Teaching Multiplication for Understanding

One thing I love about the new math standards is teaching for depth of understanding.  It makes so much sense to teach fewer things in depth, than a lot of things with very shallow coverage.  In third grade we spend a great deal of time on multiplication, and students now develop a real understanding of what multiplication is and how it works, rather than just memorizing facts.  Below are some of the strategies that I teach students to use when looking for the product of an unknown fact.

1.  Draw equal groups.  Students model equal groups by drawing a circle of each one, then putting the correct number of objects in each group.

2.  Skip count.  To find the product of 3 X 4, count three fours: 4, 8, 12.  Teach students that these numbers are multiples of 4.

3.  Draw equal jumps on a number line.

4.  Relate multiplication and addition.  3 X 4 = 4 + 4 + 4 + 4

5.  Make an array.

6.  Use the Commutative Property of Multiplication.  If you do not know the product of 3 X 4, perhaps you do know the product of 4 X 3.

7.  Use doubles.  To find the product of 4 X 4, think of the product of 2 X 4 and double it.  To find the product of  6 X 4, think of the product of 3 X 4 and double it, and so on.

8.  Use the Distributive Property of Multiplication to break apart larger factors into smaller factors.
5 X 8 can be thought of as (2 X 8) + (3 X 8).

9.   Make a bar model.

I have developed several items to help my students master both the concept of multiplication as well as multiplication facts.  The products shown below, as well as others, are available in my Teachers Pay Teachers store.

Multiplication: Adding Equal Groups Power Point

Mutliplication: Adding Equal Groups Printables

 

 Big Multiplication Flash Cards

Distributive Property of Multiplication

Multiplication Facts Practice: X8

Ideas for Teaching Rounding to Young Learners

1.  Use a number line.  If you are rounding 44, make a number line that begins with 40 and ends with 50.  Put a red line on the number that is halfway between 40 and 50.  Circle 44.  Which side of the line is on?  Is it closer to 40 or 50?  Circle the answer.  Have students practice and practice until they can do the steps mentally.

 

2.  Make a number line on the floor using masking tape and have students use their bodies.  Have them stand on the number line where their number fits.  Then decide which ten it is closer to.

3.  Make “rounding mountains”.  Draw number lines that are shaped like mountains with 5 at the peak, 0 at the bottom on the left, and 10 on the bottom at the right.  Students think of a train trying to cross the mountain.  If it makes it to the top, it will coast down the other side.  If it doesn’t make it to the top, it will slip back down to where it began.

4.  Use place value blocks.   Give students tens strips and one cubes.  Have them show the number 44 using 4 ten strips and 4 ones cubes.  Then tell them that ones are no longer allowed and they need to show the number using only ten strips.  Would they be closer to the actual number if they used 4 ten strips or 5 ten strips.  Do this repeatedly and help them to see that when they have 4 or fewer ones, they stick with the number of ten strips they are already displaying.  When they have five or more ones, they need to trade them in for another ten strip.

5.  Use the picture book Coyotes All Around by Stuart J. Murphy to help students understand why rounding and estimating is helpful.

6.  One thing that has really worked for me is using the “Strong Man” of rounding and the “Wimpy Guy”.  I created these characters to help my students decide whether the digit in the place being rounded to stays the same or gets pushed up to the next number.  After they have spent some time with number lines and are pretty good at using them to round, it is time to switch over to doing the steps in your head.  I have students underline the digit in the tens place if they are rounding to the nearest ten.  They then look at the digit behind it to see if it is a “Strong Man” number-5,6,7,8,9 or a “Wimpy Guy” number-0,1,2,3,4.  A strong man number will push the digit up to the next number.  A wimpy guy number isn’t strong enough to do that and the number will stay the same.

I have created two power points and set of printables that provide lots of practice with the “Strong Man” and the “Wimpy Guy”.  They are available here:

Rounding is a skill that takes a lot of practice to develop proficiency.  I have found that my kiddos master rounding to the nearest ten and are doing great, then when I introduce rounding to the nearest hundred, I have mass confusion!  Lots of practice is the cure for this malady.  Once I have finished the rounding unit, I do not leave rounding behind.  I have my students round numbers to the nearest ten and hundred almost every day.  They soon become masters of rounding!

Happy Teaching!

First of all, a big thank you to all current military personnel and their families, as well as all veterans, on this Veteran's Day.  I am so grateful to all of you, and grateful for this great nation.  I am so proud of my dad for his service during the Korean War.

