## What Do You Do in Your Math Intervention Group?

So, I have a math intervention group.  I have done intervention lots of ways…and the thing is, there are always core things that kids struggle with.  Those things without a double are always addition, subtraction, and multiplication facts.  Next, they struggle with the standard regrouping algorithm.  And, why do they struggle? BECAUSE, of course, no one sits with them at home to help them learn these things if the concepts don’t sink in during school time.

Enter me.  I have been working with some students the past few weeks on subtraction regrouping…with success!  Here is what I have done, and what I have discovered.  First of all, several of the intervention students were able to regroup UNTIL they had to regroup across zeros.  They weren’t sure what to do when they had to borrow two places over.  How did I figure this out you ask?  Well, with my group of four students, I gave them a worksheet. (gasp!  a worksheet??!!) Yes, I gave them a worksheet and had them work a few and checked to see which ones they were getting correct and which ones they were missing.  I would have them work one problem and hand me the sheet to check.  This way they were getting immediate feedback.  During this time, I realized that they weren’t getting the answers right unless they borrowed across zeros or had to borrow two places over.  I used and am so thankful for Super Teacher Worksheets subtraction worksheet generator!  This conveniently allowed me to print a new worksheet (complete with answer key) when I felt they needed practice.

Now when I realized they needed help with regrouping across zeros, I realized there was a regrouping misunderstanding.  So, I used the Singapore math number discs method to show them what was happening when they were regrouping.  After showing them and having them do one with me, the next day they performed a lot better on their subtraction regrouping problems.  I have a SMART board lesson and worksheets if you would like some for students to practice with.  The grid is already made for the students…these however do not have seven digits like the worksheet above.

A few other things I did to help the students think about the regrouping process were.

1.  Say this little rhyme…”More on the floor, go next door, and get 10 more”.  This way they would always know they were bringing ten over…not 9, not 8.
2. Sometimes when students want to skip over a place value column, I would describe it as driving in traffic.  Your car doesn’t just fly over the other column, it has to change lanes one at a time…it can’t be a helicopter.
3. Another idea I mention is place value columns in relation to the drawers in a cash register.  If you cash in your \$100 bill for others, you trade it in for 10 \$10, then you trade in the \$10 for 10 \$1 bills.

Try these things and soon you will be on your way to having expert subtraction regroupers!

## Could You Be Hurting Your Students by Using This?

Recently, I started doing math intervention with a small group of students.  I noticed when given a mat similar to the one above that the students didn’t really understand all of the wording beneath the boxes.  They heard the word thousand and they were completely confused.  This caused them to begin looking for the thousands box when hearing a number called out orally.  I also had students holding the mat vertically and writing the numbers vertically.  For this lower group of students, I finally just pulled out the white boards and had them begin writing numbers by filling in blanks such as this…

_____,  _____  _____  _____,  _____  _____  _____

This worked out better with much less confusion after I explained how when coming to a comma that you say the name of the period such as thousands or millions.  Show students how to cover up everything on the outside of the comma and just say the three digit numbers.  This will give students a starting point.  Most students can say three digit numbers in third grade and beyond.  If you teach kids that there is a pattern to being able to say numbers, they will feel so empowered.

In case you are having difficulties with this in your classroom, this product below may be just what you are looking for!  It completely explains how to verbalize large numbers with great ideas for anchor charts like below.

After using doubles and tens facts to learn one more and two more than all of those sums, that only leaves students with two facts to learn!!!

I allow students to tell me ways that these two facts can be easy to learn for them.  Most students say that 3+6 is 9 so it is close to a ten fact.  Some may be more comfortable with 3 +5, but after spending time talking about patterns with students, they will easily be able to discuss a way to get to this fact using a known fact.   The thing that is uncomfortable about using 6+4 is that students have to go backwards and it is uncomfortable for them to go backwards in counting.   Students favor going forward…cause more is better (like the commercial! :))  Also, 8+5 to me is an oddball.  I can think of no easy way to get to this fact, but most students will say that 8 + 5 is close to 8+4 which is 12 so they know that 8+5 makes 13.  Other students will say they know 8+2 is 10 so they can count up 3 more.  I really don’t like that they have to count up 3 more, but at least it is better than counting up 5 from eight.

I will have to say that after working with intervention groups with all of these fact strategies, their answers aren’t as immediate as I would like, and at times they still use their fingers.  I believe they still use their fingers because it is comfortable to them—more comfortable than thinking.  After a strategy is learned it is imperative that they still practice with flash cards so that the facts remain fresh in their minds.  I don’t work with a student population that readily has parents practicing with them at home on flashcards so the only extra practice they get is with me.

I plan on posting some of the materials I used to practice facts with the kids soon.

You may also like:

If you have been following the previous posts, then you will see the progression of teaching number facts strategies.  Nearly the last part of teaching addition facts focuses around doubles and doubles plus 2.  I think this is one of the hardest strategies because kids may not readily see the double when it is two numbers away. With a little thinking and prodding, however, they will see the fact without using their fingers.  Line the numbers up side by side so that students can see examples of both sets of numbers–the helping fact and the double plus 2.

