Common Core Elementary Math Progressions

First of all, a friend of mine directed to me a great resource on the common core which had math vocabulary lists for all grade levels.  This site is from a school district in Utah.  I had some concerns about one or two of the terms used on the third grade list because I couldn't find them in the standards documents.  The elementary math coordinator from their district told me that the majority of the words are common core. Actually, she believes they all are, but some did come from their math series Houghton Mifflin Go Math.  Honestly though, the site was great.  Here is the link. While looking through that site, I stumbled across a blog titled Tools for the Common Core State Standards.  It's author is Bill McCallum.  He wrote the article The Structure is the Standards.  This article is a must read for Common Core. So much great information, so little time!  Okay, now the reason I started this post in the first place.  On that same vocabulary search I found a site from the University of Arizona that published some draft papers that describe the progression of the mathematics through each of the strands.  The papers are labeled by grade level are very easy to read.  What I loved most about the papers though is the one or two paragraphs at the end of each one that explains how the math at the lower grades is setting the foundation for the math in the grades beyond.  It is very specific too.  Want to know why it's important to compose and decompose shapes? Read the Geometry paper.  Want to know why it's important to know algebra at the lower grades? Read the K-5 Operations and Algebraic Thinking page.  Here is an example excerpt from the geometry:

Where the Geometry Progression is Heading

Composition and decomposition of shapes is used throughout geometry from Grade 6 to high school and beyond. Compositions and decompositions of regions continues to be important for solving a wide variety of area problems, including justifications of formulas and solving real world problems that involve complex shapes. Decompositions are often indicated in geometric diagrams by an auxiliary line, and using the strategy of drawing an auxiliary line to solve a problem are part of looking for and making use of structure
(MP7). Recognizing the significance of an existing line in a figure is also part of looking for and making use of structure. This may involve identifying the length of an associated line segment, which in turn may rely on students’ abilities to identify relationships of line segments and angles in the figure. These abilities become more sophisticated as students gain more experience in geometry. In Grade 7, this experience includes making scale drawings of geometric figures and solving problems involving angle measure, surface area,
and volume (which builds on understandings described in the Geometric Measurement Progression as well as the ability to compose and decompose figures)   6/23/2012, comment at commoncoretools.wordpress.com.

Just for those teachers who sometimes ask, "Why do I need to teach this?" These papers answer the question.

Patterning

I had a great lesson today with my students on patterning.  Why this is such a difficult concept for children I'll never know.  Every year when we analyze our previous year's scores, our students always seem to be low in analyze a geometric or numeric pattern.  Hopefully the lessons we've gone over these past few days will have cleared up any misconceptions my students may have had.  My teaching partner and I were discussing today how we never really understood patterning when we were children.  We just don't remember being taught how to find the pattern.  I definitely hated questions that asked me to find the a certain number of shapes in the pattern ie., find the seventh shape if the pattern continues.  Hated that! I never understood the concept of the unit.  Students must find the unit, or repeating sequence, in order to determine what shape comes next.  Eventually I think I figured that much out, but until now I didn't realize there was a number pattern that would help me.  Our problem we worked on today was from Pearson's Investigations Unit 6.  It was titled Find the Greens.  We were given a cube train consisting of red, blue, green, red, blue, green, red, blue, green, up to 12 cubes.  The goal was for students to realize that we can find the number of any green cube by skip counting by three's since the green cube was in the last position.  We made an input/output table to check our work.  By figuring out what number each green cube fell on, we can now figure out the number of any of the other cubes in our basic unit sequence.  For example, I know that the 4th green in my pattern is the twelfth cube in my train.  I can now figure out the 4th blue also because it is just one less than the 4th green.  This will work for any number in the pattern.  What would the 20th cube in the pattern be?  I know that the 7th green is the 21st cube so the 20th cube will be blue. If students make a table listing all of the greens they can then add in what each blue and red should be.  This lesson is great for hitting a large majority of the mathematical practice standards.

