off the lesson with a yummy biscuit! Year 2 We used many different counting strategies but after discussing it we decided that the best way was to count 6 rows and 10 columns. 6 x 10 = 60.

15 How many eggs? Vocabulary: more less total altogether Here are three baskets. One brown, one red and one blue. Altogether they have 10 eggs in them. The brown basket has one more egg in it than the red basket. The red basket has three eggs less than the blue basket. How many eggs are in each basket? Year 2

16 We used different strategies and manipulatives to help us work it out. The answer Year 2 The answer

17 Year 2 We wrote our own similar problem. We quickly realised that we needed to start with the answer and work backwards.

18 We started by revising odd and even numbers. Take three numbers With your partner: Think of an odd number that is less than 10 Think of another odd number that is less than 10 Think of an even number that is less than 10 Write them on your whiteboards. Now choose some manipulates or resources around the room to draw or represent your numbers. Year 2

19 Now add your numbers together. Do you notice anything? Keep a record of your results on your whiteboards. Now start again, 2 odd numbers and 1 even. See if you can find any patterns. Year 2

20 Year 2 We found that two odd numbers and an even number always adds up to an even number. We explained this to our partners and the rest of the class.

21 Maths investigations Year 3

22 We have been given four money bags and 15 1p coins. The 15 coins have to be split into the four bags. All the bags must be used. All the coins must be used. We can split the coins however we like. We used place value counters to represent the money in our bags. However there was a catch! We were going to spend the money in a very special shop. Everything in the shop cost between 1p and 15p. However you can only pay in money bags. You must pay with the exact right amount. You cannot get change! Year 3

23 We started by seeing what combinations of money we could arrange in our money bags and recording our results on a whiteboard. We checked if we could buy everything in the shop by writing down each price 1p 15p and seeing if we could use our money bags to make this amount. This showed us where we were going wrong and that we needed to adjust the coins in our bags. Year 3 We realised we needed a bag with 1p and a bag with 2p. This is because we needed to be able to make 1p, 2p and 3p before we could make larger amounts.

24 After a lot of testing we thought we found the right combination. 1p, 2p, 4p and 8p bags. However we needed to test our theory to make sure we could pay for anything between 1p and 15p. Year 3 We tested our combinations to see if we could buy everything we needed too. We could! It was an excellent feeling to crack the problem.

25 This week Miss Trunchball reappeared from world book day to ask an important question, I have 5 coins in my pocket, how much money might I have? We had to work out how much money she might have from the 5 different coins. We were lucky enough to have a parent helping us too! I have 5 coins in my pocket. How much money might I have? Year 3

26 We started by seeing what combinations of money we could make with our coins and recording this on paper. We also started noticing certain patterns and trends and we recorded these too. Year 3

27 We realised there were so many combinations we were unable to find all of them! However we started looking at the smallest and largest amounts Mrs Trunchball might have. The smallest possible amount is 5p made from 5 1p coins Elsie Blu Year 3 The greatest amount of money you can possibly have is made from coins Ridwaan and Aya. After finding the largest and smallest amounts we started working through other amounts, changing just one coin at a time so we didn t miss any combinations!

28 You have to share everything equally between two people Chiemela. This week s task involved us using our knowledge of fractions to find out what each person would get at a picnic, if we divided it all up equally. Year 3 We decided it would be best to look at key variables within the question. After this we knew that we had to divided everything on the picnic table between two people. Using our knowledge of fractions we knew this was ½.

29 We started by counting out how much there was of everything at the picnic. Once we knew this then we started to work out how much each person got. I shared all the food equally onto four plates that I drew After this we had a completely new picnic table and this time we had to share everything between THREE people. This was a tricky task as we were now working with an odd number and more items on the picnic table. I used fractions cards to help me! Year 3 After completing this task we moved onto our next challenge. This time the picnic was the same but there were now FOUR people at the picnic. This meant we had to know work out how much four people got at the picnic. To finish we decided to create our very own picnic and test our partners.

30 Key Findings We found that there were many different ways to work out how to share a number or food out equally. Some of us found it was easier to use our times tables to find the answer. Others in the class decided they would use their knowledge of division to find the answer. Some other children in the class decided it was best to use manipulatives to find the correct answer. Overall we found that when sharing out food you need to remember to share things equally. Year 3

31 Maths investigations Year 4

32 Party time There are other similar parties going on at the same time. They have bigger square tables with more children sitting round on each side. Explore and compare all the tables: 2 on each side, 3on each side, 4 on each side and 5 on each side. Year 4

33 To start the investigation off, we sorted the sweets into the seats using dots. We then added up each side to find the side totals, before undertaking individual investigations to see if there were any relationships between the side, people sitting opposite other, or anything else that we noticed. Year 4 After looking at the square shaped tables, we moved on to looking at pentagonal and hexagonal shaped tables. We couldn t believe how many patterns we noticed!

