marianne aamodt
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My Grade 7/8 class responded with a huge amount of notice and wonders! I think I better limit them to one a piece next time as it took waaaaayyyyy too long to do this!
It took us 2 one hour periods to work through “Day 1″ (includes a 10 min Math Fight”)
I discovered a very large range of abilities. Moving forward, how does one accommodate the child who is still counting manips one at a time to the student who is ready to run with ratio tables? I have on student who is really fighting against putting down his thinking. Which I expected! Such an interesting process.

Well…. I ordered some wipebooks – thinking that kids can still collaborate if they each have their own marker to add to the thinking.
In SK, masks are being mandated from gr. 4 and up (in hallways or where 2 m distancing is not possible – ha – classrooms??) so that may make collaborating safer as well. Teachers move from room to room not kids.For my small groups of 3 or 4 kids who come to my room (not a homeroom), I think it’ll be hand sanitizer on the way in and on the way out plus we wear masks.
I also want to become more knowledgeable re Desmos. Maybe my gr. 7/8 Math class can do their collaboration on their cells…
Having class outdoors would be ok except SK winters are very brutal at times! That won’t work!!
Any suggestions would be appreciated!

Thank you so much!
Biggest takeaway….that one question to solve can evolve from the most basic Math concept to one of high level Math thinking!
After I take a couple of weeks off for summer holidays, I will create a year plan where Sparking Curiosity, Fueling Sense Making and Making Math Moments that Matter! I also want to spiral the math course. So… I will be accessing the Academy a great deal in the near future! Thanks, again. Enjoyed the course!

Lesson 5 and 6 really started to bring in new thinking for me.
Lesson 7 – so much to wrap my head around! Never learned Math this way before and how everything is linked together.
Lesson 8 was also an eyeopener. Math makes so much more sense now!
How did I ever teach Math before!! I know – algorithms. Here is how you do it. Such a disservice to my students. I wish I knew then what I know now!!
Thank you for sharing your knowledge and all the tools that you (and others) have created. And for putting it all together in a way that teachers can easily put into practice. Amazing work!

My number sense has definitely grown. There have been some “aha” moments and Math is Making More Sense than it did before!

What resonates with me is that one question can cover so many different curriculum objectives – depending on the grade level.
A ratio table finally makes sense to me. I never understood the point of teaching kids the “input / output” machine in the textbook. What was the purpose?? Now I see the reasoning and will hopefully be able to show my students the value of them, too. (Not by assigning #1 – 10 odds in the textbook!!)
I am wondering how long it will take for my students to learn how to use double number lines, and then move into ratio tables. I am quite sure they are unfamiliar with most of this.

A human walks at about 5 km/h. What is this speed in metres per second?
5 km = 5000 m 1 hour = 3600 sec
The ratio is 5000:3600 Divide each by 100
50:36 Divide each by half
25:18
Constant of proportionality is:
The speed is 25/18ths metres per second
Wow. I think I am beginning to “get it”!
It feels weird to think in terms of fractions instead of decimals. We are so used to using calculators. I think it is going to be a challenge to get kids used to NOT using them ALL THE TIME!

A great reminder of the two types of ratio and how to identify each. I am becoming more familiar with the mathematical language that I had never heard of before.
still wondering how I am going to put this altogether to create a spiraling math year plan!

This lesson has really made me realize how one simple problem can lead to higher level math skills. It has opened my eyes to possibilities that I was not aware of before. Thank you!
My Math classes will be SOOOO different this upcoming year. Love it!

I would use it for relationships in patterns (grade 7) moving on up to linear relations and graphing them in gr. 8.
I have a hard time envisioning what middle years kids will come up with as solutions.There is one student who will still be at the repeated addition stage. Others may be ready to graph and create algebraic equations. Because my own number sense is not that great (but getting better thanks to this course!) I don’t know what to say. I would definitely ask them to use higher numbers. Such as: how many scoops are needed for the entire class?
I am still wondering when you teach algebraic equations. Does that come into play during the consolidation area of a hero’s journey?

In my gr. 7 and 8 combined classroom, there will be one or two students who will benefit from, basically, the type of concrete work that is shown in the video of gr. 1s. Others will be ready to tackle higher numbers using more abstract thinking such as a table of values. Many will be somewhere in between. The diversity is quite extreme in this group. I love how one task can be differentiated for individual students!

