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!
Mark
Instructional Coach
Niagara Canada
My favourite is sitting outside enjoying a juicy burger and a cold beer this time of year
#elemmathchat
You are never too late for #ElemMathChat because there is always the @wakelet ! Great to have you Will! Excellent pedagogy and PLCs have no grade constraints! Super happy you are here!
Originally from NYC now living in MD. I am an elementary school resource teacher. My favorite food is any seafood. I love crabs, shrimp and lobster #elemmathchat
Mariana checking in! I’m a PK-4 math coach in Pasadena, Tx. My fave fall food combo is chili and corn bread... even though it’s still 95 degrees here in the gulf! 😜 #ElemMathChat
A1 Ooh, I like this question. I think sts should be able to count by any multiple of 10 as a unit, including counting by 0.1 and 0.01. They should also then be able to use these units of 10 in their problem solving. #elemmathchat
A1: I think it means students see the relationships between the place values. Did this today in 2nd & 5th. Like 2.38 is 23 tenths and 8 hundredths or 2 ones 3 tenths and 8 hundredths. Knowing there are 23 tenths in 2.3 because 10 tenths make a whole. That was 5th. #elemmathchat
A1 to understand, you can model (base-10 blocks, pictures, words) diff numbers, explain how they relate to the other, make sense of diff types of questions with a range of numbers -
in a variety of contexts...
#elemmathchat
A1: Ss should use concrete and pictorial models to represent numbers. Different tools as place value chart can also help students organize the numbers in order to be able to represent them accurately. #ElemMathChat
If students are expected to understand decimal numbers like tenths , and big numbers up to 10,000, I'd hope they would be able to explain how many of one digit equals another.
#elemmathchat
A1: To truly understand something Ss need to be able to be flexible with their thinking and able to make connections (an unfamiliar representation to an idea.) A1b: understanding place value might mean decomposing numbers to perform operations or building models. #elemmathchat
A1 The ability to use mental math - jump and split strategies to solve mult-idigit addition and subtraction problems. Not being tied to the standard algorithm shows a conceptual understanding of place value. #elemmathchat
A1 a&b Ss will need to understand the dynamics of #, distance, regrouping, also that #s are not always whole I think of unit cubes, empty number lines, money, estimation....... #ElemMathChat
A1: Students should be able to identify relationships between the places, represent numbers using various tools, identify the value of a digit based on its place in the number #elemmathchat
A1. I want students to recognize the relationship between the placement of the digits: e.g. one place value to the left is 10 times greater. #elemmathchat
A1: patterns in the numbers was huge for my 5th graders. Each period has ones, tens, hundreds. They also need to be able to decompose numbers - 718 is the traditional 700 + 10 + 8 but it’s also 71 tens + 8 or 718 ones, etc. #elemmathchat
A1: patterns in the numbers was huge for my 5th graders. Each period has ones, tens, hundreds. They also need to be able to decompose numbers - 718 is the traditional 700 + 10 + 8 but it’s also 71 tens + 8 or 718 ones, etc. #elemmathchat
Many students can put numbers on a place value chart or order numbers... but they lack an understanding of the magnitude of numbers.
Seems to me that many students aren't really UNDERSTANDING how big a big number is unless they are representing them somehow!
#elemmathchat
A1"Understand" means students are apply and explain their thinking. I ask Ss all the time to explain their thinking using math vocabulary and details. #elemmathchat
Yes agreed - Kids need lots and lots of experiences with those "big numbers" numbers...building them, drawing them, reorganizing numbers, and thinking about relationships. #elemmathchat
I love the visual that the ones place is a cube, tens place is a rod with 10 cubes, hundred is a flat with 10 rods, and then the 1,000 is back to being a cube made up of 10 flats stacked. Helps students visualize what the ones place looks like in each period. #elemmathchat
Katrina, I T MS math students with disabilities and they often lack understanding of magnitude of number. I find empty number lines used with activities such as @Estimation180 are a powerful way to build this understanding. @MathProjects also excellent #ElemMathChat
In reply to
@katrina_cade, @MarkChubb3, @Estimation180, @MathProjects
So what’s the main difference between “relational understanding” and sts using “relational thinking”? I’m confused. They seem to be using the term “relational” in very different ways? #ElemMathChat
Not necessarily. Procedures are important and can be understood relationally.
Relational understanding is about connections between concepts and experiences....
