Elementary math chat is a weekly math chat where participants come to discuss best practices, examine student work, explore routines for reasoning and research that guides and supports pedagogy centered on problem and student based learning.
Hi Everyone! I am Lori, K-5 math interventionist from Missouri. Last night my great-niece saw my dad sitting in his recliner eating popcorn so she climbed up in the chair next to him with her kiddie puffs #elemmathchat
I think the greatest thing I've seen all week is my husband!!! I've been gone at conferences the last couple weeks so last night it was nice to just be here at home. #elemmathchat
Hi! Margie from PA
Math Coach
Always Love when @MissMath_Teach leads #elemmathchat Favorite part of my week was so many teachers sharing on Wednesday how they are already implementing all they learned from Tuesday's math PD. So good for the heart!!
I am Melynee in OK teaching MS math for Ss w/ disabilities. Best thing I was this week was my 6th graders discovering the most efficient way to find LCM for prime numbers. They couldn't believe that I had not just told them how, but made them discover it! LOL #ElemMathChat
That's the best! It's like the most affirming thing to have so much faith in their abilities & the power of time to see it pay off for the kids #elemmathchat
A1 It is like a balance with a fulcrum. If you take or add something away from one side you have to do the same to the other to keep the balance level. #ElemMathChat
I have grown to love fractions since I learned to actually understand the meaning behind all of the steps I was taught to memorize as a kid. Decomposing is so powerful #elemmathchat
A1. Sometimes I compensate when reading by slowing down to make it easier. Compensation in math is just like that: it's how we make numbers easier. Like, if I'm adding 29 + 31, I can make it easier by taking the from the 31 and adding it to the 29 to make 30 + 30 #elemmathchat
A1: Well, if the S is there, having the child explain/define would provide meaning and show the parent how well the child can communicate mathematically. #elemmathchat
We had not anticipated just how many of the HS Ss would say that 1 and 2 are related by addition/subtraction but never think of multiplication/division. And that they weren't all so thoughtful about how to place numbers (say 10, 30, 50, and 100) PRECISELY on line #ElemMathChat
A2: composing and decomposing number, relationship between addition/subtraction, equal sign- compensating with subtraction is a different beast and helps if kids understand multiple ways of viewing the operation #elemmathchat
A2: To understand compensation in math maybe it necessary to adrees before the properties in the operations ans also decomposition of numbers. #elemmathchat
A3: Pretend I have 38 on ten frames...3 ten frames 8 ones...and then 46 on ten frames...I would move 2 from the 46 to 38 to make 40 and then still have 44...so 84. I know...too lazy tonight for a picture...imagine! Visualize! #elemmathchat
A1. I think sometimes as Ts we get hung up on specific compensation techniques & forget that easy numbers for one person is not the easiest number for another #ElemMathChat
I think I saw this today with firsties. It was 9 + 7...she drew the dots and then moved 3 from the 9 to the 7 to make 10 and then 6 left...so 16. Wondering why she saw it this way??? #elemmathchat
A3: Either do 40+46 and then subtract the 2 from the result, or change the 38 to 40 and immediately change the 46 to 44. Both work, but I tend to see students choose one or the other. They either alter the result or the other addend #elemmathchat
For me, #clotheslinemath super power is the magnitude aspect. It would be so interesting to watch secondary kids in action. I've only done it with elementary kids myself. #elemmathchat
A3: I teach my students to get to the “friendly column.” I need two more to get to 40. They seem to get that. I love when I give them a hundreds chart and it’s the first thing they do...circle that column. Then add 44. #elemmathchat
A3: (Just learned what "compensation" means - hadn't seen that word applied to that strategy) I wonder if it's more common to make the 46 a 50, or make the 38 a 40? I'm thinking 46 to 50, since 50 is "nicer"? #ElemMathChat
I am often surprised when I work with 2nd and 3rd graders to use compensation or distributive property that are not able to decompose single digit numbers. #elemmathchat
My 2nd graders had a brief discussion about this w/a 100 grid. For 45 - 34, I remember them saying that they can "jump back 30, then 5" to start. So I'm thinking 5 or 10 may fit that criteria. #elemmathchat
A:3 identifying a friendly number (number that end and 0 or 5) in this case 38 is very close to the friendly number and it is easy to add 2 in order to get 40, therefore, it is necessary to take away 2 from 46 so using compensation strategy i get the addition 40+ 44 #elemmathchat
