3 Ways To Master Multiplication Without Memorizing

By middle school students are expected to know their multiplication facts 1-12 fluently.  However, many students can’t memorize all of them.  In fact, students who are good problem solvers are often the students who don’t memorize, but rather know them through other methods such as modeling, repeated addition, and working from facts they do know.

Modeling

A common multiplication fact that many students struggle with is  8 x 7.   To get a deeper understanding, start with modeling this with pictures. For example, there are 7 soccer teams with 8 players on each team.   Have your child count until they get 56 or a total of 56 players.

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Repeated Addition

Practice with modeling should lead to the idea of repeatedly adding the same number.  Multiplication is repeated addition.  After modeling over and over, students start to realize they are doing this:

8 + 8 + 8 + 8 + 8 + 8 + 8 = 56      OR     7 + 7 + 7 + 7 +7 + 7 + 7 + 7 = 56

I tell me students this is fair game and to add every time if they need to.

Already Known Multiplication Facts

Repeated addition leads to another strategy students can do without having to memorize all facts.  Let’s say your child knows their 5 multiplication facts well.  They can use this knowledge to count to the others they struggles with.  Let’s use 8 x 7 again.  If they know 8 x 5 = 40 then they just need two more groups of 8 to get to 8 x 7.   Most students get faster at doing this in their heads.  I will have students make flashcards like these with that facts they struggle with.

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Here is another example:

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5 Tips To Raise Your Child To Like Math  

Having a good attitude is essential in being successful with math!  Start now and use these strategies to raise your child to not HATE math but LIKE it!

1. Apply It; Use It–  A topic is never interesting if it doesn’t have a purpose.   For example, use cooking to demonstrate fractions, money for decimals, the grocery store for unit rate, toys for counting, real-life shapes for geometry, and more.   Make sure YOU are doing math so your child can see how practical and helpful it is.

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2. Encourage trial and error-  Growth in math relies on failing.  Failure is GOOD in math if you learn from it!   My students learn more when they fail and are interested in fixing what they did wrong than those who just want to be right and move on.  Give your child a challenge, let them try FIRST, then give them tools to try AGAIN, and lastly walk through the correct way to solve the problem.

For example, I was working with my son on identifying his numbers.  He saw the picture of  9 and couldn’t tell me the number.  I told him to try it.  He said, “Well, it’s green.”  I told him that’s true and to try to remember the number again.   He said “Six?”.  I replied, “I see why you think that looks like 6 but that’s not it”.   We started counting and I stopped at 8.  He continued to 9 and said that’s it.

3.  It’s not about you-  Let me say it again, it is not about you! Make sure you’re not setting an example of a BAD attitude!!!!  It doesn’t matter if you hate math or were not good at it.  STOP talking badly about math!

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4. Related to something interesting- I had a student a few years ago who was a fanatic about a certain TV show.  He knew every fact about the characters and episodes.  I would translate test questions about fractions and decimals and use the characters from the show.  His brain took off like a wildfire and the problem seemed less foreign to him.

5. Get physical- Model or demonstrate a math problem as much as possible.  Visuals and hands on practice are vital to exploring, understanding, and retaining math concepts.

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Why I LOVE Area Models!

Area models come from the basic idea of solving for area.  They are a wonderful tool for younger students to do multi-digit multiplication problems (for example 14 x 17).  They develop student understanding of multiplication, place value, and the distributive property that is later used in Algebra.

I did not learn area models in school but I swear by them with my students and can’t wait for my children to do them!

Let’s review the basic idea of area.  If I want to put tile down in my bathroom and it measures 5ft by 6ft.  We multiply 5 x 6 and 30 total square feet.

Here is the model of this situation.  It shows 6 feet extended across and 5 feet extended down.  When they overlap they create 30 squares that are a foot by a foot.  This example is an area model.

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Here is an examples of a double-digit multiplication problem solved with an area model.  This example can be done by students starting in 3rd grade.  I know it is not the fastest way but it teaches students understanding and skills they can use when problems get more difficult.  By 6th grade they will learn to do it the traditional method, which yes, is more efficient.

Let’s solve 14 x 17.

First, setup a square just like real life area problems.

Take each number, 14 and 17, and break them down by place value.  14 becomes 10 and 4 and 17 becomes 10 and 7. Area-11

Just like with the bathroom floor problem, we are going to extend each number and draw 4 boxes.  Inside each box will be the answer of the over lapping multiplication problem.

We first solve 10 x 7 and write 70.  Then multiply 10 by 10 to get 100.  (This idea represents an Algebra concept called distribution.  We have distributed the 10 to 7 and 10.)

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Next we are going to multiply 4 by 7 to get 28 and 4 by 10 to get 40.  Answers go in each box. Area-33

Lastly!  We add up all the answers we got from multiplying.  These answers are called products. Area-44

238 is the same answer we would get if we did it the traditional way.

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Ratio Tables 101

Ratio Tables are my FAVORITE math thing to do and to teach!  They are an invaluable tool for ALL students.  They can be intimidating to work with at first and therefore, require practice.

Ratio Tables can be used for:

  • Solving fractions (fractions are ratios!)
  • Organizing your work
  • Brainstorming how to solve a problem

The basics of Ratio Tables can be helpful later when your child is doing:

  • Coordinate Planes
  • Functions
  • All Fraction Operations

Here is an example of using a Ratio Table when working with a recipe.

Ratio Tables use multiplication and division operations.   As well as adding and subtracting groups of ratios.  You might see ratio tables more complex with decimals and fractions within them.   I will show those next time!

Here is another example.  This table shows equivalent ratios, which are the same thing as fractions.  4/6 is equal to 2/3 and 12/18 by scaling down (division) or scaling up (multiplication).


The COOLEST part of ratios tables is you can combine, or add, any equal ratios from the table, like 2/3 and 12/18, to get another equal ratio, 14/21.


I challenge YOU to try them!

 

 

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BEST App for Modeling Fractions 

I have the luxury of having iPads in my classroom.  The app, Virtual Manipulatives! (VM), makes teaching fractions more interactive for students and it’s FREE!

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VM offers students fractions bars at their finger tips to create and compare.  Fractions can be written as percents and decimals as well.

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Here is an example of what a 4th or 5th grader will have to solve.  Adding and subtracting fractions with unlike denominators.

They have to find a common denominator in order to solve.  There are some algorithm steps to solving this but learning to model it first is key to understanding the “why“.

To model this example:

  1. Drag a 1/3 and 1/4 fraction bar
  2. Decide what both fractions  can be set equal to; in this case twelvthes (1/12)
  3. 1/3 becomes 4 of the 1/12
  4. 1/4 becomes 3 of the 1/12
  5. Now add how many 1/12 there are
  6. Answer is 7/12

Additionally, the app can be used to compare fractions, decimals, and percents.  (A common mistake I see in older kids is the idea of percents being the same as whole numbers. For example,  some students think 25% is the same as 25.  IT IS NOT!)  

For a younger child, this is a great way to introduce the concept of having less than one.  Taking half of something can be reinforced at a young age in many situations.
This app is a great tool for parents to help their child.  Virtual Manipulatives! is a must!

 

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