#elemmathchat
A2: Standard algorithm for each operations, dividing fractions, comparing fractions (butterfly). I know there are a bunch more, but these are just what i can think of off the top of my head. #elemmathchat
A2: U.S. traditional multiplication and division with whole numbers and decimals, multiplying fractions, dividing fractions, generating equivalent fractions are the first of many that come to mind #elemmathchat
YES! In addition to What do you #NoticeWonder my math teacher toolbox now includes, what relationships do you notice, & what do those relationships tell you? My Ss are able to strategize & problem solve in powerful ways because they consider these! #ElemMathChat
Both are about relationships.
Relationships between different concepts... between different representations... between different procedures...
the more connections the more solid the understanding.
#elemmathchat
A2. Multiplication and division of fractions, sometimes all standard algorithms if introduced that way, rounding, multiplying by powers of ten (just "add" zeros Ugh!). #elemmathchat
A2a Regrouping the standard algorithm is definitely something Ss use step by step procedures without understanding. I have shared strategies like using the expanded form and decomposing. #elemmathchat
A2: "Flipping the second and multiplying" for dividing fractions, "negative times a negative is a positive," two negatives become a positive when subtracting, needing to move the decimal when dividing decimals. #elemmathchat
Rounding! Rounding chants- that seem to work-until they don’t! Esp when #s get “bumped” to the next PV! Ex. 398 rounded to the nearest 10- Ss don’t know what to do when they can’t add a one to the 9 in the tens place because the 8 ones tells them to add 1... #ElemMathChat
A2: I feel like anything can be taught procedurally. I’m finding that some Ss come to me building models (arrays, bar models, etc.) w/o inderstanding. Used to be algorithms and the nine trick for multiplication. Now, anything can be memorized. #elemmathchat
Relational understanding is about the connections we make between concepts and procedures... between different areas of mathematics... between different representations...
#elemmathchat
As a MS teacher I have Ss who have multiplication facts memorized, w/ no conceptual understanding of multiplication/division. I remember being that same kid! I was also that SAME kid when + - x and dividing fractions! I didn't conceptually understand til college! #ElemMathChat
A3 with 1/2 - 1/12, I first thought about a clock
Half the clock (6 hours) - 1/12 of the clock (1 hour) = 5 hours so 5/12
and with an array - I'm imagining a 3x4, then start with 1/2 of it - 6, then take away one of the original 12... left with 5 out of 12.
#elemmathchat
I can't believe the connections my Ss are able to make, the generalizations they discover when consider relationships. They think of traits, factors, multiples, odd, even, keeping rations balanced.\ It is AMAZEBALLS! I LOVE that I get to have my Ss for 3 years! #ElemMathChat
A3: I want to show 1/2 - 1/12 using Cuisenaire rods, fraction tiles and an empty number line. Hmm, I might want to try it using a calendar
#elemmathchat
A3: 1/2 - 1/12 is the same as 6/12 - 1/12, which is 5/12. I know that 6/12 = 1/2 because I've noticed the pattern that in fractions equivalent to 1/2, the numerator is half the denominator. (1/2) #elemmathchat
A3: Also I can solve 1/2 - 1/12 by thinking of a clock. 1/2 hour is 30 minutes. 1/12 hour is 5 minutes. 30 minutes - 5 minutes = 25 minutes. When the minute hand points to 5 it is 25 minutes past the hour. There are 12 numbers on the clock 25 minutes past is 5/12 #elemmathchat
Here’s a video I made for the teachers at my previous campus demonstrating how to bridge from concrete to pictorial models to help with division. #ElemMathChat 314 ÷ 2 https://t.co/MG9ARBpXtI via @YouTube
Crocodiles have no relation to numbers. This is a very common "Instrumental" way of understanding the greater than symbol.
Shouldn't we see that it is actually just an equal symbol tilted like a balance scale?
It's all about relationships!!!
#elemmathchat
A3: I really like 3/4 + 4/5 + 5/6 because it’s less than 3 wholes for sure because all the fractions are less than 1. Specifically one less than the whole. Hmmm. So 3 wholes - 1/4 is 2 3/4. Then 2 3/4 - 1/6 hmmm. Gosh. Let me keep thinking. #elemmathchat
A3
Being able to solve a problem with a trick... or even with a "conceptual" tool like a number line isn't enough...
We want Ss to be making connections between different representations!
#elemmathchat
4/5 +3/4+5/6 =
I would share I know it will be larger than 1 whole because all three fractions are almost a whole. Then I would find the LCM (20) using multiples for 4/5 and 3/4. Then (4/5x4) +(3/4x5) =31/20 Then 31/20+50/60 =81/60 Then simplify to 1 7/10. #elemmathchat
A3: hmmm... making me think with this one. I would try a numberline with 1/2 - 1/12. I would break the number line from 0-1 into twelve sections and mark 1/2 at 6/12ths. Then I would go back one 12th to be on 5/12ths. #elemmathchat
Love the clock model! 1/2. - 1/12 30 min.- 5 min = 25min/ 60 or 5/12.