The journey into Common Core Math Standards has been interesting, to say the least.  It has been fustrating, as we have tried to shift gears in the way we think about math, and the things we expect of students.  We are using "GO MATH!" for the first time this year.  My kiddos have had a struggle with all the problem solving.  We have not, in the past, expected them to THINK so much!  They are beginning to get a little better at it.  I know it will be a process.  I am anxious to see how our American kids, overall, do with math in the next few years.  There are some things about the Common Core standards that I really like.  I think the shift toward more problem solving is good.  I think that emphasizing fewer topics and going more in depth is good.  I have to admit I'm a little worried about some of the things that seem to have been left out.  Topics that were a big part of our third grade math curriculum previously, seem to have just disappeared. . POOF!  We no longer directly teach place value, for instance.  Maybe with the emphasis in first and second grade, there will no longer be that need. . . .we shall see.
I was asked a question today on my Teachers Pay Teachers page that is a very good question, indeed.  I created a quadrilaterals unit, based on the Common Core Standards.  A teacher who bought that unit wondered why I included trapezoids, rectangles, squares, rhombi, but not parallelograms.  The answer is that the word parallelogram is not used in the Common Core.  I don't know if that's good or bad.  It's one less definition to remember, but also one less classification to use in making sense of quadrilaterals.

 We are implementing the common core standards for math this year AND have a new math program. We are having to take math one lesson at a time as we watch this unroll and try to figure out how everything is going to work together.  It's a little unsettling.  In the past, we've had our math units and lessons mapped out for the year, and have had a pretty good idea of how much time we will need to spend on each.  Of course, we made adjustments as each unit progressed, in order to provide the instructional and practice time that students needed. 
  I was dismayed to see that the new math program taught rounding to nearest ten and hundred in lesson 2 of chapter 1.  I'm convinced that people who write text books don't teach children.  Really?  They think kids who have never heard of rounded numbers can master rounding to tens and hundreds in one lesson? And the second lesson, no less?   Laughable! Needless to say, that one lesson stretched over a couple of weeks!

  I've tried many different approaches to teaching rounding over the years.  No matter how you approach it, it takes some time for kids to master.  It seems that once they get it, they get it.  But until they do, you go through it over and over.  In desperation, during that first week of school, I turned to something I started last year, and then I expanded on it.  The Rounding Robot were born! I introduced my kids to two of my creations--the Strong Man and the Wimpy Guy of rounding.  Using two different power points, classroom posters, and a set of practice worksheets, I finally got through to those kiddos who just didn't get it. 
  My Rounding Robots powerpoints and printables are available here:
http://www.teacherspayteachers.com/Product/Rounding-Robots-Powerpoint
http://www.teacherspayteachers.com/Product/Rounding-Robots-Printables
http://www.teacherspayteachers.com/Product/Rounding-to-the-Nearest-Hundred-with-the-Rounding-Robots

Those Pesky and Important Math Facts

Addition Facts Mastery

Is there a third grade, or even second grade, teacher out there who hasn't wished that every one of your students came to you already having memorized basic addition and subtraction facts?  Having these facts mastered is vital to success in elementary math, but also for success in algebra and advanced math courses throughout the school career.  Teachers of beginning algebra classes often report that the largest barrier their students face, is their lack of fluency with basic math facts. Fluency with facts requires practice. Lots of practice, for most kids.

One of the most effective and efficient ways of assuring basic facts mastery is to have a system of daily timed

assessments that students progress through. Upon mastering one family of facts, they move on to the next.

Teaching students to use strategies, rather than just rote memorization, makes mastering the basic facts much easier and faster. I developed my system of daily timings around a set of addition strategies: zero property, add 1, add 2, addition doubles, doubles plus one, doubles plus two, add ten, and add ten subtract one.  Several of the facts can actually be solved using more than one strategy. But probably the most important strategy that students need to learn is the commutative property of addition.

My addition fact mastery system is available for free download at Teachers Pay Teachers.  http://www.teacherspayteachers.com/Product/Addition-Fact-Mastery-Worksheets

There are 10 addition assessments in this packet, grouped by strategy. The first 9 assessments are 24 problems, intended to be completed in one minute. 100% accuracy must be achieved in one minute in order to move on to the next assessment. Each assessment is a half-page. I have found it easy to save paper by re-using copy paper that has had one side used. Rather than discard extra copies of assignments, etc., I save these and run my math timings on the backs of them. The final assessment, Addition Review, has 100 problems.  Students are allowed five minutes to complete it, and can pass it off with 95% accuracy.

Along with the timed assessments, I have included a record-keeping chart so you can easily track student progress, and practice pages of 100 problems each that focus on each strategy.  These are great for homework.  Enjoy these timings and practice pages.  Here's to making our math life  a bit easier!