1 00:00:00,000 --> 00:00:04,800 If you have been listening for a while, you know my wheelhouse is early elementary math, 2 00:00:04,800 --> 00:00:11,200 but recently I've been working a lot with third grade math specifically in early multiplication, 3 00:00:11,200 --> 00:00:15,920 so arrays, equal groups, and I thought that I would share some of the stuff that I have been 4 00:00:15,920 --> 00:00:20,240 working on and maybe it'll be helpful to you too. Specifically when it comes to working with 5 00:00:20,240 --> 00:00:26,080 students who may have a hard time grasping or understanding ideas of multiplication and with 6 00:00:26,080 --> 00:00:39,920 language learners. Hello and welcome to Making Number Sense Make Sense, a podcast for elementary 7 00:00:39,920 --> 00:00:44,880 teachers, specifically early elementary teachers, looking to really make an impact in the number 8 00:00:44,880 --> 00:00:49,680 sense of their students. Something that I feel that can be really challenging when working with 9 00:00:49,680 --> 00:00:57,040 arrays is just the vocabulary of a row and a column. It's kind of hard concept to understand 10 00:00:57,040 --> 00:01:02,320 and especially since row is a homonym, like you can have a row of seats but you can also row your 11 00:01:02,320 --> 00:01:09,440 boat. And if you are a language learner and you're starting to learn English, what would be the way 12 00:01:09,440 --> 00:01:14,160 that you would think of that word most commonly? A row of items or like row your boat, especially 13 00:01:14,160 --> 00:01:19,040 if it's a song that they're hearing a lot younger kids, it can be kind of tricky. Same thing for a 14 00:01:19,040 --> 00:01:23,920 column, it's just like what does this word mean that's equal representations. So I think that's 15 00:01:23,920 --> 00:01:30,080 something that you can really kind of focus on like which ways the rows go and which ways the 16 00:01:30,080 --> 00:01:35,840 columns go. That and also that you can have two arrays that have the same product, that have the 17 00:01:35,840 --> 00:01:42,000 same expression or equation can also be kind of tricky. I feel like the way or a way to really 18 00:01:42,000 --> 00:01:48,880 support students and understanding that is hands-on and something that I notice as kids get 19 00:01:48,880 --> 00:01:55,920 older is they start to do kind of math centers less. And sometimes I wonder about that because 20 00:01:55,920 --> 00:02:01,040 when working with younger kids, center time is their absolute favorite time. Now there has been 21 00:02:01,040 --> 00:02:06,000 back and forth of centers, like if students are not doing it correctly then what are they really 22 00:02:06,000 --> 00:02:11,280 learning? But I think especially if you're working with like second grade, third grade, the opportunity 23 00:02:11,280 --> 00:02:17,200 to work with different mathematical concepts in that way and just kind of have the opportunity 24 00:02:17,200 --> 00:02:23,040 to play with the math can be really helpful in making the concepts feel more tangible and more 25 00:02:23,040 --> 00:02:30,320 like things that are accessible to them versus so abstract. So I came up with some center ideas that 26 00:02:30,320 --> 00:02:35,360 are kind of similar to what I've created or used in the past with younger kids and just kind of 27 00:02:35,920 --> 00:02:40,480 switched the subject and have the similar concepts. So we're not reinventing the wheel, 28 00:02:40,480 --> 00:02:46,320 we're just making it work for the grades that we're at. So the first one is roll an array treasure 29 00:02:46,320 --> 00:02:52,320 hunt. So using dice which I love, using a hundreds chart mat which I also love, it doesn't have the 30 00:02:52,320 --> 00:02:57,920 actual numbers on it but basically students would roll two die and then that would be the numbers 31 00:02:57,920 --> 00:03:02,240 that they're multiplying together. They would have to draw an array on their work mat that would be 32 00:03:02,240 --> 00:03:06,320 the product of the two numbers that they rolled. And now the way you kind of take it up here is 33 00:03:06,320 --> 00:03:12,320 there's three different versions of this game. In the first one there are coins all over the map, 34 00:03:12,320 --> 00:03:17,520 so what their goal is is to make sure that their arrays can cover as many coins as possible 35 00:03:17,520 --> 00:03:22,800 and then at the end the person who has the most coins in their arrays is the winner. The second 36 00:03:22,800 --> 00:03:28,880 version is roll an array but collect the treasure and so this one has coins but it also has gems, 37 00:03:28,880 --> 00:03:32,960 it has treasure chests and they have different values. So your kids are going to be really 38 00:03:32,960 --> 00:03:38,960 creative and thinking about okay how can I put my array, do I need to make it the long way, do I need 39 00:03:38,960 --> 00:03:43,760 to make it horizontal, do I need to make it vertical, that it can cover the most space so I can get the 40 00:03:43,760 --> 00:03:47,760 points for the treasure or I can get the points for the gem. And again this kind of is helpful 41 00:03:47,760 --> 00:03:52,640 for the concept of an array can be vertical or horizontal and still represent the same thing 42 00:03:52,640 --> 00:03:57,600 because they're really trying to figure out how to make that work for them. And the last one is 43 00:03:57,600 --> 00:04:03,360 roll an array and avoid the traps. So in this one they're trying to avoid different spots on the 44 00:04:03,360 --> 00:04:07,040 mat instead of trying to cover them. So again they're going to have to be creative with how they 45 00:04:07,040 --> 00:04:14,800 fit their arrays to not lose all of their gems or all of their points if they hit one of the traps. 46 00:04:14,800 --> 00:04:20,640 So that was roll an array treasure hunt three ways. The next is spin multiply and find the expression. 