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#mathchat Wiki
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! guided tour
001 Differentiation
002 'Real' maths
003 Fractions
004 Manipulatives
005 Assessment
006 What technology?
007 Adult curriculum
008 Reflective Learners
009 Engagement
010 Class Time Use
011 Why I hate maths
012 Terminology
013 'Mathphobia'
014 The Nature of Maths
015 Show and Tell
016 Vertical Integration
017 Product to Process
018 Investigation Length
019 Preparation for Work
020 Success in Mathematics
021 Groupwork
022 Effective lessons
023 Impact of ICT
024 Mathematics Websites
028 Why under 16?
2010.07.15 Differentiation
2010.07.19 Differentiation (2)
2010.07.22 'Real' maths
2010.07.26 'Real' maths (2)
2010.07.29 Fractions
2010.08.02 Fractions (2)
2010.08.05 Manipulatives
2010.08.09 Manipulatives (2)
2010.08.12 Assessment
2010.08.16 Assessment (2)
2010.08.19 What tech?
2010.08.23 What tech? (2)
2010.08.26 Adult maths
2010.08.30 Adult maths (2)
2010.09.02 Reflective learner
2010.09.06 Reflective learner 2
2010.09.09 Engagement
2010.09.13 Engagement 2
2010.09.16 Class Time Use
2010.09.20 Class Time Use 2
2010.09.23 Why I hate maths
2010.09.27 Why I hate math 2
2010.09.30 Terminology
2010.10.04 Terminology 2
2010.10.07 'Mathphobia'
2010.10.11 'Mathphobia' (2)
2010.10.14 Nature of Maths
2010.10.18 Nature of Maths (2)
2010.10.21 Show and Tell
2010.10.25 Show and Tell (2)
2010.10.28 Vertical Integration
2010.11.01 Vertical Integratn 2
2010.11.04 Product to Process
2010.11.08 Product to Proc. 2
2010.11.11 Investigation length
2010.11.15 Investigation leng 2
2010.11.18 Prepn for work
2010.11.22 Prepn for work 2
2010.11.25 Success in Maths
2010.12.03 Groupwork
2010.12.06 Groupwork 2
2010.12.10 Effective lessons
2010.12.13 Effective Lesson 2
2010.12.17 Impact of ICT
2010.12.20 Impact of ICT 2
2010.12.24 Maths Websites
2011.01.03 Maths Website 2
2011.01.07 Ideal curriculum
2011.01.10 Ideal curriculum 2
2011.01.14 Short or longterm
2011.01.17 Short or longterm2
2011.01.21 Continuing PD
2011.01.24 Continuing PD 2
2011.01.28 Why under 16?
2011.01.31 Why under 16? (2)
2011.02.04 Which is more fun?
2011.02.11 Blended learning
2011.02.14 Blended learning 2
2011.02.18 Fast tracking
2011.02.21 Fast tracking (2)
2011.02.25 Misconceptions
2011.02.28 Misconceptions 2
2011.03.04 Good Reads
2011.03.07 Good Reads (2)
2011.03.11 How do I  fractions
2011.03.18 How do I  lang
2011.03.21 How do I  lang (2)
2011.03.25 How do I  curric
2011.03.28 How do I  curric 2
2011.04.01 How?  next topic
2011.04.04 How?  nxt topic 2
2011.04.08 How?  Geometry
2011.04.11 How?  Geom 2
2011.04.15 How?Investigation
2011.04.18 How?Investigatn 2
2011.04.22 How? Do vs. learn
2011.04.25 How?Do vs learn 2
2011.04.29 How?Dig deeper
2011.05.02 How?Dig deeper 2
2011.05.06 'Big Ideas'
2011.05.09 'Big Ideas' (2)
2011.05.13 High school skill
2011.05.16 High school skill 2
2011.05.20 Journals
2011.05.23 Journals (2)
2011.05.27 Studentdriven
2011.05.30 Studentdriven (2)
2011.06.03 How?  Maths play
2011.06.06 How?Maths play 2
2011.06.10 Deeper thinking
2011.06.13 Deeper thinking (2)
2011.06.17 How?  Disjointed
2011.06.17 How?  Disjointed 2
2011.06.24 How?  Problems
2011.06.27 How?  Problems 2
2011.07.01 Holiday maths
2011.10.28 Extent of plans
2011.10.31 Extent of plans (2)
2011.11.04 Authentic is..?
2011.11.07 Authentic is..? (2)
Z_1 Thursday raw
Z_2 Monday raw
Z_consolidated
2010.08.02 Fractions (2)
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Topic (followup to Thursday 26th July):
What is the problem with fractions? How can we fix it?
