Oh Math Planning... How I Love and Hate You

Ok, I am a total math girl, especially 5th grade math.  The rigor and content is just so exciting!  It's right about where even adults have a difficult time with the math.  I'm sure most of you teachers (and non-teachers) have heard of the Common Core Standards.  The Common Core math is our district's focus since it is a shift when it comes to the depth of knowledge kids are expected to comprehend certain concepts.  Modeling and explaining WHY things work takes time, energy, and effort (students and teachers).  I love planning it, and I hate it for the time it sucks out of me.

Yes, there's stuff out there, especially on Teachers Pay Teachers, but not all of it is Common Core aligned, even if it is labeled as so.  FRAUD!  You have to really look at it.  I've seen things called "Common Core" and it's just a worksheet with problems and maybe one number line.  No, not Common Core.  And if it is pretty Common Corey, it's usually more expensive because it's good.  I don't know about you guys, but I can't spend an arm and a leg on one unit, much less a bunch of units!  Plus, after the time it takes me to sift through everything, I realize that I could have created something myself.  No, it wouldn't be with the cute graphics or pictures, but it would be what my kids needed specifically this year.

I am in no way saying I'm a Common Core expert, but I am doing the best I can with not as many resources available.  I teach them the algorithm when appropriate and model the others when necessary.  With 5th graders (compared to primary), they're really getting the short end of the stick since so much of what 5th CC builds on is what they really "know" from the previous years, such as the 3rd and 4th grade fraction units.  However, since CC didn't really roll out for our district until last year and teachers are still experimenting, I have to know that pre-teaching 3rd of 4th grade concepts is necessary to continue with what I need to do sometimes.

What I like about creating my own stuff is that:
1) I can use their names in contextual problems
2) I include things they're interested in
3) It's electronic so I can change and reuse as needed for future years

So anyway, enough rambling.  I wanted to share a few concepts we've been working on.


ADDING & SUBTRACTING WHOLE NUMBERS & DECIMALS
With adding & subtracting, I did this with whole numbers and decimals together, emphasizing lining up by PLACE.  By 5th, they should be able to do this with the algorithm, so I didn't spend too much time on the other models.  It's not the main focus for 5th grade... although you wouldn't believe the amount of kids who can't add or subtract with regrouping by the time they're in 5th.  It's shocking!

I added tree diagrams in, but really didn't push it, since the algorithm is much more efficient & they should be doing that by 5th anyway.

MULTIPLY WHOLE NUMBERS
For multiplication of whole numbers, 5th graders should be able to multiply with the standard algorithm, but understanding what the regrouped numbers mean, the place holder zero, etc.  However, I taught this with the open rectangular array model also since I knew I would need this model when moving into multiplication with decimals.  I know lattice is NOT very Common Corey, but I did add that in as a strategy because in the past, so many of my students worked better with that than the algorithm.  I had plenty of resources to supplement this unit, but here are the notes and some things that I created.

Some word problems I created for this concept can be found here: Multiply Whole Numbers Word Problems.

I also created a test that you can find below.  These are just a couple student responses for a few of the questions.

Student math test sample. 

Student answer on math quiz. She missed half a point for incorrect calculations, but the rest is pretty accurate.

You can access my Mulitply Whole Numbers Quiz here.

MULTIPLY WHOLE NUMBERS BY DECIMALS (Mixed & Decimals)
For multiplication with decimals, I separated out whole numbers by decimals and decimals by decimals since they require different models.  For multiplication of whole numbers and decimals, I used the open rectangular array model.  KNOWING they would come to me with a lack of fluency on how to read whole numbers and decimals in muliple ways, I even inserted this verbal fluency lesson prior to my unit:

However, talk about the lack of place value knowledge that comes out of this, even with manipulatives.  There are definitely gaps.  Most of my higher kids got this, but my lower ones couldn't do this AND the model.  It was too much at once.  I ended up having to make them think "money."  (Thank goodness Common Core 5th we manipulate decimals up to hundredths; explaining "money" with thousandths to struggling kids would be CRAZY.)

I used play money as an enactive way to break down money.  This was one of the centers I used.

Anyway, some kids multiplied whole numbers and decimals with the standard algorithm instead of the model I taught.  Because there's only one decimal, they simply "brought it down" and their answer "happened to be correct."  However, they couldn't tell me why the decimal belongs there.  I told them that if they couldn't explain why the decimal belongs there using the proper math vocabulary (multiply and divide by powers of ten), then they cannot use the algorithm since "bringing it down" won't fly when we multiply decimals by decimals.

Notes we took together.  I added estimation because we would work with word problems later.  That step was too much for my lower kids, so only certain groups had to estimate answers first.  Notice I listed some numbers multiple times with the decimal in different places.  This was to go through the process of elimination on what makes sense especially when we're multiplying money.  It has to make "cents."  Get it? :)

I wanted kids to note the patterns/differences they see when multiplying a whole # by a mixed vs a whole # by a decimal.

Multiply Whole Numbers with Decimals Word Problems
We did this around Halloween, so the second set of word problems were tailored for that purpose.  Also, I had early finishers from the previous day's activities help me create those word problems.  :)

Multiply Whole Numbers by Decimals Quiz


MULTIPLY  DECIMALS BY DECIMALS
For multiplication of decimals by decimals, I started with just tenths by tenths, so I used a hundredths decimal grid. I have not hit the multiplication of tenths by hundredths yet (which will require a thousandths decimal grid), so that will be left to another post!

These are the notes we took for multiplication of decimals by decimals.

These are the practice problems we did together as guided practice.  I threw in a number line for the last one since it's difficult to "see" the race problem in a grid model.  I traced the tenths on some of them so they could see how the orange part was broken into tenths horizontally.

This is a snapshot of what they had to work on after. They used the guided practice as a model, but also had to be able to read all colors/parts of their model.

Students moving on to draw their own hundredths grid.

Here is a pdf of my samples and creations for multiplying decimals by decimals (notes, word problems, and quiz): Multiply Decimals by Decimals Modeling

For the page where students had to create their own hundredths grid, I used graph paper.  They also had to "read" the graph as in the example.


EEEK! NEED SUB PLANS TO REVIEW EVERYTHING SO FAR! 
Anyway, I am going to be at the Daily 5 conference for three days next week.  That's three precious days of math that cannot be wasted!  But I just can't have my sub introduce something new... so I decided it's a good time to break and review some major concepts we've learned thus far.  I could have printed out a worksheet for the following:

• adding & subtracting whole numbers & decimals
• multiplying greater numbers
• multiplying whole numbers with decimals
• multiplying decimals by decimals

... but a worksheet for the last two concepts would be difficult because I didn't teach it with the traditional algorithm!  I also wanted things to stay contextual, so I decided to do word problems.  They need the reading comprehension anyway.  I created 30 word problems that are mixed with all those concepts.  This will be a challenge for some since they are not used to getting problems of all different operations and models.


Here is a copy of the word problems I created and some pictures: Review Word Problems (add, subtract, & multiply whole #s & decimals)

I color coded the types of questions they would encounter.  I felt this would help them when it came to using their notes and what type of models they should use.

If they encountered a problem where they would need a hundredths grid, they would need to get one to glue in to model it, as in #9 in the picture. 

Basket full of hundredths grids.

I created this Tutor & Pupil sheet for my sub to read out as a guide on how to work together while I'm gone.  I want to make sure some kids don't get lost.  The tutors will benefit from explaining what they know and what they're doing.  

Oh, I totally forgot to mention that the notes I take with them are in pen because it stands out better under the document camera, not because they are allowed to do this!  Haha.  :)