Oh, it was fascinating, alright! I think @pegcagle might have continued with it more this week - maybe she'll chime in because she can't possibly have anything else to do.... I don't think it looks a lot different in HS as Elem, when you get right down to it. #ElemMathChat
A4: I would definitely use a manipulative or a visual. Maybe ask them if there is a way to rearrange the pieces to get an easier number to use? #ElemMathChat
YES YES YES YES!!!! So I've been noticing that 3rd graders can draw an array and break it apart with equations about 50 different ways to show distributive property....BUT when asked to use distributive with bare number they can't...we have to help them visualize. #elemmathchat
Maybe she is really comfortable with 7+3 or she is really excited that she just learned that fact? Or maybe she really likes moving dots and wanted to move more than less? Or maybe she sees 7 as less scary than 9 to focus on? Did you get a chance to ask her? #elemmathchat
A4 We talk about friendly numbers. Sometimes what is friendly for one is not friendly for others. Doubling and halving to multiply is highly effective, but I forget to do it, but I compensate and adjust often. #ElemMathChat
A4: At the Math Forum (and in @maxrayriek's book), when Ss are stuck, we ask, "What makes this hard?" Then strategize about how to make the "hard" thing go away (might be fracs, decs, big numbers, whatever). #ElemMathChat
A4: Bit torn on this one. I'd first ask myself how important it is to "unstick" them on this particular strategy. Do they have others they use with fluency? If so, I can be okay if compensation isn't their go to. #elemmathchat
A4 Also if students identify a favorite number and play games and engage in ways to decompose or create that number they learn about relationships & start doing so with other numbers. I play around with 12 all the time just for fun! #ElemMathChat
A4: Otherwise, choosing numbers that lend themselves to compensation, encouraging mental math, and engaging class in critiquing each others' reasoning supports "unsticking" #elemmathchat
I am not sure why I let it bug me so much that we call numbers nicer or friendly. It's like saying 37 is a mean girl. Anyone have better alternatives? #elemmathchat
Do all "friendly" numbers have to be a multiple of 10? I am personally a huge fan of multiples of 25...grew up counting a lot of quarters #ElemMathChat
A5: Well...I like subtracting from 80...because I know my tens. Sooooo 80 - 42 would keep the distance between the numbers the same. I like what this looks like on a number line. #elemmathchat
While "mean girl" evokes certain vivid images for sure, we often talked about numbers that make you grumpy or happy. So maybe happy numbers? #ElemMathChat
I was going to add in some fraction problems for this chat but I was worried we would run out of time. Maybe a follow up chat would be fun #elemmathchat
I think of a friend. You know a lot about that friend. You play with that friend with comfort. That doesn't mean others are not nice, you just know your friend better. Some numbers I know better than others and they play nice with me. I get along with others too! #ElemMathChat
Try some whole numbers sometime and see what moves they make to be really precise. It's one thing to decide that 50 should be halfway between 0 and 100, it's another to say EXACTLY where 30 should go. #ElemMathChat
In reply to
@MissMath_Teach, @Mkrenzer20, @pegcagle
76-40=36, but since I took too much away, I'd add 2 to the answer, giving 38. I find number lines to be useful for compensating with subtraction. It really supports conversations about difference and how you could alter the numbers while maintaining the difference #elemmathchat
On the other hand, if a S doesn't find them easy, or not all of them, then does that S feel stupid? How do we label things from the Ss perspective and acknowledge that each S might have different perspective? #ElemMathChat
I like this one better than mine...I want to take away 40 instead of 38...so because I want to take away more....I need to add 2 back in the end. SOOOOO 76 - 40 is 36...but since I took away 2 toooo many...36 + 2 is 38 ??? Is that right? #elemmathchat
A6: I notice you crossed out 100...could you explain what the 9 and 10 mean? I would want them to discover that 9 tens and 10 ones is 100... #elemmathchat
Fun! Once met father of 7th grader who explained that his son was good at arithmetic because son could have dad's pocket change if he could calculate the total. Watched them play Name that Number with cards for a LONG time at parent teacher conferences. #ElemMathChat
A6: I would say that the student understand the positional system of the numbers, the student know the algorithm of subtraction, however, the student does not use his/her reasoning. maybe just use the algorithm without meaning #elemmathchat