As it happened on
Monday, 2nd August 19:30  21:00 GMT
7:34 pm
ColinTGraham
:
Hello everyone, welcome to the repeat of last week's topic What is the problem with fractions? How can we fix it? #
mathchat
7:34 pm
ColinTGraham
:
#
mathchat
7:35 pm
ColinTGraham
:
If it is your first time, feel free to lurk and jump in when you are ready! Try to focus on one or two conversations only! #
mathchat
7:35 pm
MmeVeilleux
:
For the next 90 minutes my tweets will be related to #
mathchat
7:37 pm
ColinTGraham
:
Maybe we should start by talking about what we mean when we say "fraction" #
mathchat
7:37 pm
MmeVeilleux
:
Who facilitates #
mathchat
? I once saw an episode of the Bernstein Bears where the girl was suffer from an attack of mathphobia b/c of frctns
7:38 pm
MmeVeilleux
:
#
mathchat
parttowhole relationship  is that too simple a definition?
7:40 pm
ColinTGraham
:
@
MmeVeilleux
I think it is just you and I at the moment Ingrid! #
mathchat
7:41 pm
MmeVeilleux
:
RT @
ColinTGraham
#
mathchat
ColinTGraham Part to whole is one definition, but how about decimal numbers, ratio, algebraic...?
7:41 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
Lol! I was thinking the same. I RT'ed bc there was no hashtag. I agree w/your comment.
7:42 pm
MmeVeilleux
:
#
mathchat
Aren't decimals, ratio, algebra under the parttowhole umbrella?
7:44 pm
ColinTGraham
:
@
MmeVeilleux
Yes parttowhole covers everything, but is that what you think of when someone says fraction? #
mathchat
7:45 pm
MmeVeilleux
:
MmeVeilleux @
kelalford
Isn't the = sign for teaching equivalency? Do U mean bc the parts are equivalent to each other? #
mathchat
7:45 pm
jagkise
:
@
ColinTGraham
I like the Chinese emphasis on area, set and length models for fractions to deepen parttowhole #
mathchat
7:46 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
I like to start with geometry and lines and fold lines bc then it's not as 'messy' as cutting apples or sthg.
7:47 pm
ColinTGraham
:
@
MmeVeilleux
For example 2/4 and 27/9 are both fractions symbolically... #
mathchat
7:47 pm
MmeVeilleux
:
#
mathchat
I did not know that the Chinese use length. I wd like to know more about their representations.
7:47 pm
jagkise
:
#
mathchat
I like to start with three students on their feet as a set. Have them describe themselves in fractions. 1/3 wearing jeans, etc.
7:47 pm
ColinTGraham
:
@
jagkise
Do you have any examples of this Chinese approach? #
mathchat
7:48 pm
jagkise
:
@
MmeVeilleux
#
mathchat
Division: If half a length is 1 and 3/4 feet, how long is the whole?
7:48 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
I mostly teach primary so I like to start off first with 1/1 or 2/2 whole numbers into fractions
7:49 pm
jagkise
:
@
ColinTGraham
#
mathchat
Singapore does it too. Area...coloring shapes, working with tiles, etc. Sets...boys out of all students, etc.
7:50 pm
MmeVeilleux
:
@
jagkise
#
mathchat
For reasonableness (estimation), I'd take a strip of paper that length and fold in half then word w/pictures
7:50 pm
jagkise
:
@
ColinTGraham
#
mathchat
They ensure students understand multiple models for fractions. I find US students don't recognize all as fractions
7:51 pm
MmeVeilleux
:
@
jagkise
#
mathchat
I had heard of Singapore math a little and I have read some obscure articles about Vygotskian math w/out numbers
7:52 pm
MmeVeilleux
:
#
mathchat
I sometimes deemphasize numbers to start and give names or letters to pieces so that primary stu are thrown off by numbers
7:52 pm
ColinTGraham
:
One of the 'issues' we identified last Thursday was the idea of equivalent fractions. 2/4 is not seen as 'the same' as 4/8 #
mathchat
7:54 pm
MmeVeilleux
:
#
mathchat
Y do U think this confusion about equiv fractions exists? I think it might be b/c we often privilege only 1 solution method &
7:54 pm
Sundayteatime
:
#
mathchat
I tend to play a lot of equivalent fraction snap on the interactive whiteboard
7:55 pm
MmeVeilleux
:
#
mathchat
con't & it is probably good to start with more expansive definitions. Example of pre and postassmt I like to use in a moment
7:56 pm
ColinTGraham
:
Equivalency maybe confusing if we introduce the symbolic notation too early or use terms like 'reduce' when values don't change #
mathchat
7:56 pm
jagkise
:
@
ColinTGraham
#
mathchat
We have six students stand. Students "see" how 3 of 6 is half of the whole group. Really effective.