Geometry: Shapes, lines, rays

Recently I posted an activity to help students with the concepts of lines, rays, and angles.  You can visit that post here.  The students and I read together the book The Greedy Triangle by Marilyn Burns shortly after our activity and my students began to wonder about creating a circle.  If you aren't familiar with The Greedy Triangle, this book is about a triangle who decides he doesn't like being a triangle anymore.  He goes to see the shapeshifter who keeps giving him one more side and one more angle until he can barely walk since he is almost round.  He finally decides that being a triangle isn't so bad afterall.  It is a great story that the kids LOVE!   Some of my students began putting their lines they made (see the first post again) together to create different shapes.  I am almost ashamed to admit it but I've never thought to do this before during this activity. I was elated.  Here are the shapes we made:

So much fun!  They learned alot!  Visit my TpT store for some great math, reading, and writing resources!

Area and Perimeter using Pentominoes

I began using math stations today.  One of my kids favorite stations was the area and perimeter station.  I filled a black tub with one inch square tiles and pentominoes.  Pentominoes have five squares hooked together on a flat plane in 12 different variations.  Students can do so many activities with them in relation to shapes, rotations, reflections, translations, area, and perimeter.  I created a set of pentominoes which you can download for free. Click here for your free download. Ideas for using the pentominoes includes:

1. finding the area and perimeter of each pentomino
2. using the pentominoes to cover a given shape (like a puzzle)
3. combine the pentominoes together to create a shape with a given area
4. combine the pentominoes together to create a shape with a given perimeter
5. using the pentominoes to cover a given shape and then find the area and perimeter

Do you use pentominoes in your classroom? If so, do you have an idea you can share? I would love for you to leave a comment and let us know.

Informal Assessment: Making the most of every moment

I am trying to make the most of every moment in my classroom this year.  I have been doing a lot more informal assessment which has really helped inform my teaching.  I use my white boards a ton especially in math class for doing quick checks for understanding.  I decided to also use the exit slip idea as well.  I created a bunch of number cards, money cards, and clock cards.  As the students leave the room, I flash one of the number cards at them.  The students either have to read the number, identify a digit in a place, or tell me the value of a digit.  I haven't done the money or time cards yet because I've really been drilling place value these past few weeks.  My plan is to also use the cards as the students enter the room as well.  I can't get over how the students have responded to this idea.  If I don't get the cards out on the way out the door, they ask for them.  I hung library pockets on my door frame and put the cards in them so all I have to do is grab them as they line up.  I've been using them at restroom time and any other time we have to wait in the hallway.  It's been great!

Doubles and Doubles Plus One Facts and Rounding

I love breaking the addition combinations into categories.  I'm sure many of you do also.  Yesterday as I was reviewing the doubles and doubles plus one combinations it occurred to me that my students may not realize exactly what a doubles plus one combination means.  I know they've heard of it before in earlier grades but I always just want to make sure they conceptualize what they are learning.  I made the following with them and it seemed to really help.
First we folded our papers like a hot dog or vertically and placed the fold to our right.  We then started to draw out the doubles facts and wrote the combination that matched it next to it.

 Then we opened the paper up and we added the one.  Students started recognizing patterns and were able to visualize what I meant by plus one.  At 6 + 7 I started writing it out as 6 + 6 + 1.  I was very clear though that they had to recognize a plus one combo by seeing that the two addends are next to each other on a number line.

I hope this is helpful to your students as it was to mine.  Leave me a note and let me know if you use this.  I'd love to hear from you.

I also wanted to let you know that I've created a new product on my Teacher's Notebook store! It's called Rounding Mountain!

Manic Monday Freebies

I haven't posted all week last week! I miss my blog when I don't post! I didn't want to miss Manic Monday though so here it is! I can definitely post a picture of what mine look like but this is a glyph.  A glyph uses pictures to represent pieces of information.  I usually do a me glyph each fall with a paper plate as the students faces and each part of the face represents a piece of information.  The color of the eyes matches the students eye color. The shape of the mouth stands for the number of siblings the student has and so on.  I created a Cowboy Me Glyph to go with my Western theme.  Here it is for you if you would like to do a glyph also.  Let me know what you think!

