Today we started talking about mental math, and some strategies we can utilize when added numbers mentally.

I know that addition is combining terms.  This means I can break apart those terms as I see fit and combine them in any way that would make it easy on myself.

For example a simple problem like 9 + 7

I can see that my answer is going to be larger than 10.  So I try to make a ten easily first.  I know that 9 is one away from ten.  This means I’m going to break up my 7 into a 1, and a 6.

So my problem goes from

9 + 7

to

9 + 1 + 6

10 + 6

16

This is a good strategy for students to have when adding numbers, and one of many we will be working on.

Tonight students should finish this simple worksheet on this idea.  Please make sure you read the directions:

mental-math-practice

We also did a good round of centers today, some focused on base number systems, and others on our own base 10 system.

We also got together some of the parts that we will be using tomorrow to make an abacus!

We will be adding and subtracting with our abacus, and we’ll have to make a video where we solve a problem using the abacus.

Finally we took some quick notes on addition:

addition-notes

Have a good one,

-Mr. Potter

Another day, another discussion of base ten!

Today we talked about powers of ten, and how as we have a base 10 system, each place value in our system is described by a power of ten.  This means that multiplying or dividing by 10 in our system is fairly simple and straightforward.  We took some notes on this:

base10andpowersoften

And then we talked about how our system is actually TOO good at representing numbers.  It’s so good, that we often forget just how big or how small numbers are.  For example a number like 222 doesn’t look that large..

until I ask you to draw 222 dots, or make 222 tally marks.

Which is what we did next in our example book!

multiplyingby10makesthingsbig

And what if I asked you to draw 2222 things?  Yeah…no thanks.

To hit home this  ideas that multiplying by 10 makes things very big very fast (exponential growth!) and that dividing by 10 makes things very small very fast, we watched this neat video about relative size in the universe:

Powers of Ten

Have a good one,

-Mr. Potter

The days are too short!

Today we quickly finished up those notes from yesterday in some classes (others were already finished thankfully)

base10_notes

We then talked quickly about exponentiation.

And how something like:

2^3

Does NOT mean 2 x 3!!

We discussed powers of ten, and how in our BASE 10 system, the BASE of all of our place values, is 10!

So something such as 456

Is made up of:

4 x 10^2

5 x 10^1

6 x 10^0

We did a quick example of this in our example notebooks, and also a quick explanation of why anything raised to the 0 power is 1.

dissectinganumberexample

So in any base system, the base is what we group in, and each place value is based on that number.

Finally we talked a bit more about base 2, and then did some work writing numbers in base 2.  Tonight students should finish this worksheet (the front) if they have not already:

base2exercise

Tomorrow we will do some more work with base 10 and other bases, and do some centers that give us a good bit of practice.

Have a good one,

-Mr. Potter

Today was an extremely short day as we had early dismissal.

As such, we didn’t get much finished.  First we took some notes on Base 10 that is essentially rehashing our conversation from yesterday:

base10_notes

After that we had an i-ready growth check we had to do.

And then we were out of time!

Early releases can be annoying.

Have a good one,

-Mr. Potter

In class today we talked about expectations, and what perfect students in the perfect class would be doing.  Students came up with lists and then we shared some of our lists.  Many students had very similar lists that included things such as:

Students are working diligently

Students are talking quietly when appropriate

Students are listening and paying attention

Students are respectful of the teacher and other students

Students are kind to each other

I was quite impressed with the students’ responses.  Both for their obvious understanding of what good classroom behavior looks like, and for their use of fantastic vocabulary as they described these things to me.  I am confident that both the students and I are  on the same page when it comes to what our classroom should look like.

Next we discussed the base 10 system.  We talked about how it is called the base 10 system because we have 10 different numerals (digits):

0  1   2  3  4  5  6  7  8  9

These are the only numerals we have.  Quite some years ago some very intelligent individuals in India devised this system of counting and grouping things in tens.  It is ingenious how we can use these simple 10 digits in order to represent literally any number we can think of.

We also discussed very quickly what a base 2 (binary) system would look like.  In a base 2 system, the only numerals would be 0 and 1.  We talked very briefly about how we could count in such a system.

This week we will continue our discussion of base 10 and counting systems.  We will also do some exploring of other base systems.

Here is a quick video recapping our discussion today of the base 10 system:

Base 10 review

Have a good one,

-Mr. Potter

Today was some more discussion involving the base 10 system, and other base systems.  This entire discussion is meant to encourage a deeper understanding of our own system, and how this system is used in mathematics.  If you understand better how numbers are grouped and constructed, you are better equipped to manipulate them.

First we wrote down an example in our math examples notebook just like yesterday:

expandednotationexample2

Next we played around with creating numbers in base ten, focusing on how they are made up of ones, tens, hundreds, thousands, etc.

Students made number on the Smart Board using ones, tens, and hundreds.

Then we talked about what the place values would be in a base 2 system.

Instead of ones, tens, and hundreds we would have ones, twos, fours, eights, etc

Students made some more numbers on the Smart Board using these place values.

We also took down a few more examples:

base10and2example

We finally ended the day by watching a short video about black holes.  I do this because I would like students to have a bit of a better sense of scale as we begin talking about bigger and bigger numbers.