Again, when having students recognize patterns and see relationships, I like to write them out of order so that students don’t say that the numbers are counting by 2’s etc.  If students struggle to see the patterns, underline numbers to help them focus on what you want them to see such as underlining the second addends on both sets of equations.  Then underline the sums on both sets of equations.  Step back for a few moments and let the prolonged silence aid students in thinking about the relationships in the two sets of numbers.  Give students time enough to generalize about how doubles can be a helping fact.  * Note that students have already learned sums of 10 and 10s plus 2 more so they have strategies for 5+7, 4+6, and 6+8.

After this, students only have a few more facts to learn!!

You may also like:

Thank you Erin Cobb!  Frames Courtesy of Lovin Lit.

## You’re Kids Aren’t Learning Their Addition Facts? Try This…Part 5

(Thank you Erin Cobb from Lovin’ Lit for the pretty border!)

Now after I have taught everything that I previously blogged about in Parts 1, 2, 3, and 4, which includes tens and tens plus one.  Learning the sums/bonds of 10 is the foundation for this discussion.  One of the tens plus 2 will already have been learned because it is a double, but there is no harm in learning multiple strategies to reach one fact.  Also, doubles plus two facts will be learned later and doubles plus two will also give students a strategy to reach 7+5=12 and 5+7=12.  Allow students to recognize this on their own when you reach that lesson.  The more ownership students can have of the strategies without you telling it to them, the more they will remember the strategies and feel smarter for being able to discuss the strategies.

Again when you introduce these facts write them out of order on the board.  Step back, wait, have children quietly look at the number facts and find relationships or patterns in their head.  I use the Number Talks strategy and have them put their thumb on their chest when they find a pattern.  This keeps everyone attentively looking for more patterns without the dramatic hand raisers flailing their arms in the air.  If students say that they see lots of tens and twelves acknowledge this and then ask students to look for more.  Eventually you will get what you are looking for if you have the foundation built from the previous lessons.  If no students say that one of the addends goes up by 2 and the sum goes up by two, offer a hint by underlining these numbers so that they are focusing their attention there.  Follow this up by fact (flashcards if you prefer) practice over the sums they have just discovered a strategy for and over previously learned facts.

Happy Thanksgiving!

You may also like:

## Have You Taught Multi Digit Even and Odd Numbers Like This?

I thought I KNEW how to teach even and odd numbers until I saw this!  Knowing that our third graders always miss the simple skill of even and odd numbers with two and three digits, I thought I would target this misconception.  I told them that even numbers have partners and odd numbers have a lonely someone left out.  To teach even and odd numbers,I asked if several small numbers like 4, 5, 6, 7, 8 were even or odd and drew pictures of counters to ask if they had a partner.  With this idea, I asked if 227 was even or odd.  I told the kids to write this down on a scrap of paper and cover it over with their hand so no one could see what they wrote.  The teacher and I surveyed the room as kids secretly moved their hand.  Just about half of the class thought it was even and half thought it was odd.  Thinking of the 8 Mathematical Practices, I didn’t want to spill the beans.  I wanted the students to really think about whether this number would come out with an even number of partners.  I told them to start drawing 227 counters on their paper to see if each counter would come out with a partner.  I knew this could be a tedious task, but to my astonishment,  I saw a few kids actually drawing base ten blocks….WOW!  I couldn’t believe they had thought of this.  I had never thought of drawing base ten blocks!!!

Even and Odd with Base Ten Illustrations

This student started drawing counters but when he realized this would take way too long, he drew base ten blocks.

This is my favorite illustration of student work because the student drew the place value chart and plainly matched up each block with a partner

Through all of their work building numbers in second grade, they were so comfortable and flexible with base ten blocks, they actually saw them as tools!!  After we did this little exercise, which took about 15 minutes, we resurveyed the class and only 3 of the 25 students still thought the number was even.  Success through taking the time for students thinking!

## How Do you Teach Regrouping with Understanding?

Counting you ask?  Yes, we spent time counting and looking at patterns in numbers.  I know it is in the standard so that is part of why we counted, but counting is so much more important than teaching because it is the standard.  How can students reason about whether their answer makes sense if they can’t count?  Reasoning about math is in the mathematical practices several times.  Students who can’t count, can’t estimate and can’t round because they have NO idea about where the number comes in the whole sequence of numbers.

Second graders last year solved a CGI word problem each day while they were learning addition and subtraction.  Students spent several weeks using base ten blocks to solve their addition and subtraction regrouping problems.  When students weren’t permitted to use the actual blocks, we prompted them to draw illustrations of the blocks to help them solve their problems.  Even after students were shown how the traditional algorithm worked with their blocks, most of them tended towards drawing a picture of the blocks to solve the problem.  Most were successful doing this.  I was satisfied with this progress because I knew in 3rd and 4th grade that they would again have an opportunity to learn the traditional algorithm and other addition/subtraction strategies.

