TEACHING THE COMMON CORE-Go Math or Math in Focus?

What are you using to teach the Common Core?  Two years ago we piloted Math in Focus. We found ourselves supplementing several different books (examples above).  Last year we piloted Go Math.  I am very impressed with Go Math because it supports the Common Core and was written after the Common Core came out.  It also has engaging concrete activities and I really like how the Common Core Standard is shown above each new lesson.  We used it more than we used Math in Focus and I am very happy with it.  I consistently refer to other resources; e.g., Primary Mathematics Calif Edition, Math in Focus, and Singapore Primary Mathematics for ideas to help me, as well as help my students gain a deeper understanding.  They have been great resources in helping me teach Concrete, Pictorial, and Abstract.

SUBITIZING

“Subitizing” is being able to instantly recognize the amount of objects without actually counting them. Much like the importance of being able to calculate estimates, subitizing is something that comes up in the every day lives of students.  One example of subitzing is counting the dots on the faces of dice: when you roll a six, chances are you don’t actually count out each of the dots. Rather, you have come to recognize the pattern of three rows of two as being equal to six. - See more at: http://mylearningspringboard.com/subitizing-as-an-important-math-skill/#sthash.aoaE2idd.dpuf

 Subitizing is the instant ability to recognize objects without counting them.  Subitizing is something that is done everyday in each of our lives.  One example of subitizing is when you roll a dice.  If you roll a six, do you count every dot or do you identify two rows of three?
Developing automaticity with addition and subtraction fact begins with subitizing.  It is very important that our k, 1, 2 students get a lot of practice at this skill.  Do your remember playing Yahtzee and having to add the dot dice?  You were subitizing. 


http://mylearningspringboard.com/subitizing-as-an-important-math-skill/

Games to practice Subitizing:

SUBITIZING FORMATIVE ASSESSMENT 

CAN YOUR STUDENTS SUBITIZE?
At the beginning of the year we even give our fifth grade students a quick subitizing quiz (shown below) to assess their ability to "see" numbers at a glance, without one-to-one counting.  It's amazing how many of our 5th graders struggle with subitizing!  
We use several different subitizing activities to help them build this foundational skill. One activity we use throughout the year is the "First to 100 Game."  We also use warm-up smartboard activities and have the games (above) in our classroom to again reinforce subitizing.

This 23 page assessment is available on Smartboard or Powerpoint.  You can purchase it on Teachers Pay Teachers for only $3.50.  

While “subitizing” may not be a well-known word, it is certainly an important mathematical skill.  “Subitizing” is being able to instantly recognize the amount of objects without actually counting them. Much like the importance of being able to calculate estimates, subitizing is something that comes up in the every day lives of students.  One example of subitzing is counting the dots on the faces of dice: when you roll a six, chances are you don’t actually count out each of the dots. Rather, you have come to recognize the pattern of three rows of two as being equal to six. - See more at: http://mylearningspringboard.com/subitizing-as-an-important-math-skill/#sthash.aoaE2idd.dpuf

While “subitizing” may not be a well-known word, it is certainly an important mathematical skill.  “Subitizing” is being able to instantly recognize the amount of objects without actually counting them. Much like the importance of being able to calculate estimates, subitizing is something that comes up in the every day lives of students.  One example of subitzing is counting the dots on the faces of dice: when you roll a six, chances are you don’t actually count out each of the dots. Rather, you have come to recognize the pattern of three rows of two as being equal to six. - See more at: http://mylearningspringboard.com/subitizing-as-an-important-math-skill/#sthash.aoaE2idd.dpuf

BONDING-Helps students' number sense- Kindergarten through 5th Grade!

Developing automaticity with addition and subtraction fact begins with subitizing. 

Why Bonding?
*Builds on fact families so the students can make sense of number combinations and become fluent.
*Helps students compose and decompose numbers.
*If children memorize number 0-12 they will have difficulty multiplying larger numbers and finding factors.
*Students foundation crumbles if it is based on memorization.  Greg Tang

Free on Teachers Pay Teachers

Early Grades 
In early grades k-1 students learn their bonds of 5 and 10. (K.0A.4)

This is a concrete way to show part-part whole relationships using any kind of manipulatives.  Pictorial helps students visualize, and bonding bridges the gap to the algorithm. 
Bonding also helps students see the different fact families.

                           I have a Ten Card over my desk!

In first grade students are required to add and subtract fluently within 20.  (1.0A.6)  If students have instant recall of number combinations/bonds 2 + 8 = 10.  They are able build on the bonding concept that 5 + 8 = 13. 

This is a concrete way to teach bonding.  Once students see bonding this way, it helps them become more fluent when adding the algorithm. 