Pattern blocks: whole = 2yellow hexagons covered by twelve green triangles. Half is six green triangles. - 1/12(1 green triangle) = 5/12 (5 green triangles) #elemmathchat
A3: Build 1/2 - 1/12 with cuisenaire rods. I would build the wall, and then build 1/2 and replace it with the twelve white unit pieces (12ths) and take one of them away to be left with 5/12ths.
#elemmathchat
Sometimes my Ss can't draw a visual representation, but they can describe a way for me or someone else to draw it. Visual processing, fine motor skills, and such are sometimes barriers that can be removed with productive discourse. #ElemMathChat
A3) I definitely have them start by estimating the closest number they feel safe submitting. Maybe that’s in whole numbers, maybe it’s even finer. #elemmathchat
I started doing this one the exact same way... then wanted some paper and pencil to do it on a number line to keep working backwards with it. LOVE this idea. #elemmathchat
A4. Want Ss to be able to compare fractions fluently
1. with common denominators
2. with common numerators
3. Using benchmark fractions
4. with 1 unit fraction away from one whole #elemmathchat
A4 I ask my students how they can create a balanced relationship between fractions so they can compare them, calculate with them and explore them. Are there other ways to represent a fraction (decimals, percents, ratios) that will make them friendlier to play with? #ElemMathChat
A4
- Model/represent an operation
- Create samples of operations that meet specific criteria (i.e,. 3 fractions added together is almost 2...)
- Solve problems knowing which numbers to use, which operations...
- Create a problem situation given a number sentence
#elemmathchat
A4) I think estimating a result based on what they see before they start computing. Rewriting an expression with equivalent substitutions they like more, and why they prefer them. #elemmathchat
A4: Listening/noticing, comparing, contrasting, connecting. I want kids to notice why the work of others works and how it is similar/different than their work. #elemmathchat
Yes, manipulatives, technology, conversations, partner work, Anything and everything that promotes conceptual understanding, joint construction of knowledge, the Math action processes and problem solving! I am game! #ElemMathChat
A4: they should be using what they know about unit fractions, composing, decomposing, looking for relationships and making connections to benchmark fractions. #ElemMathChat
My brain does not go there! But, benchmark fractions took me a while to internalize, so clock thinking is next on my list to practice and get more comfortable with! 🤔 #ElemMathChat
Yes! We can't forget how important it is for students to really understand that fractions can be composed and decomposed (pay attention to unit fractions here)
#elemmathchat
A5: Division and subtraction. The relationship seems obvious but students will have a hard time with 1 1/4 ÷ 1/4 when it's easy to compute when we think of repeated subtraction. #elemmathchat
A5 My 2nd graders are starting to understand how skip counting and place value are connected. We are using 1,000 charts, place value charts, and number lines. They could not believe how many tools could be used to figure out the pattern. #elemmathchat
I went on strike in 3rd grade! I had never had to memorize information in math and I thought that was a waste of my time! I eventually caved so I could get the icecream sundae. It did not hurt me in the long run, but I saw math as memorization work for many years! #ElemMathChat
I designed my iPad app 'Show it...Draw it!' To help Ss see the links between their concrete work, visual reps and abstract thinking. It helps interconnect thinking. #ElemMathChat
Last question...
How are you continuing to develop a relational understanding of the concepts your students are learning? This one seems really important doesn't it!?!
#elemmathchat
A5: Division and fractions. Kids often have "numerator is on the top, denominator on the bottom" drilled into them without understanding the relationship between the two, or how division is related to the fraction. It can take a while for that aha! moment. #elemmathchat
Wow! Check out some of the instructional strategies & activities that we explored during our 09.19.18 after-school PD session! All students are math language learners! Mathematicians learn & grow together! #PISDMathChat#PISDELL#PISDMSMath
When I first got my Ss they did not get the connection between multiplication and division. They don't always connect fractions, decimals and percents, but are getting there! #ElemMathChat
A8: I read a lot. I follow the right people on Twitter. I DO math. I hang out with other geeky (hear the affection) math teachers who love to learn. @linday528@kristenjmb#elemmathchat
Last question...
How are you continuing to develop a relational understanding of the concepts your students are learning? This one seems really important doesn't it!?!
#elemmathchat
A8 I do ALL of my Ss math work in as many ways as I can. I often problem solve along side them even after that! When we talk they will say things that make me go OHHHHHHH and I see the math in a whole new light w/ more connections! We are all teachers & students! #ElemMathChat