47 00:04:20,640 --> 00:04:26,640 In this game they have a spinner that has an array for each kind of set of number facts. So it's like 48 00:04:27,360 --> 00:04:32,640 two by two, two by three, two by four, two by five and so the students would spin and then on either 49 00:04:32,640 --> 00:04:38,080 side the expressions are written both ways. So it might say two times three and also three times two. 50 00:04:38,080 --> 00:04:43,920 So then your students would color in and your kids would mark off if they got that array and see if 51 00:04:43,920 --> 00:04:49,520 they can get it again. So that again forces them to think about the arrays being vertical or horizontal 52 00:04:49,520 --> 00:04:55,680 or two expressions can represent the same array. The next one is array pick build and cover. So 53 00:04:55,680 --> 00:05:01,840 students pick up an expression card and represent it on the work mat. So for this one they have a 54 00:05:01,840 --> 00:05:06,800 large space to work with so you will need a lot of manipulatives for this to make it work. So they'd 55 00:05:06,800 --> 00:05:12,960 pick an expression say they had five times six and then they would actually build an array that shows 56 00:05:12,960 --> 00:05:19,600 five rows and six columns five times six and then cover the product on the work mat until they can 57 00:05:19,600 --> 00:05:24,720 cover all of them. So it helps students work on their math facts, helps them kind of build arrays 58 00:05:24,720 --> 00:05:30,400 and really get that hands-on experience with building them for a purpose. The next game is 59 00:05:30,400 --> 00:05:36,240 more about multiplication facts than arrays but it still kind of works in the same wheelhouse in 60 00:05:36,240 --> 00:05:42,320 the same family. Empty the board multiplication or multiplication facts they would have either one die 61 00:05:42,320 --> 00:05:47,280 or two dice and if they had two dice they would add those together and that's the number that 62 00:05:47,280 --> 00:05:52,080 they're going to multiply by the target number. So for example if they rolled a two and a six 63 00:05:52,080 --> 00:05:58,160 that would be eight. If the board they're working on is the nine facts multiplication board then 64 00:05:58,160 --> 00:06:04,640 they would multiply eight by nine and then remove one cube from where the product is. So the setup 65 00:06:04,640 --> 00:06:08,800 of this game is they have their mat with their target number on it so they're working on nines 66 00:06:08,800 --> 00:06:14,240 facts or they're working on five facts and they would put a cube in each space that's available 67 00:06:14,240 --> 00:06:20,960 and on the bottom it has the product of these multiplication facts. So they roll the die to 68 00:06:20,960 --> 00:06:26,000 get the number that they're multiplying the target number by and then they would take off a cube if 69 00:06:26,000 --> 00:06:30,720 they rolled that number that makes that product and they would continue until their board is empty. 70 00:06:30,720 --> 00:06:36,160 So again they're getting a lot of practice with multiplication especially in a kind of target 71 00:06:36,160 --> 00:06:41,840 number but in a different way than just doing drills or flashcards. And if doing all 12 numbers 72 00:06:41,840 --> 00:06:47,600 is a bit intimidating you can also just start with one die and multiply your target number by one 73 00:06:47,600 --> 00:06:54,960 through six before moving to one through 12. And next is an array thinking task. Now if you have 74 00:06:54,960 --> 00:07:00,720 tried the escaping ants task that's more of an equal groups task than an array task but I have 75 00:07:00,720 --> 00:07:07,040 seen students without prompting even kindergarten students without me showing them how to create 76 00:07:07,040 --> 00:07:13,840 an array created an array on their own to represent what they were doing. So that's a great way to 77 00:07:13,840 --> 00:07:19,520 kind of bridge equal groups repeated addition and multiplication together. Or if you're 78 00:07:19,520 --> 00:07:25,680 looking for something a little more challenging you can work on this bake sale array task. So 79 00:07:25,680 --> 00:07:32,240 basically in this task the students are baking cookies for a bake sale and they have to figure 80 00:07:32,240 --> 00:07:38,320 out how many trays they'll need to have enough for the bake sale. So that task has an unknown 81 00:07:38,320 --> 00:07:44,000 factor included into it to make it a little more challenging but still has you know thin slicing 82 00:07:44,000 --> 00:07:49,520 questions as well as check your understanding questions as well as the opportunity to create 83 00:07:49,520 --> 00:07:54,080 their meaningful notes. So there's lots of versions of notes that they can use. One that has their 84 00:07:54,080 --> 00:07:58,560 that's broken up into quadrants so in their first quadrant and be kind of a fill in the blank. 85 00:07:58,560 --> 00:08:04,000 Their second quadrant can be kind of a worked example that they write or there's versions that 86 00:08:04,000 --> 00:08:09,760 have a worked example already there. And then the other two is where they can choose to write down 87 00:08:09,760 --> 00:08:14,400 things that they think will be important for them to remember. And in the last one they can kind of 88 00:08:14,400 --> 00:08:19,120 look around to see what other students were doing and see if there's a different strategy that they 89 00:08:19,120 --> 00:08:25,840 really like that another student used. Using notes in the older grades so third grade fourth grade 90 00:08:25,840 --> 00:08:30,960 even second grade really can be helpful for them to solidify their learning and understanding. I 91 00:08:30,960 --> 00:08:36,480 wouldn't necessarily do notes for kinder at the beginning of the year but probably midway through 92 00:08:36,480 --> 00:08:41,280 they can start to kind of create their own notes or their own rememberings. So I hope that that 93 00:08:41,280 --> 00:08:46,560 gave you some ideas about working with arrays and early multiplication with your students. 94 00:08:46,560 --> 00:09:07,600 Let me know if you give any of them a try and I will talk to you next time.