Greg Tang's site has many free concrete activities to teach bonding.  He also has worksheets like the one below to get the students practicing bonding without the manipulatives.
Greg Tang believes to move students from concrete to algorithm quickly, so you can to get them to think abstractly.

"Games are the perfect way for kids to practice and extend their math skills.  Smart Sums dice games teach kids to use the Make 10 addition strategy to add quickly and efficiently rather than count or memorize."   Greg Tang

http://gregtangmath.com/Apps/AppDataAuthorizedOnly/Materials/Downloads/Puzzles/Dice.Add.Make10.pdf

This is an example of his worksheets.

Greg Tang has some very good worksheets to help reinforce bonding.

Smartboard Activity-Roll the dice.  Students find bonds to 10 (or 5) and show the answer on their whiteboards.  The first person to show the correct answer will roll the dice the next time.  If you do not have dice have the students work in partners and find the bonds to 10.

My students love this activity.  For younger students start out with less dice.  It really helps them practice and improve their bonding and subitizing.  My students show their answers on whiteboards.

I tell my students "10 is our friend."  10, 20, 30 etc. are (friendly numbers)

In Third grade students fluently add and subtract with 100 using strategies based on place value, properties of operations, and or the relationship between addition and subtraction. (2NBT.5)
When my students are confident with bonding to 10 and bonding to 10-90 and adding the rest-we start to bond to 100.  I will say, "38-bond to 100."  The students think... 38 bond to a friendly number then add the rest.  They show the correct number on their whiteboards.  After they visually see it with the abacus they become very good at doing this activity mentally.  We use this mental math activity throughout the year.

Teach Pictorial
We have found that some of our students struggle with bonds to 100.  Here is another way bonding can be taught.  Students fill in the amount 33.  Ask 33 bond to a friendly number...(40) They fill in to 40 with a different color.   Then add the rest...(60)  Fill in with the same different color. 

FREE on TeachersPayTeachers!!!

http://www.teacherspayteachers.com/Product/FREE-Bond-to-100-Pictorial-Representation-using-100-Chart-1005153

The SmartBoard Presentation below has ENGAGING activities (some shown above) with instructions of how you can strengthen your students' Number Sense using Bonding & Mental Math Strategies-(2nd-5th). Your students will also be Subitizing with the dice activities.

TeacherspayTeachers (JANCY)


This is a Free Bonding Race Track on TPT and it is also in the Mental Math-Bonding Presentation on TPT.
 

!

STRATEGY :
This is one example of a quick bonding activity to help students become fluent with their bonds to ten and hundred. Students use mental math strategies to quickly bond to 100.  There are two on my TPT site.  The first one is a ten bonded to 100.  Example:  10 + _____=100
It is very engaging as the students try to hurry around the track and make it to the finish line.

http://www.teacherspayteachers.com/Product/NUMBER-BONDS-TO-100-RACE-TRACK-835023

MENTAL MATH

  (You can also find more mental math on my Bonding Page.)

This is our 70 page presentation that has some excellent ideas that will help you teach mental math in the classroom.  It is on Teachers Pay Teachers.

Teachers Pay Teachers

Examples:
 Double the Number

My students become very fluent at doubling the number by first doubling the tens then the ones.  After I teach this concept they are able to do it mentally.

Half the Number

Half the number-I teach them to half the tens then half the ones.  When they are able to decompose the tens and ones it makes it easier for them.  

                                                            Multiply by 5

Multiply by 10-Multiply by 10 then half it.  When my students are good at halving numbers they can do this!!

Strategies to become fluent with math facts

BUILDING A STRONG FOUNDATION

SDE 2013 National Conference on Singapore Math Strategies Nancy and I will again be presenting two different sessions at the SDE Conference this year!! I'm so excited to hear Greg Tang,  Ron Clark, Dan Myer & Yeap Ban Har!

BUILDING A STRONG FOUNDATION

I have been teaching Singapore Math for the past 7 years.  Since I have started pinning, I've decided to share some of the ways I have helped my students gain a better understanding of Math.   
I have found that without a strong foundation our students math understanding crumbles.
At the beginning of they year I focus on the foundational concepts in my class.  I hope you enjoy some of the examples of how this is done.

BONDING GAME

For the past week we have been working on bonding to 10, bonding to friendly numbers and adding the rest, and bonding to 100.  On Friday we had some fun activity stations to review bonding. This Magic Trick Card Game was the students' favorite station.

 

Car Race Track-I had some questions after our presentation.  This is an example of how the students would show their bonds to 10 on the track.  I circled (so you could see) what the students would write.  We let our students practice a few times then we see how fluent they are by giving them a timing.  If they do not know their bonds they practice using this race track, the Al Abacus, ten frames, hands, etc.  If they are fluent, we start working on larger bonds.

