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Understanding Multiplication

Multiplication – The art of increasing gold or silver by magic, — attributed formerly to the alchemists

Younger students need to have the magic of multiplication broken into little pieces of reality! I think the best starting point is showing that multiplication is repeated addition. If I add two 6 times, I have multiplied two by six. It actually takes saying that word “times” quite a few times before everyone catches on to the idea that we also say “times” when we multiply.

Of course, by showing I actually mean showing. Students need manipulatives in their hands. If they are edible all the better! 15 candies in one roll of Smarties. If everyone on your team has one roll, how many candies does your team have? We make arrays out of cubes, then we draw the arrays with circles or Xs. Sometimes we get fancier and do hearts or stars, but it is important to be able to draw quick arrays to see that they can be useful in problem solving when you get stuck on a problem.

Important vocabulary surrounds multiplication. I love to have them figure out the analogies such as, plus: addition :: times: multiplication and addend: factor :: sum: product. Later on, we realize addition: multiplication:: subtraction : division. Besides factor and product, there’s other important multiplication vocabulary or key words. Each and every usually mean to multiply. I tell my class to watch out for same number and equal groups, because those words change each and every to division, every time. Kids need to know the words twice, double, triple, and quadruple means to multiple. Then we have total and altogether, which they already recognize as addition words. These words provide a chance to reinforce the idea that multiplication is actually just FAST addition.

When learning our facts, we use many strategies: fact families, number lines, repeated addition, arrays, groups, sets, music, movement, discussion, breaking apart numbers.

I made this poster for my kids to discuss all the ways they know to multiply. I have attached the pdf for you.

Understanding Multiplication

Understanding Multiplication

I have made an Understanding Multiplication Scavenger Hunt. Here is a page from it:

Understanding Multiplication Scavenger Hunt.

It also explores multiplication as repeated addition, arrays, skip counting, and fact families.

I hope that you find some magic in multiplication in your classroom!

Ann

 

Saturday Extra: Example and Non-example Edition

“Few things are harder to put up with than the annoyance of a good example.” —Mark Twain

Sorry, I found more appropriate example quotes, but I love Mark Twain.

Example and Non-example is a great way to build concepts that provide students a deeper understanding of the vocabulary terms they are learning.

The activity itself is fairly simple. You need several examples of things that have all of the characteristics of a concept. It is important that you determine the characteristics that the object must have to perfectly represent the concept. This week we are going to use the word “polygons.” So, by definition, polygons have straight sides, are 2-dimensional, and are closed figures. Examples will be easy to come by: triangles, squares, trapezoids, star, etc…

Then you need several good non-examples. The non-examples should have at least one of the characteristics of the example. They should not be something completely off target, like “fire.” For things that are not polygons, we would present a figure without straight sides such as a circle or oval, a 3-dimensional object such as a cube, and a figure with all straights sides that isn’t closed.

To begin, one object is presented and placed on one side of the display area (example). A second object is presented and placed on the same side. Students are then asked to determine what is alike about these objects. A third object is presented and placed on the other side (non-example) of the display. Students are given the opportunity to discuss why it doesn’t belong with the others. Continue in this way with several more objects until the students feel certain they know how the objects are being sorted. Ask for their explanations. Allow students to determine the place for the remaining objects and/or allow students to suggest additional objects for the example side.

At the end of this particular activity, we will create a definition of polygons based on the ideas the students have brought forth themselves. Finding their own understanding is an important element in retaining the lesson.

This activity can be done with very simple concepts. You could do lowercase letters, not lowercase letters (use some capital letters and a number for non-examples) or short-a words, not short-a words (use some long-a words or other short-vowel words for the non-examples). It can also be used with very complex concepts.

Older students could be given a chart of examples and non-examples and be asked to determine how they were sorted, on their own or with a partner. Conversation is a very important learning tool! Students can even be given a list of objects to sort themselves and be asked to write their rationale for sorting them into two categories.

Check out this article with a great description of this strategy.

Find more vocabulary development ideas at my TPT store.

Ann

Probability

“The 50-50-90 rule: Anytime you have a 50-50 chance of getting something right, there’s a 90% probability you’ll get it wrong.” —Andy Rooney

 

 

I created a product today for math vocabulary. It contains a Word of the Day card on probability.

 

 

It also contains posters about more likely, less likely, most likely, least likely, equally likely, certain, and impossible.

 

Word of the Day

 

Set 2 # 12

More available at my TpT store.

Have a great Tuesday. I am hoping to post pictures of my classroom tomorrow!

Ann