Using arrays to teach multiplication and division


http://nrich.maths.org/8773

Long Division Can Be Difficult

Several of my students still struggle with long division.  Here is another strategy that I think could be very helpful written by Greg Tang.

https://dl.dropboxusercontent.com/u/9303952/Tang%20Division%20Article%207-14-14.pdf

Changing Schools Is Exhausting!!

This next year I will be working at an Elementary School (Edith Bowen) at Utah State University located on the Utah State Campus in Logan, Utah.  It will be a wonderful experience for me.  I'm excited to learn and grow as I learn from great teachers at this school.
I've found that the only thing intact is my math manipulatives.  They have a spot, they are organized in their containers, and are ready to go!

SDE Conference, Las Vegas

We are hoping to attend this conference

We can't get enough of Greg Tang!  We love math!!
SDE Conference 2013

 



Nancy and I had a great time at the National Singapore Convention.  We love teaching and learning new ways to teach math more effectively.

If you attended any of our presentations, we are working on getting some games/activities on Teachers Pay Teachers!

Jan & Nancy
JANCY











Greg Tang (in Las Vegas)- I can't tell you how impressive Greg Tang is.  He is always sharing something I can use and is introducing new interactive games.  Two year I learned about Kakooma.  I have it on my Iphone, Ipads, and worksheets are available.  Last year he  added Kakooma with negative numbers and multiplication.  This year he is adding more!  He has several other games you can access on his free site. 

Ron Clark was the opening speaker!! I have never seen or heard such a dynamic speaker in my life!  If you haven't heard of Ron Clark, there has been a movie made about him called The Ron Clark Story.  For more information you can go to  
Ronclarkacademy.com












Las Vegas Presentation

During our presentation we forgot to mention this valuable book by Jana Hazekamp.  This book gives ideas and steps on Why and How to teach basic math strategies.  Some of the teachers in our district did a book study using this book.

 

Some of you might have seen Jana present at SDE.  She is another one of their amazing presenters!

Happy November!!

We enjoyed presenting Mental Math Strategies at the UCTM Conference!!  Our Presentation- which we share examples of how we begin with bonding and move to mental math is now on Teachers Pay Teachers.
"We teach addition/subtraction bonding strategies even to our 3rd, 4th and 5th grade students.  Although it is not in the Common Core for 4th and 5th grades-the students should already know these bonding strategies. We find our fifth grade students are lacking in these foundational strategies.

These strategies help their number sense and also helps them become fluent in their addition facts so they can process them mentally!"

 Presentation Link

This blog shows the same progression as the math foundation blocks below.  It is the same progression we use at the beginning of the year in our 5th grade classroom to review and give our students a strong math foundation.

We will be presenting at the UCTM Conference in November.

Thanks,                                      
Jan & Nancy







Don't miss out on our Teachers Pay Teachers Calendar JANCY Teachers Pay Teachers! 

  We have used and tried several different calendars from different publishers.  We have found that the ones we have created align with the New Common Core.  They have also been very effective while we teach and review math concepts.   

Here is an Example of one of our Common Core Calendars on TPT.  It is also available for your Smartboard.

Place calendar and fraction wheel in a clear sheet protector.

The Fraction wheel is very useful in helping students see fractions, percents, part-part whole, and  also helps them use estimation.  Copy on colored cardstock.

 

This is our newest Calendar-Our students needed more review with expanded form.  The common core shows both ways (as a decimal and as a fraction). We also added multiplying and dividing decimal numbers.   

 

 Building a Strong Foundation

 

Nancy and I have been teaching Singapore Math for the past 8 years in our 5th grade classroom.  Since we have started pinning, we've decided to share some of the ways we have helped our students gain a better understanding of Math.   
We have found that without a strong foundation our students' math understanding crumbles.
At the beginning of the year we focus on the foundational concepts in our classes.  We hope you enjoy some of the examples of how this is done.

Nancy Stewart and I will be presenting again this year (July 16th, 2013) at the SDE Singapore Conference in Las Vegas!!

We are also starting to add many of the activities and strategies we present and use on this blog.  We have just started posting them on  Teachers Pay Teachers under JANCY

 

FIRST TO 100 Game!!

Teachers pay Teachers

This is my students all time favorite game.
This game is very fast paced, engaging, and your students will want to play it as often as you will allow.
This game is very good to help students number sense. 

Math Strategy Focus: 

Subitizing
Counting
Multiples 
Decimals
Fractions. 
All the counting activities can be differentiated in small groups or individually.

Students Play in groups of 3-6. This game is on
 Teachers Pay Teachers.

EXAMPLE OF STUDENTS PLAYING:

  Example of students playing first to One Whole.  The bonding sheet helps the students avoid errors.  When they get to the tenth square, there will always be a friendly number of ten.    

They could also play first to zero starting at 100 and writing backwards.

If they are writing decimals the bonding sheet will help them understand when they write .10 or ten hundredths-ten hundredths equals 1 tenth.  When they get to 100 hundredths 

 they will understand 100 hundredths equals 1 whole.   I would also ask questions after this activity to check their understanding. 

 We played First to 100 to practice counting,  noticing bonds of ten, and working in teams.  Then we used it to help with math facts writing multiples (depending on the math fact they are struggling with).  When they say the number, they are practicing subitizing. It's amazing how many of my students struggle with counting the dots quickly.

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