7:56 pm
ColinTGraham
:
@
Sundayteatime
What ages are you working with? #
mathchat
7:56 pm
MmeVeilleux
:
@
Sundayteatime
#
mathchat
Is it a timed game? Do U find snap to B effective?
7:57 pm
jagkise
:
#
mathchat
Just finishing research on how students with different #
MBTI
types learn fractions. Statistically significant www.edcoaching.com
7:58 pm
ColinTGraham
:
@
jagkise
Seeing 3 out of 6, though, is not the same as seeing 4 out of 8, which is where some of the confusion may arise #
mathchat
7:58 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
In Grades 2&3, I don't intro terms like 'reduce'; reducing seems to be needed 4efficiency later on
7:58 pm
jagkise
:
#
mathchat
Many students need to work with physical tools like fraction strips to see equivalencies as well as the labels.
7:58 pm
ColinTGraham
:
@
jagkise
What is MBTI for those unfamiliar with it? #
mathchat
7:59 pm
jagkise
:
@
ColinTGraham
#
mathchat
We do groups of 3, 4, 6 as a matter of fact. Then repeat concepts with color tiles and drawings
7:59 pm
MmeVeilleux
:
#
mathchat
One stumbling block in Math is to teach number as usually being discrete objects (3 apples) instead of liquids, lengths,etc Agree?
8:00 pm
jagkise
:
@
ColinTGraham
#
mathchat
#
MBTI
refers to Jungian learning preferences for being energized and how we process information
8:01 pm
jagkise
:
@
MmeVeilleux
#
mathchat
Agree! I even get teachers saying "You can't divide 3 by 2." Well yes you can!!
8:01 pm
ColinTGraham
:
@
MmeVeilleux
So you see some of the problem with fractions being related to countable and 'uncountable' things? #
mathchat
8:02 pm
malcolmbellamy
:
@
ColinTGraham
explore equivalency then use scales..... two smaller cubes is equivalent to one larger #
mathchat
8:02 pm
ColinTGraham
:
Imprecise use of language seems to be a recurrent factor in confusion in mathematics #
mathchat
8:02 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
I think it is inherently confusing to think about 3 apples div by 2 b/c the last one U cut in half whereas it is
8:03 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
more 'natural' (to me) to take 3cm and divide in half or 3 litres and pour into 2 equal amts
8:03 pm
ColinTGraham
:
I use Smarties or M&Ms or packets of coloured sweets... to get away from cutting things! #
mathchat
8:04 pm
MmeVeilleux
:
#
mathchat
I think the whole apple prob is that the first two apples are not cut in halves, only the last 1 which gets a dif name, ie. 1/2
8:04 pm
mthman
:
A lil' boy keeps me from #
mathchat
2day
http://twitpic.com/2b1oxv
8:04 pm
ColinTGraham
:
RT @
Sundayteatime
: @
MmeVeilleux
by reduce do you mean simplify? In uk we tend to use that term. Can still cause confusion though. #
mathchat
8:04 pm
ColinTGraham
:
@
Sundayteatime
Don't forget the hashtag! #
mathchat
8:05 pm
ColinTGraham
:
@
mthman
It's ok Ron, no point in spoiling his summer! #
mathchat
8:05 pm
MmeVeilleux
:
@
Sundayteatime
Yes, I mean simplify. #
mathchat
8:06 pm
Sundayteatime
:
@
ColinTGraham
#
mathchat
oops yes sorry. I'm a first timer.
8:06 pm
MmeVeilleux
:
@
mthman
Adorable and those shapes remind me of a logic game whose name escapes me! argh on tip of my tongue #
mathchat
8:07 pm
ColinTGraham
:
@
Sundayteatime
Yes, I much prefer 'our' term, rather than reduce to lowest terms.... ;) #
mathchat
8:07 pm
POWERORGmath
:
@
ColinTGraham
#
mathchat
The M&Mks get their attention too.