So here is how we are beginning with the kiddos in 3rd and 4th grades this year to teach addition regrouping.  The kids are still given the opportunity to use blocks if needed to formulate understanding.  Now I know that in showing them how to regroup the kids aren’t really “discovering” or “constructing” the algorithm themselves, but they are gaining an understanding.  I just don’t think we have enough time in the year for the kids to discover everything and they must be shown some things.  I haven’t arrived at that place yet where I think in CGI utopia…maybe I will get there someday??  (Don’t get me wrong, I find value in CGI)  For right now the kids are getting this method of teaching addition regrouping and making sense of it.  I’m happy and the kids are learning.

Now what I’m about to show you is the students’ first experience with regrouping like is pictured above.  It isn’t cute at all…not worthy of for sale anywhere…but it is real and handwritten.  To make it on a handwritten page was just so much faster than doing it on computer so it is what it is.  I wanted to create columns so the students wouldn’t get their numbers confused.  This worked well.  I didn’t have the kids put pluses between the numbers like true expanded form to keep them from confusion later on when we do subtraction regrouping similar to this.

We discovered that students had a difficult time in the hundreds column when they had a number regroup to the thousands place.  They weren’t used to putting two numbers together that weren’t zeros so this seemed to confuse them.  If we had three digit adding to do over, we would have the kids include a thousands column so that they could regroup their thousands there at first until they made the connection that they could put two digits other than zeros in the left hand column.  In other words, we would have them add one column more than the number of digits that there were in the number.  For example…

Later on last week, we taught the kids to regroup without the columns drawn and without the numbers being decomposed into hundreds, tens, and ones.  We continued to have the kids draw the arrows and to estimate their answer.  It was rocky at first and about half of the class got regrouping with numbers written in standard form (just normal).    They will be working on regrouping again early next week.

## Teaching 3 Dimensional Solids?

Check the trash first!  Whenever teaching  dimensional solids, I look around the school building for large boxes that may be thrown out.  Especially in the teacher workroom, there are always bulletin board paper boxes, toner boxes etc. that are being thrown away.  This is where I have found some of the best trash for treasure pieces for my 3D solids collection.  When I have found one, I wrapped it in colored bulletin board paper with the name on each one to help students have a constant visual of prism pieces.  At the time I teach solids, I also have the students bring in items they find at home that may be prisms, cubes, spheres, or other solids.  They relish sharing their found items with the class.  When they share them with the class, they must ask the students how many faces, edges, and vertices there are.  Students get extra credit for bringing in solids.  The best solid that I ever had a student bring in was an almost perfect triangular pyramid made out of rock! Below are pictured my recycled trash 3D solids.

## Could This Be the Reason Students Confuse Many Word Problems?

After years of seeing students mix up math operations in word problems, I have finally figured out how to help students understand what operation to use in word problems.  This little word is causing students much of the confusion–EACH.  Haven’t we all taken for granted that students understand what this word means.  The word ‘each’ is in nearly every multiplication and division problem, but many students don’t know what it means–every one in the group.  If we teach students to read a word problem and replace the word each with its meaning, every one in the group, students somehow have a light bulb experience.

In conjunction with teaching students to understand the word each, also asking them questions about the problem helps facilitate understanding.   For example when you ask, “Is this a joining or a separating situation,” students start to  make sense of word problems.  Students generally understand that words like altogether and in all mean that they are joining groups.  The word total may need to be taught as a word that means in all, but  total isn’t a difficult term for students to become comfortable with.

To help students further differentiate between multiplication and addition, ask questions like:  are we adding the same amount over and over or are we adding two different sized groups?  If the answer is adding the same amount over and over, then multiplication is repeated addition of equal sized groups.  If students are confusing division and subtraction, ask, “are we subtracting different amounts or are we subtracting the same sized amounts over and over.  If the answer is subtracting the same amounts over and over, then teach students that division is repeated subtraction of equal groups.

## Do your students know what a group is? or what a group of ten is?

I’ve been wanting to incorporate counting collections at school for a while, but I haven’t had the understanding of how to organize counting collections effectively.  I recently attended a colleague visit where a kindergarten teacher showed the procedures she used for teaching counting collections.  So, after attending this training, I initiated counting collections at our school with the 1st and kindergarten teachers.  In the meantime, one of the kindergarten teachers shared with me at school that she realized her students didn’t know what a group was– much less know what a group of ten was.  She began her instruction with just discussing groups and what kinds of things can come in groups.  They talked about groups of three, four, or six etc.  They made groups of different amounts in  whole group discussion under the document camera.  Students were able to have a foundation to understand a “group of ten.”  Then the teacher was able to place a different amount of counters underneath the camera to ask if she had a group of ten.  First, she placed less counters under the camera like 8 and asked if she had a group of ten.  After that she placed more counters under the camera, like a group of ten and 3 more, and asked if she had a group of ten.  Doing all of these seemingly common sense-ical counting procedures before hand led to a much more successful counting collections lesson for students to count their collections effectively.  These are the rudimentary things that no college or textbook teaches you!