Skip Counting, Multiplication, And How To Get From One To Another.

 

As I have been doing more research on number lines, I realized that many of my students get to high school with the ability to skip count but didn't know their multiplication tables.  I've accepted that skip counting might be the only way they know but I've often wondered why they didn't make the jump from one to the other.

Skip counting is often the first thing students are taught in their journey into multiplication.  From there , they move on to learning multiplication and multiplication facts but some students never make the jump.

It is never too late to do things to help students make the jump from skip counting to multiplication.  These steps can be done in middle school or high school as part of the scaffolding activities. First, think about using visual representations such as number lines, counters, or arrays to help make students see how skip counting and multiplication is related since both are a form of repeated addition.

Another activity using counters, cubes, or blocks is to have students arrange these manipulatives to represent skip counting. So if a student is skip counting by three's, arrange the manipulatives in groups of three so they count by three's, then they can ease over to the idea of counting the number of groups to arrive at the total. Both ways get the student to the total but one is strictly addition and the other ways shows the idea of groups times number in group gives total.

Look at having students explore patterns and extensions associated with skip counting.  For instance, list the pattern for four's skip counting and leave blanks such as 4, 8, ____, 16, _____, etc.  Extend this to the idea that one 4 is 4, two 4's is eight, so three four's is 12 which is the missing number.  This helps students make the jump from skip counting to multiplication.

Throw in some questions which require students to use skip counting in a real life situation such as buying 5 packages of 12 screws so a student might do 12, 24, 36, 48, 60 or 5 x 12 is 60. This provides a real life connection between skip counting and multiplication.  

Finally, give students a chance to practice, practice practice.  Provide students the opportunity to play games, make posters, and other methods to give them a chance to practice. Start with easier problems and move to problems that are more complex.

These are just a few ways to help students move from skip counting to multiplication.  Once students have multiplication down, it is important to include continued practice.  Let me know what you think, I'd love to hear.  Have a great day.

Multiplication signs

  Yesterday, while I wrote about division, I realized many of my students arrive in high school missing some base knowledge for operations.

This lack of knowledge creates a major misunderstanding when students begin taking algebra or pre-algebra.

Too many students arrive in high school thinking multiplication is always represented by the "x".  So if you are multiplying numbers only such as 8 x 5, its is not bad but once we add variables into it like 2x + 3, confusion arises.

I've had student turn in papers with 2xx+3 meaning two times a number plus three.  I have to  teach them 2x means two times a number.

I've often wondered why we do not introduce the idea that multiplication can be expressed using a symbol other than x.  Why are we not using the * or dot to indicate it.  Many of my incoming students have trouble with 2(x + 3) because its not written as 2 x (x + 3).

I have not found any real explanation for why the x is used vs the dot in elementary.  I've read comments regarding using the x in elementary as it really doesn't matter.  I think it does or at least it does by the time you get to 5th grade.  I think its important to expose students to the different ways of showing multiplication before they arrive in high school.

Even in elementary, we can show students multiplication in at least three different ways, 3 x 5, 3 * 5, or 3(5) so they become used to using the other ways.  Unfortunately there is one problem with using the dot.  When working with vectors and scalars, you have a dot product which might confuse people but you don't usually get that until you are much higher in mathematics.

Is it practical to teach the three ways to multiply in elementary?  I believe it should since its almost like a progression and each method could be incorporated each year beginning in 3rd or 4th so by the 7th grade, students are familiar with the symbols and upper level teachers can focus on teaching other things. 

I don't know if this is possible but I do know it would make it easier to introduce new concepts in high school if I do not have to backtrack by teaching the various forms of multiplication signs.  Let me know what you think?