8:07 pm
malcolmbellamy
:
by simplify can we say "see it in a different way"? (visualisation) #
mathchat
8:08 pm
MmeVeilleux
:
#
mathchat
And it occurs to me that simplifying is easier when you U know ur multiples v. well. Requires lots of prior number experience.
8:08 pm
mthman
:
@
ColinTGraham
LOL. He keeps me on my toes! #
mathchat
8:09 pm
jagkise
:
@
malcolmbellamy
#
mathchat
We've said, "Is there another fraction name that describes that amount?"
8:09 pm
POWERORGmath
:
RT @
ColinTGraham
: Imprecise use of language seems to be a recurrent factor in confusion in mathematics #
mathchat
<~Yes at K16 level.
8:09 pm
MmeVeilleux
:
#
mathchat
Simplify does sound more motivating than reduce to the lowest terms!!
8:09 pm
ColinTGraham
:
@
POWERORGmath
The thing I do with sweets/candies is get them to count various fractions... they are not allowed to eat of course! #
mathchat
8:10 pm
mthman
:
@
MmeVeilleux
It started as a simple game of redlight, greenlight...6 pieces of sidewalk chalk later... #
mathchat
8:10 pm
jagkise
:
@
MmeVeilleux
#
mathchat
We provide very accurate fraction strips (which bridge to the most iimportant numberline model) They "see" multiples
8:10 pm
malcolmbellamy
:
@
jagkise
name or picture? #
mathchat
8:10 pm
MmeVeilleux
:
@
jagkise
That is lovely wording! Must use that. #
mathchat
8:10 pm
ColinTGraham
:
@
POWERORGmath
Then I go round and steal a sweet from each group, eat it, and they have to start again.... evil teacher! #
mathchat
8:10 pm
POWERORGmath
:
RT @
jagkise
: @
MmeVeilleux
#
mathchat
Agree! I even get teachers saying "You can't divide 3 by 2." Well yes you can!! <~*frown* but true
8:10 pm
jagkise
:
@
POWERORGmath
#
mathchat
Catch Deborah Ball at any math conference and her talk on teacher knowledge, precision of language
8:11 pm
MmeVeilleux
:
@
mthman
#
mathchat
What a hoot. My competitive husband likes to make racetracks. The kids add parking lots etc so much fun!!!
8:11 pm
jagkise
:
@
malcolmbellamy
#
mathchat
at that stage they would have a picture or manipulative in front of them. Concretepictorialabstract sequence
8:12 pm
ColinTGraham
:
Write another way maybe better? RT @
malcolmbellamy
: by simplify can we say "see it in a different way"? (visualisation) #
mathchat
8:12 pm
POWERORGmath
:
@
jagkise
#
mathchat
Yes. Color tiles are good for tactile & visual learners (esp w/fractions)
8:12 pm
MmeVeilleux
:
@
jagkise
#
mathchat
Do you think the numbers are confusing or helpful for them? Wd numberless #
lines
be useful?
8:12 pm
POWERORGmath
:
RT @
jagkise
: #
mathchat
Just finishing research on how students with different #
MBTI
types learn fractions. (cont)
http://tl.gd/2stg28
8:12 pm
malcolmbellamy
:
@
jagkise
gr8 good practice for everyone #
mathchat
8:13 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
That is really really funny! I will have to try that!!! haha
8:13 pm
ColinTGraham
:
@
POWERORGmath
Give two teachers $3 and tell them to divide it by two... oh no, you can't, no money for you then... They get it! #
mathchat
8:14 pm
jagkise
:
@
MmeVeilleux
#
mathchat
I like the concretepictorialabstract sequence. But the strips are labeled from the start.
