A Multiplication "Trick" To Know When You Are Multiplying by 11

Knowing how to do math does NOT require magic; although, sometimes working a problem can appear to be done magically.  This week I want to talk about multiplying by eleven. Before I demonstrate the "trick", I have to get on my soap box for just a moment. In my humble opinion, all students should know their times tables through 12 even though the Common Core Standard for third grade says through 10 x 10. Remember, Common Core is the minimum or base line of what is to be learned. In Algebra, I insist that my students know the doubles through 25 x 25 and the square roots of those answers up to 625. It saves so much time when we are working with polynomials.

Now to our our amazing mathematical "trick". Let's look at the problem below which is 231 x 11.

 

First we write the problem vertically. Next, we bring down the number in the ones place which in this case is a one. Now we add the digits in the ones and tens place which is 3 + 1 and get the sum of four which is brought down into the answer.


Moving over to the hundreds place, we add that digit with the digit in the tens place 2 + 3 and get an answer of five which we bring down. Finally, we bring down the digit in the hundreds place which is a two. The answer to 231 x 11 is 2,541.

Now try 452 x 11 in your head. Did you get 4,972? Let's try one more. This time multiply 614 by 11. I'm waiting...... Is your answer 6,754?

Now it is time to make this process a little more difficult. What happens if we have to regroup or carry in one of these multiplication problems?

We will multiply 784 by 11. Notice that we start as we did before by just bringing down the number in the ones place. Next, we add 8 + 4 and get a sum of 12. We write down the 2 but carry or regroup the one. We now add 7 + 8 which is 15 and then add in the 1 we are carrying. That makes 16. We bring down the 6 but carry the 1 over. We have a 7 in the hundreds place, but must add in the one we are carrying to get a sum of 8. Thus our answer is 8,624.

Let's see if you can do these without paper or pencil. 965 x 11 768 x 11 859 x 11 After working the problems in your head, write down your answers and check them with a calculator. Try making up some four and five digit problems because this is a non-threatening way to have your students practice their multiplication facts. Have fun!

Hands-On Math Using FREE Milk Lid Jug Lids

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Start saving milk jug lids because there are countless hands-on math activities you can do in your classroom using this free manipulative. Here are just four of those ideas.

1) Sort the lids by various attributes such as:

• Color
• Snap-on or Twist-on 
• Label or No Label
• Kind of edge (smooth or rough)

2) Let the students grab one handful of lids.

• Ask the students to count the lids.
• See if the students can write that number.

3) Make a pattern using two different colors of lids.

 

• Identify the pattern using letters of the alphabet or numbers. The pattern above would be an A, A, B pattern or a 1, 1, 2 pattern.

• Now ask the students to use more than two colors to make a pattern

• Once more, have the students identify the pattern using alphabet letters or numbers.

4) Decide on a money value for each color of lid. (Example: Red lids are worth a nickel, blue lids are worth a dime, and white lids are worth a penny.) Put all of the lids into a bag and have the students draw out four lids. Have the students add up the total value of these four lids.

• Use play money (coins) to have the students show the value of the lids. 

• Have the students practice writing money as either a part of a dollar or as cents.

• Another idea is to have the students find all the combinations of lids that would equal a nickel or a dime or a quarter.

The resource, Milk Lid Math, contains over 15 hand-on ideas with numerous activities listed under each idea. The activities may be used with a whole group, small groups or as center activities.

Using Bloom's Taxonomy on a Geometry Test

As one of their assignments, my college students are required to create a practice test using pre-selected math vocabulary. This activity prompts them to review, look up definitions and apply the information to create ten good multiple choice questions while at the same time studying and assessing the material. Since I want the questions to be more than Level 1 (Remembering) or Level II (Understanding) of Bloom's Taxonomy, I give them the following handout to help them visualize the different levels.  My students find it to be simple, self explanatory, easy to understand and to the point.

Level I - Remembering


 What is this shape called?



Level II - Understanding

Circle the shape that is a triangle.



Level III - Applying

       Enclose this circle in a square.




Level IV - Analyzing

What specific shapes were used to draw the picture on your right?

Level V - Evaluating

How is the picture on your right like a real truck?  How is it  different?

Level VI - Creating

Create a new picture using five different geometric shapes. (You may use the same shape more than once, but you must use five different geometric shapes.)

As teachers, we are only limited by our imagination as to the activities we ask our students to complete to help them prepare for a test. However, we still need to teach and provide information so the students can complete these types of tasks successfully. With the aid of the above chart, my students create well written practice tests using a variety of levels of Bloom's. When the task is completed, my students have also reviewed and studied for their next math exam. I consider that as time well spent!

FREE

If you would like a copy of the above chart in a similar but more detailed format, it is available on Teachers Pay Teachers as a FREE resource.

Also available is a simple math dictionary. This 30 page math dictionary for students uses easy and clear definitions as well as formulas and examples so that students can learn and understand new math words without difficulty or cumbersome language. Most definitions include diagrams and/or illustrations for the visual learner. Over 300 common math terms are organized alphabetically for quick reference.

Explaining the Difference Between Odd and Even Numbers

Sometimes we think everyone knows the difference between an odd and even number. When I was teaching my remedial math college class, we were learning the divisibility rules, the first of which is that every even number is divided by two. I wrote the number "546" on the board and asked the class if this was an odd or even number. I had one student who disagreed with the group answer of even. I asked him why he thought the number was odd, and he replied, "Because it has a "5" in it. " It was obvious this student got all the way through high school without a clear understanding of odd and even numbers. So the moral to this story is to be sure to discuss the difference between an even and an odd number with your students.

A good definition for an even number is that it can be put into groups of two without any left over, like giving each person a partner. But when you have an odd number of things and put them into groups of two, one will always be left out.

Try this approach. Make your hands into fists and place them side by side as seen in the illustration. Say a number. Now count, and as you count, put up one finger for each number said, alternating between hands, with fingers touching.

For instance, if you said “3”, you would count one, (left pointer fingerup) two, (right pointer finger up and touching the other pointer finger) three, (left middle finger up). Three is an odd number because one finger does not have a partner to touch.

Here is the sequence to use if the number given were "2". Two is an even number because each finger has a partner.

Repeat this several times, giving the students odd as well as even numbers. By always having a concrete visual (their fingers) will help the kinesthetic and visual learner to "see" the odds and evens.

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Activities such as this can be found in a math booklet entitled Number Tiles for The Primary Grades.  It contains 17 different math problem solving activities that extend from simple counting, to even and odd numbers, to greater than or less than to solving addition and subtraction problems.