Black holes

Please remember – quiz on Friday on base 10, and number systems.

You should know how to break a number down into it’s individual place value parts (in base 10 and in any other base).

You should be able to count a number of objects in base 10, as well as in a base given to you.

Have a good one,

-Mr. Potter

Today we continued our talk of Base 10.  We took some notes in our notebooks:

base10notes

Next we talked about how base 10 numbers are made up of different parts, and talked about how we can write things in expanded form.

For example we might have something like 654.

This number is made up of:

6 hundreds = 6 x 100 = 6 x 10^2

5 tens = 5 x 10 = 5 x 10^1

4 ones = 4 x 1 = 4 x 10^0

Which led us into the discussion and explanation of how anything raised to the 0th power is 1.

We did an example of this expanded notation in our example notebooks:

expandednotationexample

We then talked about counting in base two. Base two only has 2 numerals: 0 and 1.  This means we can only count up to 1 of anything, and have to group in twos.

We did some counting in base 2 together:

base2exercise

And then before you knew it, it was time for us to go.

Have a good one,

-Mr. Potter

In class today we talked about expectations, and what we envision to be the ‘perfect class’.  The students were mostly on the same page with this.  They came up with lists of what the perfect classroom looked like independently, but many of the lists were quite similar. We then shared our ideas of what students in the perfect class would look like. They included things such as:

Students are working diligently

Students are being productive

Students are talking quietly when appropriate

Students are listening and being engaged

Students are respectful

Students are kind to each other

I was quite impressed with the students’ responses.  Both for their obvious understanding of what good classroom behavior looks like, and for their use of fantastic vocabulary as they described these things to me.  I am confident that both the students and I are  on the same page when it comes to what our classroom should look like.

Next we discussed the base 10 system.  We talked about how it is called the base 10 system because we have 10 different numerals (digits):

0  1   2  3  4  5  6  7  8  9

These are the only numerals we have.  Thousands of years ago some very intelligent individuals in what is now the Middle East devised this system of counting and grouping things in tens.  It is ingenious how we can use these simple 10 digits in order to represent literally any number we can think of.

We also discussed very quickly what a base 2 (binary) system would look like.  In a base 2 system, the only numerals would be 0 and 1.  We talked very briefly about how we could count in such a system.

Tomorrow we will continue our discussion of base 10 and counting systems.  We will also do some exploring of other base systems.  One of the questions on the quiz Friday may or may not ask students to count up to 10 in a system other than base 10….

Have a good one,

-Mr. Potter

This week is project week!

This week we will have essentially the same homework each night.  Students *should* have enough time in class to finish these.  However if they would like to do some work at home, they are more than welcome to do so.

Three final projects:

Math project – Students will create a video showcasing a division word problem that they created themselves.  They will solve the problem using math manipulatives AND the standard algorithm for long division.  At each step they will explain the process and show how using the manipulatives and the standard algorithm line up.

All video recording will happen at school.  If students wish to work on their script and practice at home they may.

Math video example: Sorry for vertical filming!

Language Arts Project – Students will type out their Bad Road for Cats version 2.

If students have not yet finished their draft of their story, this should definitely be completed at home.

Science Project – Biome Brochure.  Students will have time in the computer lab to put together the brochure.  However if there is still research that needs to be done, at this point they should try to get some done at home.

so, tl;dr

Work on projects

Read!

Have a good one,

-Mr. Potter

PS: Dr. Elrod dropped by today and paid us a visit.  He also brought us cookies.  mmmmmmmm    cookies.

Thanks Dr. E!

Ah yes, Thursday, the day when everything seems to come crashing down, and the children and I suddenly realize we only have 1 more day left this week to get things done.

We spent a great deal of time today working on math.  Together we looked at the way we have been performing division using manipulatives, and the standard algorithm for long division.  We looked at each step and talked about what is happening and how it equates to what we have been doing with our play money.  We took copious amounts of notes on this, that will hopefully help us when it comes time for us to explain it in our math videos.

longdivisionnotes

Tonight students have one division problem to work out.  They should do this using the standard algorithm (but are more than welcome to work with their manipulatives as they do it), and they should explain at each step what is going on by labeling each number, and what they are doing.  As always, there is an example:

mathhomeworksep21

In between bouts of math, we also read a ton of The Mysterious Benedict Society today.  Things are getting super interesting.  The kids are spying, cheating, lying, and all sorts of secret-agent type stuff.  Trenton Lee Stewart (the author) does a great job of leaving each chapter on a cliff hanger, and I make sure that I always stop reading at the end of a chapter!

Tonight students should continue writing their stories.  Tomorrow I would expect the stories to be near completion as far as a rough draft goes.  Tomorrow we will be doing some peer editing, and revision.

Please also remember that tomorrow is quiz day, and we’ll have some final review quizzes on everything we’ve done so far this quarter.  Some students are still having some issues with food webs and transfer of energy, so I would recommend reviewing notes on those as well as the chapter in our science book.

so, tl;dr

Do this one problem using the standard algorithm, labeling each step with what each number represents, and what you’re doing.

longdivisionnotes

longdivisionhomeworksep22

Keep working on your rough draft of A Bad Road for Cats version 2. This should be close to done.

Review your food webs/ecosystem notes

And read!

Have a good one,

-Mr. Potter