Milk costs $4.50 for 4 L. What is the unit price?
COST  Litres
$4.50 X 1/4  4 X 1/4

$1.13  1
Ratio as a quotient:
$4.50 divided by 4 L of milk
Ratio as a rate:
Milk is $1.13 per litre of milk
I have to get used to thinking of multiplying by a fraction instead of dividing. I’m curious as to why this is easier for kids. Don’t they still have to think about division to “do the math”?
I am interested in moving farther and seeing how to do this algebraically. I’ve always found the input/output “machines” (table of values) that are found in MMS texts starting about gr. 4 (?) to be very confusing – not only for kids! I wonder: how does this turn into graphing linear relations? Looking forward to finding out!
 This reply was modified 2 years, 4 months ago by marianne aamodt. Reason: formatting of chart did not work when posted

Well. For some reason, the last post only put up the image, not the notes I wrote. My reflection is that the problem seems to have two parts to it. First in order to figure out the width of suitcase B, I had to think of it as a “table of values” chart where I worked out the multiplicative comparison of the the heights of A and B. Then I completed the problem by thinking of that ratio as a composed unit.
Is this the right way (one of many) to do it?
It appears that multiplicative comparisons and composed units are very closely related.
My wondering is how to draw the pictures out! I also did another problem, included in the last post which did not upload properly. It had large numbers. That can be very time consuming! Don’t I sound like a lazy kid??

OK. I just watched part of the next lesson. Apparently my definitions in my last comment are wrong!! Obviously, I did not know what multiplicative comparison and a composed unit are!

I have never thought of a multiplicative comparison as a ratio before.
At this point, I am thinking that a multiplicative comparison is about “how many” whereas a ratio that compares the size of the trucks, for instance, is about “how big or small”.

There was a good reminder to always follow your curriculum guide closely. Not everything is in the textbook.

SK Grade 8 Math
Multiplying integers:
I had a peek at
http://mathisvisual.com/series/integermultiplication/
First I would have students play around with coloured tiles which represent negative and positive integers. (review addition/subtraction of integers) Then I would show the video, but stop during viewing so discussion could begin about how they would group/unitize the tiles. After discussion, we’d watch the solution. Over the course of a few lessons, we’d develop the rules to multiply integers.
I also like how the number line is included in this video as another way to visualize the process. Teaching multiplication with number lines was something I always found difficult. The above video makes so much sense!

Absolute thinking is addition and subtraction.
Mulitplicative thinking is when you compare an attribute such as volume of two objects.
If kids are thinking multiplicatively, you’d notice them perhaps using repeated addition or subtraction. Maybe they’d be using the words “times”, “groups of”, “sharing”” or ” divided by”.
I, too, would like to find an investment with such great interest!

When teaching elementary math, I’d never really thought of using a balance scale to represent equations. Makes total sense. I have used that analogy when teaching middle years but , thinking back, definitely not enough. I was always in a rush to get to the algorithm.
Briggs” Grandpa gave him some money to buy ice cream. He bought an ice cream cone for $3.50. He got $1.50 in change. How much money did his Grandpa give him?
Subtraction:
X – 3.50 = 1.50
 This reply was modified 2 years, 4 months ago by marianne aamodt.

There are 4 geese swimming in a slough. 6 more come to swim. How many geese are there altogether?
The student might describe the comparison by counting out a set of 4 counters and a set of 6 counters. Then he/she might place the counters on a ten frame and notice that 5 and 5 make 10. Making friendly numbers/compensation.

There are 4 geese swimming in a slough. 6 more come to swim. How many geese are there altogether?
For a student who is counting, they would probably take 4 “counters” and put another 6 with the first 4. Then they would count 1,2, 3..etc up to 10

When giving a child 2 differing quantities, adults often seem to ask, “Which is more?” So it’s not surprising that kids use the word “more” more often than “less”. It was interesting to me when I heard the statement that this reflects in student comfort working with addition/subtraction, and multiplication/division later on.
The word “less” doesn’t seem as common in everyday language as “more” is.

I have lots of learning still to do! And planning for the fall. It amazes me to see how Math ideas/concepts are interlinked in so many ways. Since my discovery of nontraditional math teaching 2 years ago, I am understanding why our Math Makes Sense texts are set up the way they are. We’ve had them for a very long time and only now they are beginning to make sense. (We were told to use them with no training.) Now our division is implementing Mathup – an online course by Marian Small for gr. 1 to 6. Looks great! A lot of nontraditional ways of teaching math. I am so thankful for the learning I am getting now. Even though it’s a bit overwhelming when I think of starting to totally change my practice! (and exciting!)