34 Year 4 Our key findings

35 Mr Russell s money saving tips! Number 1: Sharing is caring! Our investigation We were introduced to Mr Russell s money saving schemes! This week s one was about saving money when buying gifts for your family! Year 4 I use my mathematical genius to save money when I buy my niece and nephew presents! My secret is to buy gifts for them individually and gifts they need to share! (The secret is that the shared gifts count as a present for both children!)

36 To start the investigation off, we recapped what a Venn diagram is and how it works. We solved problems using a Venn diagram with only 2 sub-sets. We were set different challenges of how to distribute the presents between 2 children. If we placed a present in the intersection then that meant the gift belonged to both children! This is the basis to Mr Russell s money saving scheme! But then. My sister has just had another child! My brilliant plan is ruined! I must find a way to solve this.. Can you help me? Year 4 So this meant we had to use a Venn diagram with THREE subsets! We familiarised ourselves with what all the sections represent. Finally we had to distribute 10 gifts between the 3 children so that the eldest had 7, the middle child had 6 and the youngest had 5.

37 Our key findings We found that being systematic in our approach to the investigation was the quickest and most efficient way to find the combination. We also found using manipulatives really useful for this investigation. Having physical representations of the gifts and purses to move them between, really enabled us to independently investigate the problem. We also found that different groups had different methods of finding solutions, this inspired some really interesting discussions about finding ways to problem solve that suits each individual. Year 4

38 Mr Russell s money saving tips! Number 2: You don t get tips for free! Our investigation Mr Russell challenged the student teachers to earn their money saving tips by completing a game. Year 4 The aim of the game is to arrange four digits taken from dice rolls to make the largest or smallest number. Be careful where you place your first few throws!

39 To begin with, we worked together to work out where the teachers were going wrong if they have a larger number, they need to put it in the right column! We then tried playing this game with our own partners. The hardest part was predicting whether or not we could use our numbers effectively. But then. You are getting too good at this, what if we tried to get the smallest number or put a decimal in there? So this meant we had to change our tactics slightly and remember to put the lower numbers in thousandths and hundredths columns and the higher numbers in the tens and units columns. Then we had to decide where to put our decimal points. Tricky! Year 4

40 Our key findings Year 4 We found that we had to keep in mind that when rolling the dice, we could not predict what number we would roll next. Because of this, we used our knowledge of place value to use our numbers effectively. When the challenge changed, we had to make sure that we changed our tactics and changed where we were placing our numbers

41 Maths investigations Year 5

42 Abundant numbers This week in our maths investigation we investigated abundant numbers. But what is an abundant number?? To be an abundant number the original number should be less than the sum of it s factors (not including itself). Let us show you with the number 72. Year = 123

43 Once we had mastered how to work out if a number was an abundant number we were given challenges! Challenge 1: We had 10 minutes to find as many abundant numbers between 0 and 100. Challenge 2: Can you find a rule that fits abundant numbers? For example are all odd numbers abundant? Year 5

44 Key findings: As hard a we tried, we didn t find any rules that fit abundant numbers! Some of us almost found a rule for example all numbers which have a 2 in it are abundant but then we d stumble upon a number than didn t fit it! So we are passing the challenge on to you! Year 5

45 Some games that may be nice This week we were challenged to investigate tactics when playing dice games. or nasty The rules We played lots of different games that used our understanding of place value. For game 1 we took turns to roll the dice and decided which of our four boxes to fill. We repeated this four times until all our boxes are full. We compared our four digits number to our partners. We found the difference between them and whoever had the biggest number won the difference! Year 5

46 Nasty games The games got nasty and we were able to choose where we put the digit on our PARTNER S card! Our tactics changed and we had to think about the chances of rolling big or small digits. It got very exciting! Cooperative games Finally we played in a group cooperatively. We chose a target and worked out who would be closest, second closest and third closest to the target. Year 5 We then decided as a group, who used each digit after the die was rolled.

47 Our findings We started to talk about probability. Some of us thought we were good at throwing big numbers and some thought we were good at the smaller numbers. When we looked at the chances of throwing a 1,2,3,4,5 or 6 on a dice we realised that the PROBABILITY was the same 1/6 She did roll a 6!!!!!! Year 5 Have a look at our bar to show the probability of Rosa rolling a 6 and winning the game!

48 20 divided into 6 This week we walked into the classroom and on the whiteboard it said: Most of us thought 20 divided by 6 well that s easy, the answer is 3 remainder 2! That s when we saw number cards from 1 to 20 and the real investigation began Year 5 The rules: Arrange the number cards into six unequal piles that all add up to the same value!

49 We tried a range of different methods to try and solve the investigation. We thought that each pile must equal a number bigger than 20. So we used trial and improvement and worked tried to see if we could get the 6 piles all to equal 21 and so on We added up all the numbers on the digit cards then divided it by 6 (210 6). Our answer 35 so then we tried to make all of the piles equal 35. Year 5

50 I ve almost got it! I just need to make 35 with these remaining cards! Our findings Year 5 There were many combinations to get the correct answer as long as each pile had the value of 35! You have to choose which numbers to use in each pile very carefully as if you used all of the bigger numbers first it was challenging to make 35 with the smaller numbers!