Number sense game

One of my favorite games to play with my students to reinforce number concepts is what I call Number Twenty Questions.  I use the interactive 100 board on my Smartboard Notebook software but I've used my regular 100 board also.  I start the game by secretly choosing a number.  I then have students ask me yes or no questions about my  number.  I try to teach them what types of questions to ask.  For example, does your number have two digits?  Is your number even?  I just get them started at the beginning when I first teach the game but then the students get very creative. This game could also be played with a 200 or a 300 chart.  I do not have an interactive one of either of those though.  Using my interactive board, I will color out numbers as we eliminate them because that way students are connecting their question with the numbers being colored out.  I also make a rule that students cannot guess my number until there are 6 or less numbers left on the board.  The student who guesses my number correctly gets to pick the next secret number.  The kids love this game and will beg to play.  Here is a screen capture of my 100 board. I was going to ask if you could guess what questions had already been asked but I just realized I forgot to block out a whole column. (The 9  column)  OOPS! Sorry.

Autumn Addition Facts

I have fall fever!  I really wanted to create something new that had a fall flavor to it, but I decided to use my Monster Number Crunchers as a Template and change it to an Autumn theme!  This is a perfect set for a center or as I use them...flashcards for assessment.  As the students master each set check off the box on their assessment card included in the set.  Check the set out on my Teachers Notebook site!

Pet Parade Unit Debut

I have finally finished the Pet Parade Center Unit.  It is my first one that I created so I hope it is right.  :)  Here are a few pictures of what the unit looked like when my Title I teacher was teaching it with my students.    Remember this unit was originally created by Wendy Speer but with her permission I created the documents to go with it.

Click on the Pet Parade picture below to visit my Teacher's Notebook Store.

Linear Measurement Station

Mass Station

Capacity Station

Weight Station

Fun Math Literature!

My favorite books for that down-time/extra two to three minutes before lunch or between classes are the Greg Tang books. My students love them. I first came across Grapes of Math at Wal-mart! It was a Scholastic book and it looked nifty so I picked up a copy. I LOVE it! Grapes of Math shows the students pictures of objects along with a riddle. The objects are grouped so that they are easy to count quickly. The goal is for the students to not count one by one but to find the pattern or grouping situation. I like to put my book under my document camera. There are several Greg Tang books that follow this same concept. Math Potatoes, Math-terpieces: The Art of Problem-Solving, and Math for All Seasons: Mind-stretching Math Riddles are a few of his others.
                                                                   

Calendar Math

I love Calendar Math and have always wanted to do it for the upper grades but have never taken the time to put it all together.  I found this on Teaching Blog Addict from Teaching in Room 6.

Pigs Go to the Fair

I work with an amazing Title One Math Teacher.  Actually she is retired but she has been coming to our school to help us prepare our third and fourth grade students for our state testing.  She read the book Pigs at Odds: Fun with Math and Games by Amy Axelrod to my students and then had an amazing set of centers for them.  Check out my Amazon astore to see all of her books! I will post the worksheet the kids used after I type it up.  I don't have her file of it on my computer.  This series of books by Amy Axelrod is a great math series.  I've used Pigs will be Pigs for counting money and counting back change.  The following games were all about probability.
Leave a comment and let me know what you think! I love comments!!

Knock Down Cans

Students record the number of cans they knock down

Birthday Guess: Spin a spinner to see how many times your month is spun

You Quack me UP! Choose the #2 duck and you win!

Ring Toss!

Pet Parade beginnings

I've started working on creating documents.  I'm really excited about it.  I know my classroom is definitely going to benefit from it!  I'll post a picture of one piece of my unit that I'm working on.  Let me know what you think! This is from a unit that my friend Wendy Speer created called Pet Parade.  It is on measurement.  She really is one phenom of a teacher.  She has so many creative ideas.  She gave me permission to create this unit as I have done so.

Capacity

I looked throughout the halls yesterday and saw that the first grade students had created a gallon-man which I too usually do with my third graders.  I decided since the first graders had also done it that maybe I'd better just stick with my usual visual that I learned back in college.  I like to have my students draw it themselves, but it is always nice to have a good copy for them to keep in the math section of their binder.  I tried to create one on publisher.  I am still new at this creating documents thing, so please bear with me. Let me know if you can't open it.  I linked it to my dropbox and it is a PDF file.

Gallon 

Teaching Blog Addict: Math Work Stations: Spring 2012

I have always desired to use math stations in my classroom, but I just couldn't figure out the logistics of it all.  I especially couldn't handle the paper chase.  I just  found a great idea from the following fellow blogger: Thank to TBA!!

Teaching Blog Addict: Math Work Stations: Spring 2012: If you are like me, you are always changing how you do things in your classroom.  I have posted previously about how I use work stations in ...