Multiply on Your Fingers 6 x 6 through 10 x 10

Multiplying by nine using your hands

Multiplication Strategies

I am teaching multiple strategies to assist in solving multiplication problems.  We have solved problems using the strategies described below.  Please encourage your child to use these strategies when solving multiplication problems.

REPEATED ADDITION
In this strategy, students see the multiplication problem as an addition problem.  For example, 6 x 8 can be solved by adding 6 to itself 8 times, or by 8 to itself 6 times.  Your child's work may look like this: 
  6         8
  6         8
  6         8
  6         8
  6         8
  6       +8
  6        48
+6
48

This strategy works well with single-digit multiplication and some two-digit problems.  It is not going to work for all problems.

ARRAYS
Physical arrays or models are another effective means to solving multiplication problems.  This is a pictorial representation of the problem.  In the problem 6 x 8, students will draw 6 rows and place 8 objects in each row.  This is how it would look:
1 ********
2 ********
3 ********
4 ********
5 ********
6 ********
Once the student has drawn the array, all that's left to do is to count the total number of obects (48) to determine the answer.  The student could also solve the same problem using 8 rows with 6 objects in each row.

NUMBER LINE
This strategy requires students to be strong skip counters and to utilize addition strategies.  Students draw an empty number to assist in solving the problem.  Here is how this would look when solving 6 x 8:

The student made 6 jumps of 8 and ended at 48.  This could also be done with 8 jumps of 6. 

Multiplication

We have started learning our basic multiplication facts!!!  The program I am utilizing is called "Times Tables the Fun Way!"  This program teaches the students stories and songs to assist them in remembering some of the most commonly missed facts.  Here are the facts and the stories we have learned thus far:
3 x 3 = 9  the three blind mice
3 x 4 = 12  and 4 x 3 = 12 the cheerleaders
8 x 8 = 64 the snowmen
7 x 7 = 49 the soldiers
4 x 4 = 16 the hang glider
6 x 4 = 24 and 4 x 6 = 24 the magic pond
8 x 7 = 56 and 7 x 8 = 56 the trampoline
6 x 6 = 36 the thirsty sixes
3 x 6 = 18 bigfoot
6 x 8 = 48 the birthday cake
3 x 7 = 21 butterfly tree
7 x 4 = 28 fireman
7 x 6 = 42 high jump
8 x 4 = 32 pigs
Your child should be able to retell these stories. We have also learned the zeros, ones, twos, fives, and nines.  Your child should be familiar with the commutative property, identity property (when you multiply by 1, the answer is always the other number), and the zero property.  They should also know the terms factor and product.

Empty Number Line Strategy

The empty number line strategy helps students visualize the "counting back" nature of subtraction.  This strategy allows students to break the problem down into more manageable steps and to solve easier problems.  This method can take up a LOT of space!  Students continue to improve their number sense by utilizing this strategy.  It also allows students to solve from left to right.

Invented Strategies - Partial Differences

In this method, students use the expanded form of numbers to create simpler subtraction problems and avoid regrouping.  One of the most common problems students face in solving problems is that they want to begin on the left and work to the right.  In the traditional regrouping method, this is not possible and leads to errors.  In the partial difference method, students can work left to right, leading to fewer errors.  The students have enjoyed this method because of the exposure to negative numbers.  If an answer is a negative number, the student puts a minus sign in front of it.  If the answer is a positive number, the student puts a plus sign in front.  Students must be flexible in their thinking and be able to do mental computations.

Invented Strategies - The "Matthew" Plan

On the first day of teaching subtraction with regrouping, one student began explaining his own way of solving problems so that he didn't have to regroup - he could use mental strategies instead.  I listened intently as he showed us how he worked through a problem.  At first, I thought it was a fluke!  Then, I realized this strategy would work well with almost any subtraction problem.  The students have loved Matthew's method!  In Matthew's strategy, he makes the initial problem easier to solve by forcing his first answer to be a "nice" number.  From there, he uses several different strategies including counting up, counting down, and mental math.  This plan works best with 2 and 3 digit numbers because the subtraction becomes difficult with more complex numbers.