8:15 pm
ColinTGraham
:
So let's try another question: What problems do your students have with fractions? #
mathchat
8:15 pm
POWERORGmath
:
RT @
ColinTGraham
: Equivalency maybe confusing if symbolic notation is intro'd too early #
mathchat
8:15 pm
POWERORGmath
:
RT @
ColinTGraham
: Equivalency maybe confusing if we use terms like 'reduce' when values don't change #
mathchat
8:16 pm
ColinTGraham
:
For example: Students understand what fractions are, but cannot manipulate (4rules +x/)...) #
mathchat
8:17 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
My primary stu confuse numerator & denominator & s.times get MAD if we use 6/2
8:17 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
My primary stu confuse numerator & denominator & s.times get MAD if we use 6/2 #
mathchat
8:17 pm
mthman
:
@
MmeVeilleux
The cul de sac is my canvas all year long. We buy large (80 piece) boxes of chalk 23 times per year. #
mathchat
8:18 pm
Cassyt
:
Why the emphasis on simplifying fractions? Don't we force students to focus on the wrong skill? #
mathchat
8:19 pm
mthman
:
@
MmeVeilleux
That's how he learned his alphabet, numbers, & shapes. Who says learning has to be boring?! #
mathchat
8:19 pm
ColinTGraham
:
@
MmeVeilleux
Is this because 6/2 is difficult to name or label... 21/9 twentyone ninths seems ok, but not six halves? #
mathchat
8:19 pm
MmeVeilleux
:
@
mthman
#
mathchat
I should buy shares in sidewalk chalk too. I'd like to get up the nerve to post inspirational quotations in chalk!
8:20 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
Because they tell me the smaller number always has to go on top!
8:20 pm
jagkise
:
@
Cassyt
#
mathchat
I think equivalency, not simplifying, is maybe the learning objective.
8:20 pm
ColinTGraham
:
That is a question for the curriculum designers! Maybe for algebra...? RT @
Cassyt
: Why the emphasis on simplifying fractions? ... #
mathchat
8:21 pm
ColinTGraham
:
@
MmeVeilleux
Ah, so for your students their concept of "fraction" is "less than one", whereas yours is part to whole relationship #
mathchat
8:22 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
Now that you say that, yes, that is exactly it.
8:22 pm
ColinTGraham
:
@
Cassyt
I also think it is another way to 'test' if kids know their times tables... :( #
mathchat
8:26 pm
POWERORGmath
:
@
ColinTGraham
#
mathchat
The money examples always work & reinforce decimal rules too!
8:27 pm
mthman
:
@
MmeVeilleux
Yes, only in our neighborhood the signs are for the REAL cars!! #
mathchat
8:27 pm
POWERORGmath
:
RT @
ColinTGraham
: Another 'trick' is that 1 pack is shared between three or four. There are often leftover sweets... for teacher! #
mathchat
8:28 pm
ColinTGraham
:
@
POWERORGmath
How many people see decimal numbers such as 1.50 as being 'mixed numbers': whole number+decimal fraction though? #
mathchat
8:28 pm
POWERORGmath
:
@
ColinTGraham
Food examples and items in class help students visualize the math #
mathchat
8:28 pm
MmeVeilleux
:
@
mthman
#
mathchat
LOL!! UR inspiring me. Next time, I think I will make crosswalks, bike lanes, etc I think it's time2get more elaborate!!
8:29 pm
jagkise
:
@
POWERORGmath
#
mathchat
U of Mich Deborah Ball's NCSM talk Learning to do mathematics as a teacher. at
http://tinyurl.com/2bq7n3o
8:29 pm
ColinTGraham
:
@
mthman
What's your son's favourite fraction Ron? #
mathchat
8:30 pm
POWERORGmath
:
@
jagkise
#
mathchat
U of Mich Deborah Ball's NCSM talk Learning 2 do mathematics as a teacher. at
http://tinyurl.com/2bq7n3o
<~Thx
8:30 pm
ColinTGraham
:
@
POWERORGmath
Scaling recipes can work very well too, especially if you have cups and spoons as well as weights #
mathchat
8:30 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
Mixed numbers has always confused me as have all the terms: natural #
s
, real #
s
. I can't remember which is which.
8:31 pm
mthman
:
@
MmeVeilleux
How can you create the illusion of a speed bump w/sidewalk chalk? #
mathchat
8:31 pm
jagkise
:
@
ColinTGraham
#
mathchat
Yes but if "strip families" are in different colors numbers don't seem dstracting. For ex
http://tinyurl.com/2v4zk2t
8:31 pm
POWERORGmath
:
@
jagkise
#
mathchat
We need more practice with teaching fractions at the preservice level!
8:31 pm
MmeVeilleux
:
#
mathchat
Do you think it is acceptable for me to say numbers when I mean mixed numbers? eg. in name #
s
btw 1 & 2 Thoughts?
8:32 pm
ColinTGraham
:
@
MmeVeilleux
Yes, terminology can be a big problem when all you students see is a number... 3/2 1.5 and 3:2 aren't seen as related #
mathchat
8:32 pm
jagkise
:
@
POWERORGmath
#
mathchat
I teach fractions to teachers any chance I get!