I used the Math Learning Center apps and copied and pasted into my reply. Sadly the fraction strips I used did not show up when i submitted my reply so I edited with no pictures. (BTW it’d be really great if you could create a “redo” button for the replies. Sometimes, I accidentally delete stuff and have to retype it!)
Gr. 7 question:
5/8 – 1/2
Direct comparison: Place 2 fraction strips, of the same length, showing 1/2 and 5/8 side by side. Notice which strip’s coloured spaces is longer.
Indirect comparison: hmmm… I didn’t know what to put here. I played with pattern blocks – which don’t work at all as they do not have “eighths” – and number lines.
direct measurement : Place the strips over top of each other . Note that 5/8 is an 1/8 bigger than 1/2
Indirect measurement; we can see that 1/2 = 4/8 so…
5/8 – 1/2 = ____
5/8 – 4/8 = 1/8
This process was much more difficult than I anticipated. Thanks for taking me out of my comfort zone. I am sure the synapses in my brain are firing like crazy. Hope they are creating a pathway for all my new learning!!
But seriously, what should I use for the indirect comparison?
 This reply was modified 2 years, 4 months ago by marianne aamodt.

Well. Even though I have taught various grade levels of Math (depending on the year – anything from K to gr. 10) I have never seen this type of visualization of division of fractions before. To be honest, I need to go over it again – i find it rather confusing!! (Hey, I was the memorization queen of algorithms in high school.) So i guess this is the lesson example that resonated with me the most. So much to learn!! Is there somewhere I can access more of this – trying to wrap my head around it.

The thing that resonated with me was the idea that a unit could have 2 or more items in it. I never used to think of a unit that way. To me, a unit was always made up of only 1 thing. So, It becomes sort of a brainbender. How can I put together a unit to count – but then, if you expect someone else to use the same unit, you must explicitly tell them what the unit is comprised of.
Very interesting and enlightening!

3 or 4 years ago, I taught math to a group of 3 gr. 8 boys ( yes, the smallest class in our small school) I tried to make Math more interesting while teaching surface area (before I had stumbled onto Christina Tondevold and Kyle and Jon’s nontraditional ways of teaching Math – I wish I would’ve had these experiences long ago!!) I had them measure the surface areas of various sizes of boxes. One of the boxes was even a triangular prism. Woohoo. We measured using centimetres as our unit. My students were very diligent and worked hard at measuring and using the formulas as espoused by the text (and, ahem…me) So. First of all, do I think they retained the formulas? Probably not. Did we discuss how they arrived at answers? Nope. Did I spend hours measuring and figuring out the “answers” myself. Yup.
This upcoming year, the students will be working together to answer the questions re total surface area of an object and we will be sharing how we arrived at our answers. It will probably take longer to do but I have the feeling it will be more beneficial for all in the long run.

I am an instructional support teacher for grades 1 – 6 plus will be teaching gr. 7/8 math in the fall. The delving into proportional reasoning is going to be a great thing for me to do! I hope to become better at thinking “on my feet” because I will have a better understanding of this concept. I have always been the person who follows the steps and comes up with the “correct” answer. The idea of being creative and having discussions and debates about how to find the “correct” answer is still fairly new to me.

After all the years I have been teaching Math, I never really knew what proportional reasoning meant. Of course, I taught multiplicative thinking but never heard it called proportional reasoning…. Oh so many learning gaps to fill. But that’s why I am here!!

I use a document camera fairly often. It’s really great for sharing a book or doing a handson demonstration that may be difficult for everyone to see.

Hi, I am also looking forward to exploring and becoming part of this community of lifelong learners.
Marianne

Hi! I, too, have been in the Education game for awhile – 25 years. I am looking forward to learning along with you.
Marianne

I love the 3 part framework. I hope to inspire and engage my students especially the ones who are “falling through the cracks” and just floating along which creates even more learning gaps than they already have.
I am excited to try using curiosity and problem solving as a means of learning.
The 10 assessment strategies are extremely helpful and make total sense. Assessment has always been a struggle.
The whole course has been amazing – so many new learnings for me. Thanks, Kyle and Jon, for sharing your knowledge, intellectual property, and your goofiness. (Your praise videos always make me laugh )

Spiraling curriculum will be a great deal of work but so worth it! I love the ideas of checkins” instead of “tests” and interleaving strands. I have so much planning to do this summer!!

I do not know anyone who teaches in a spiraling format! A lot of traditionalists in our school. I definitely plan on using spiraling in the fall. Thanks for the websites that have plans in place for spiraling. That will give me a place to start!

I found this difficult! I guess I am “unconsciously competent” leaning towards “Consciously Competent”! I chose a lesson on drawing parallel lines.
1. Student does not know /remember definition of parallel lines or protractor.
2. is able to draw parallel lines using a ruler and is beginning to figure out how to use the protractor to draw parallel lines
3. Can follow the steps to draw using a protractor but this is still difficult
4. Can use a ruler easily to draw parallel lines.

This is a very timely comment. Just yesterday, I came across a URL that was shared on the Build Math Minds FB page that I will try with my 7/8 class as a prealgebra experience. It looks like it may be helpful for my weaker students.