Friday, October 16, 2015

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.


Friday, October 2, 2015

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!