8:32 pm
MmeVeilleux
:
@
mthman
Now that is going to require some shading. However, what about using pieces of leftover wood as miniramps? #
mathchat
8:32 pm
mthman
:
@
ColinTGraham
1 1/2  His and half of everyone else's...! #
mathchat
8:32 pm
POWERORGmath
:
@
ColinTGraham
#
mathchat
I do. Knowing place value, decimal names help with converting to fractions
8:34 pm
POWERORGmath
:
RT @
ColinTGraham
: @
POWERORGmath
Scaling recipes can work very well too, especially if you have cups and spoons as well as weights #
mathchat
8:34 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
So would you call 1.5 a mixed number? Shd I rephrase my prob to What mixed #
s
are btw 1&2?
8:34 pm
jagkise
:
#
mathchat
For summary of student learning need differences see "Why are These Students 2 Years Behind" at
http://tinyurl.com/3xbbb42
8:34 pm
MmeVeilleux
:
#
mathchat
Most disastrous fractions lesson I did was in Gr5/6 & require Ss to make circles divided in 100 sections to represent %
8:35 pm
ColinTGraham
:
@
jagkise
Similar concept to cuisenaire rods, or using Lego as I do! #
mathchat
8:35 pm
MmeVeilleux
:
#
mathchat
Eventually we all seemed to understand % but I'm sure there is an easier way, eg. sliding % into daily convo more often etc
8:36 pm
ColinTGraham
:
@
MmeVeilleux
I think 'names' for things should only be introduced when the name has a clear function or purpose #
mathchat
8:36 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
So do you use Cuisenaire rods a lot? I have tried but w/out much success.
8:37 pm
POWERORGmath
:
@
MmeVeilleux
instead of having looking at fractions as how many pieces, you see full + partial packs #
mathchat
8:37 pm
MmeVeilleux
:
#
mathchat
Another essential concept in fractions seems to be: What is 1? b/c "1" can change from context2context
8:37 pm
ColinTGraham
:
@
MmeVeilleux
Cuisenaire rods cannot really be 'introduced' but for reinforcing concepts, I find them useful. Lego seems easier! #
mathchat
8:38 pm
mthman
:
@
MmeVeilleux
If I could pull off the speed bump just once...maybe, just maybe...ya think? #
mathchat
8:38 pm
MmeVeilleux
:
@
POWERORGmath
#
mathchat
That is gd language: full & partial packs. I like that.
8:38 pm
ColinTGraham
:
@
POWERORGmath
Yes and you can put three packs together and then do a sharing activity or use average pack size as the unit #
mathchat
8:39 pm
MmeVeilleux
:
@
mthman
#
mathchat
Go for it Michaelangelo!
8:40 pm
ColinTGraham
:
@
MmeVeilleux
I used the idea of sharing out packs when we talked about Egyptian fractions, were there was a 'little bit' ignored #
mathchat
8:40 pm
jagkise
:
#
mathchat
We found that Singapore Model Drawing, combined with fraction strips, was huge in helping students understand mixed numbers
8:40 pm
POWERORGmath
:
RT @
jagkise
: @
POWERORGmath
#
mathchat
I teach fractions to teachers any chance I get! «Awesome. We need many ways to C the math! :)
8:41 pm
ColinTGraham
:
@
jagkise
Do you have an online reference for the Singapore model... for the archive! #
mathchat
8:41 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
Q: To clarify, are we talking about packs as 1 full pack = 1 or 2/2? Q2: What R Egyptian fractions?
8:41 pm
POWERORGmath
:
RT @
jagkise
: #
mathchat
student learning need differences see "Why are These Students 2 Years Behind" at
http://tinyurl.com/3xbbb42
8:42 pm
mthman
:
@
MmeVeilleux
Okay...this is going to take some planning! Any tips? #
mathchat
8:43 pm
ColinTGraham
:
Egyptians expressed fractions as sums of parts but numerator was always 1, except for 'special' fractions #
mathchat
8:43 pm
MmeVeilleux
:
#
mathchat
Has everyone here read the Teaching Gap by Stigler & Hiebert? Explains Y Ss are behind. It changed my math teaching.