A6: Oof! When I see stuff like this I know I've pushed procedural fluency too early. Kids with a strong conceptual foundation only make this mistake if they're distracted. Let Ss progress at their own pace and you can usually avoid this sort of approach. #elemmathchat
A6: I would probably ask them what they know about 99 and 100, and/or use context to present 100-99 to see if they are actually thinking about it... #ElemMathChat
A6: I’d ask them to plug into a part part whole visual model (like math mountain or number bond or #line)so they can more clearly see the relationship between the numbers. Vertically, they”see” algorithm. Models tend to help@them@see relationships (just one apart)! #ElemMathChat
Q6: "Remind me what the problem is." Or maybe wanting to respect their thinking, "Tell me about what you did." Fingers crossed for the big "A ha!" moment. #ElemMathChat
I love multiplication A7: Although I didn't think of it like compensation... SOOOO, 50 x 25 is 1,250. Take away 2 groups of 25 which is 50...so 1,200. #elemmathchat
A7 I would divide 48 by 4 because I know there are 4 quarters in a dollar. Then I would multiply 12x100 =1200 12 is my favorite number. I know 12 is a factor of 12 and I love doing math with 12! #ElemMathChat
These are the nuggets of gold that I hope Ts are sharing with parents when they ask what they can do at home to help their children with math #elemmathchat
Q9. Many parents & teachers have told me that they feel like compensation is too confusing for their child/students. Thoughts? How would you respond? Supports? #ElemMathChat
A7 I would divide 48 by 4 because I know there are 4 quarters in a dollar. Then I would multiply 12x100 =1200 12 is my favorite number. I know 12 & 4 are factors of 48 so 48 is a friendly number! I love doing math with 12! #ElemMathChat
Instead of focusing only on multiples of 10, focus on the factors that you are usually most comfortable using. It can help you find patterns or friendly numbers within the problem #elemmathchat
A9: it requires a deeper understanding rather than rote memory, and it will benefit them so much more in the long run than following a set of steps ever will! #ElemMathChat
A9 children naturally use compensation from the very beginning but unless we ask students to explain their strategies they will think what they are doing is not the 'right" way. Allowing Ss to compensate in ways that makes sense to them builds great # sense/fluency #ElemMathChat
A9: I think it's important to acknowledge that compensation is A strategy, and it's really useful in certain contexts. If students are allowed to develop meaning of operations in their own way, some students will find it really useful, but it won't be everyone's fav #elemmathchat
I see what you are saying but not related to the division problem? Maybe I just can't see it. Funny I can see it with the 48 x 25...cause I'm taking more groups of 25 and then subtracting groups...hmmmm #elemmathchat
A9: I would respond that compensation help students to get mental calculus, it is necessary students learn some strategies of estimations and through practicing students will gain confident #elemmathchat
Think about it like an algebraic equation. What you do to one part of the problem you have to do something to the other part to keep the value balanced. Are you thinking of additive options or multiplicative? #elemmathchat
A9 children naturally use compensation from the very beginning but unless we ask students to explain their strategies they will think what they are doing is not the 'right" way. Allowing Ss to compensate in ways that makes sense to them builds great # sense/fluency #ElemMathChat
A9: I think they (and some of their children/Ss) might think there are "rules" for how to do it (like everything else in math), instead of actual thinking, and who needs more rules?? I guess I would talk through one with them that might have multiple approaches. #ElemMathChat
A8: So 140 divided by 14 is 10... 126 divided by 14 must be 9...112 divided by 14 must be 8... which means 98 divided by 14 must be 7 which is why Therefore 84/14 is 6. Hmmmm #elemmathchat
A9. Students need to have a solid understanding of numbers in relation to each other to use it successfully. Sometimes I think it has potential to be a sticky issue at times - more so if they've already been using a traditional algorithm first. #elemmathchat
A9:flexibility is a key part of the fluency standard.Flexibility is the transferable skill to problem solving. Seeing simpler problems within larger ones seems like a pretty applicable life/work skill. Computers can do the calculations. We are teaching so much more. #elemmathchat
Q9. Many parents & teachers have told me that they feel like compensation is too confusing for their child/students. Thoughts? How would you respond? Supports? #ElemMathChat