FREE on Teachers Pay Teachers

Teaching CPA- Concrete, Pictorial, Abstract

When we teach a new strategy we always get out the manipulatives.  We collaborate and ask each other, "How can we teach this concretely so the students can gain a deeper understanding and show a visual model?"  Once they practice with concrete manipulatives,  they show it using a pictorial representation.  We might use other manipulatives to show multiple representations and to tap into the students different learning styles.  The second picture shows a student showing fractions using a bar model.  After she shows it with a bar model (pictorial), we have asked her to write a story problem to show how it can be used in the real world.  Last we teach the algorithm.  We have found when we take the time to teach CPA the students have a deeper understanding and need less time learning the algorithm.  We also try to tie in a game or activity to reinforce their learning.  They can work with partners or teams.  Many times we put a high student with a low student.  This gives one of them the teaching role and the other a role of learning from their peer. 

 Activities-Here is a fun concrete/pictorial activity to reinforce Place Value.  Each student has a place value mat on their desk.  These are free at  http://www.teacherspayteachers.com/Store/Barbara-Child/   

http://www.teacherspayteachers.com/Product/Place-Value-Mats-Ones-Thousands-Millions-Billions-Decimals-FREEBIE-769003  JANCY

The Place value strips are also available at http://www.teacherspayteachers.com/Product/Small-Place-Value-Card-Templates for only $2.00.  I keep them organized in folders (shown in Place Value).

 

PLACE VALUE

Place Value-This is in the front of my room so my students see multiple representations of Place Value. (There's a dime and a penny to compare to the base10 units.)

Place Value-
It is very important that students have a strong foundation of Place Value.  In upper grades we teach place value and review it the first three weeks of school and continue reviewing throughout the school year.  We use concrete and multiple representations to help the students visualize and make connections.  It is also an opportunity to tap into the variety of learning styles within a classroom.  We first start with base 10 blocks, then move to discs.  We use the discs so we can work with larger numbers.  Jana Hazekamp's book below shows other ways to use the discs.

Multiple Representations of Place Value

Organizing Base 10 Blocks

I got this idea from Bomb-Diggity Classroom.  Thank you!
My Base 10 Blocks are always disorganized in plastic bags!
I'm excited to finally have them in their own compartments!

Organizing Place Value Strips

http://www.teacherspayteachers.com/Product/Small-Place-Value-Card-Templates

I organize my place value strips in stronger folders I purchased at Wal-Mart.  I just stapled the sections with a long stapler.  These are smaller place value strips that are easier for the students to manipulate.  They are available using the link above.  I copied them on colored card stock then laminated.

Organizing Place Value Discs

Our Math coach, Barbara Child, bought these Utility Boxes through Maurice Sporting Goods.  We tried several others and these work well with bingo chips and the tiles.

Place Value Mats  -I love using these mats to teach Place Value!  You can use the periods you need and set the periods side by side.

FREE on TEACHERS PAY TEACHERS

SINGAPORE MODEL DRAWING

Model drawing has helped my students become very confident in solving word problems.  Instead of guessing, or giving up on word problems, they have strategies they can use to solve the problem and be successful.  Step 1 is to READ the entire problem.  Step 2 is to REWRITE the question in sentence form.  Step 3 is to determine WHO or WHAT is involved in the problem.  I tell my students they can do Steps 1, 2, and 3.  Once they do the first three steps it is easier for them to understand what the problem is asking.  When they get to Step 4- Draw the unit bars they are showing their work using a visual model.  Step 5.  They are re-reading or CHUNKING the problem.

 

This poster is on my wall for my students to refer to.  They also have a small copy in their own Singapore Model Drawing Books.

I love Model Drawing and I couldn't imagine teaching anything other than model drawing with my students!  I wish my own children would have learned problem solving this way.

My students struggle when they see a problem like the one below.  When they see the three times they want to show 4 unit bars.  I explain it first using pencils (below).  This makes it easier for them to understand.

  This book is a great resource if you are just starting out with model drawing.  Char Forsten is amazing and her ideas are very helpful.  When I started model drawing I was taught by Char Forsten and the SDE staff in Boston.  Before I went to Boston I used this book (actually her older version) with my students.

DECIMALS

 
http://www.teacherspayteachers.com/Product/Small-Decimal-Place-Value-Cards
Another great idea from Barbara Child, our math coach.
Here is a great way to organize place value discs and tiles.  We have one student show a number on the place value chart.  We use dice to make a number and another student will make the number using decimal place value strips.          

I help my students understand decimals by having them use base ten blocks (concrete).  This helps them break up 1 whole into tenths and show it on a number line.  It also gives them a deeper understanding of decimals.

Showing tenths on a number line.

      

Showing hundredths on a number line.