8:43 pm
ColinTGraham
:
@
MmeVeilleux
For example: 7/8 = 1/2 + 1/4 + 1/8 #
mathchat
8:43 pm
POWERORGmath
:
@
MmeVeilleux
#
mathchat
I don't emphasize proportion %. Can b confusing. But moving dec & chgng to dec equiv helps!
8:44 pm
ColinTGraham
:
@
POWERORGmath
A big confusion with % is that increase by 200% = multiply by 3... EEK! #
mathchat
8:44 pm
mthman
:
@
MmeVeilleux
No, but I'll add it to my list! Thx. #
mathchat
8:45 pm
POWERORGmath
:
@
MmeVeilleux
#
mathchat
Partial & full lang is familiar; helps trans to formal terms; easy to connect 2 prior knowldge
8:45 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
The numerator was always 1??? Now that I visualize it, that makes sense! That is sooo awesome!!!
8:45 pm
POWERORGmath
:
RT @
ColinTGraham
: @
POWERORGmath
Yes & U cn put 3 packs tgthr & then do a sharing activity or use average pak size as the unit #
mathchat
8:46 pm
MmeVeilleux
:
@
ColinTGraham
The Egyptian math fractions made my day. #
mathchat
8:47 pm
ColinTGraham
:
Personally, I think early fractional notation was developed by/for engineers, dividing things until 'error' was negligible... #
mathchat
8:47 pm
POWERORGmath
:
@
jagkise
#
mathchat
Haven't used Singamore math but models always make 4 meaningful connections. Esp when studs draw model
8:48 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
I had also not thought about 200%increase as X3. I had never thought about that B4.
8:48 pm
POWERORGmath
:
@
ColinTGraham
#
mathchat
See www.greatsource.com for Singapore Math info
8:48 pm
Cassyt
:
Crikey! 1 phone call and suddenly I can't keep up! #
mathchat
8:49 pm
jagkise
:
@
POWERORGmath
#
mathchat
Singapore model drawing a powerful heuristic through algebra. "Why wasn't I taught this" is common reaction
8:49 pm
MmeVeilleux
:
@
Cassyt
#
mathchat
LOL!!
8:49 pm
ColinTGraham
:
I have also used tangrams and origami for fractions. Origami can be very useful for geometric 'proof', too. #
mathchat
8:50 pm
jagkise
:
RT @
ColinTGraham
: I have also used tangrams and origami for fractions. Origami can be very useful for geometric 'proof', too. #
mathchat
8:50 pm
Cassyt
:
I train teachers on Singapore Math  model drawing can be powerful. @
POWERORGmath
: #
mathchat
8:50 pm
POWERORGmath
:
@
MmeVeilleux
#
mathchat
full pkg=3/3 All parts present out of total original in pkg to make 1 whole.
8:50 pm
ColinTGraham
:
@
Cassyt
Don't worry, the archive will go online after about 30 minutes and the discussion often continues through the week! #
mathchat
8:51 pm
POWERORGmath
:
RT @
ColinTGraham
: Egyptians expressed fractions as sums of parts but numerator was always 1, except for 'special' fractions #
mathchat
8:51 pm
MmeVeilleux
:
#
mathchat
I'm making my own archive by favoriting thgs I really want2 remember.
8:52 pm
Cassyt
:
That's my favorite moment in a training! @
jagkise
: @
POWERORGmath
#
mathchat
Singapore model drawingTeachers ask"Why wasn't I taught this?"
8:53 pm
Cassyt
:
Great idea  I'll need to check out the archive this time. RT @
MmeVeilleux
: #
mathchat
I'm favoriting thgs I really want2 remember.
8:53 pm
jagkise
:
@
Cassyt
#
mathchat
do you have the Singapore Min of Ed's most recent book on model drawing? Algebra great
http://tinyurl.com/jmbmf
8:53 pm
MmeVeilleux
:
#
mathchat
I understand Xfractions. Eg: I need 2/5 of 3/4 or sthg (licorice  a personal fave) but I don't get dividing fractions.
8:54 pm
POWERORGmath
:
@
MmeVeilleux
Haven't read that. Thanks for sharing. #
mathchat
8:54 pm
MmeVeilleux
:
#
mathchat
I may be beyond help for dividing fractions as I've asking this Q many X in the last decade. It could be me hitting the wall.
8:54 pm
Cassyt
:
@
jagkise
I've got every book, from the Ministry's to Ban Har Yeap's. #
mathchat
8:55 pm
MmeVeilleux
:
@
jagkise
Must get my hands on some Singapore Math bks. Have heard about them but have not seen them. #
mathchat
8:55 pm
jagkise
:
@
MmeVeilleux
#
mathchat
Read Ma's "Knowing and Teaching Mathematics" to see needs in division of fractions.
8:56 pm
ColinTGraham
:
@
MmeVeilleux
I demo the dividing of fractions buy having say 20 lego bricks, which I give to 2 groups of 2 (8 +12) then they share #
mathchat
8:57 pm
MmeVeilleux
:
@
jagkise
#
mathchat
Thx. Is Ma the author? Also is it an article or bk? TY so much. I certainly will look it up.
8:57 pm
ColinTGraham
:
@
MmeVeilleux
so one group has 12/20, another has 8/20 which they divide into two parts, not necessarily 1/2 each though #
mathchat
8:57 pm
ColinTGraham
:
Did I say buy and not by...? Money on the mind! #
mathchat
8:59 pm
POWERORGmath
:
@
jagkise
#
mathchat
So sad the number of teacher prep institutions that only show limited ways of solving problems. Failing kids/teachers
8:59 pm
ColinTGraham
:
In the last couple of minutes... any 'burning' questions or thoughts about fractions? #
mathchat
8:59 pm
jagkise
:
@
MmeVeilleux
#
mathchat
A book. Ma is author
http://tinyurl.com/29f9ubu
Scholarly but important
8:59 pm
Cassyt
:
Read Ma and Wu. RT @
jagkise
@
MmeVeilleux
#
mathchat
Read Ma's "Knowing and Teaching Mathematics"
8:59 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
I'm flabbergasted. That makes sense! I have been on this quest for a decade. I need a moment!!! sharing lego...
8:59 pm
POWERORGmath
:
RT @
Cassyt
: I train teachers on Singapore Math  model drawing can be powerful. @
POWERORGmath
: #
mathchat
<Awesome.
9:00 pm
jagkise
:
@
POWERORGmath
#
mathchat
We first need to adapt the truth that everyone can learn math. Too many teachers math phobic
9:00 pm
ColinTGraham
:
@
MmeVeilleux
@
tcash
uses an eggbox and a piece of string to divide holes... #
mathchat
9:01 pm
ColinTGraham
:
Another topic! RT @
jagkise
: @
POWERORGmath
We 1st need to adapt the truth that everyone can learn math. Too many teachers phobic #
mathchat
9:01 pm
POWERORGmath
:
@
Cassyt
#
mathchat
Yes. That's a gr8 intro to open their minds! "Why wasn't I taught this?"
9:01 pm
MmeVeilleux
:
@
jagkise
#
mathchat
TY for the link. I will get my hands on it. Scholarly is good!
9:02 pm
jagkise
:
@
ColinTGraham
#
mathchat
Start with Gladwell's great chapter in Outliers on cultural attitudes toward math. Powerful with teachers.
9:02 pm
ColinTGraham
:
OK thanks everyone for another stimulating chat! Follow @
mathchat
for updates. And don't forget to vote for the next topic! #
mathchat
9:03 pm
iDianne2
:
RT @
ColinTGraham
: Another topic! RT @
jagkise
: @
POWERORGmath
We 1st need to adapt the truth that everyone can learn math. Too many teachers phobic #
mathchat
9:03 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
I like the eggbox & string idea too. So the string cuts each box in half by threading thru lengthwise?
9:04 pm
MmeVeilleux
:
#
mathchat
TY for a gr8 conversation. I don't know if others lrned but I am good at asking questions & I lrned a lot. TY for yr insights!!!!
9:04 pm
ColinTGraham
:
@
MmeVeilleux
Yes and you can use it widthwise too to give 1/4 holes... #
mathchat
9:05 pm
ColinTGraham
:
Vote for the next topic here:
http://mathschat.wikispaces.com/Current
+Poll Catch you all next time! #
mathchat
9:05 pm
MmeVeilleux
:
@
ColinTGraham
#
mathchat
Gr8. Just wanting to confirm that I understood correctly.
9:07 pm
POWERORGmath
:
@
MmeVeilleux
#
mathchat
Multiple by recip of 2nd frac. "Keep 1st frac, Change Oper to mult, Flip 2nd frac"
9:10 pm
jagkise
:
#
mathchat
Thanks everyone for new ideas. Fractions are so key to algebra that we really can't overdo chatting about the topic!!
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As it happened on Monday, 2nd August 19:30  21:00 GMT