**Long, long ago, during my elementary school years, I enjoyed mathematics. I quickly memorized math facts and followed the traditional algorithms. I zipped through my homework, and I always had A's on my report cards. When I entered junior high, the enjoyment turned into misery! Why? Because I was expected to think mathematically! I was expected to understand the process and explain why the mathematical outcome was true. Something that was not required during those elementary years.**

**It wasn't until I became an elementary teacher that I truly realized the importance of the combination of mathematical procedure and understanding. Yes, knowing basic facts is quite helpful, but they don't have meaning if I don't understand or cannot explain why a fact is a fact. Why does 3 x 8 = 24? Algorithms for basic operations are useful but only when I understand how they work. If I can only solve a problem by using an algorithm and cannot explain why I arrived at a particular outcome, then I lack mathematical understanding. Without mathematical understanding, I could not truly teach my students. Luckily for me and my students, I worked in a district that provided quality professional development and adopted materials in which students explored math concepts. In addition, I taught with teachers who excelled in teaching mathematics and shared their knowledge with me.**

**As a result, when teaching multiplication for example, I didn't begin by expecting my students to memorize the multiplication tables. First we brainstormed things that came in groups such as animals with four legs, windows with six panes, egg cartons that hold a dozen eggs. Next, we grouped items together, created arrays, and drew pictures to represent multiplicative situations. From there, we moved on to skip counting. Then we learned how to use friendly numbers to find solutions:**

*If we know that 2 groups of 8 equals 16 or 2 x 8 = 16, we can add another 8 to 16 (16 + 8 = 24) so 3 x 8= 24.*

**Throughout our study of multiplication and eventually into learning division, we also read fun and engaging picture books which reinforced multiplication and division concepts as well as providing situations for trying out our understanding of these concepts. Here are a few book recommendations:**

Amanda counts anything and everything but isn't convinced that multiplication is helpful as a counting method until she dreams about bicycle riding sheep. First she wants to count the wheels on all their bikes which leads to counting all their legs which leads to counting all their balls of yarn which leads to counting grandmas knitting sweaters! When Amanda becomes frustrated with the one by one counting, the sheep tell her to MULTIPLY!

What is terrific about this book is that there are so many illustrations of things to count using multiplication!

**Each Orange Had 8 Slices by Paul Giganti Jr. and Donald Crews**

There were 2 oranges. Each orange had 8 slices and each slice had 2 seeds. How many slices were there in all? How many seeds were there in all?

Within this wonderful counting book are numerous things to count. The great thing is children have choices on how to count based on their ability. They can count one by one, use skip counting, or multiply.

**Bean Thirteen by Matthew McElligot**

Ants, Ralph and Flora, are picking beans for dinner. They have twelve beans, but before Ralph can stop her, Flora picks one more bean. Now they have 13, the unlucky number! When they get home, they try to divide the beans equally between the two of them, but there's one extra bean, the unlucky 13! Now what do they do? Do they invite a friend to have dinner with them so the three of them can equally share the beans? But wait...there still will be one extra bean! How do they solve this dilemma!

**Divide and Ride by Stuart J. Murphy**

It's Carnival Day for 11 best friends. For each ride they visit they must divide to fill the seats, and all the seats must be filled. On the roller coaster, it takes two people to fill a seat while the next ride seats three per chair. Each time they divide there is one or more friends left over. How do they find a way to get their friends on the ride and fill all the seats?

One of the features I like most about this book is the array of stars used to illustrate each dividing situation.

Stars remind me of a wonderful game called Circles and Stars

which I discovered in Third Grade Math: A Month to Month Guide by Suzy Ronfeldt. This is a useful game when students are first learning about multiplication.

Here are the basic directions:

Students play in pairs. They will need a single die numbered 1-6. Also each student folds a sheet of paper into eight equal sections. In the upper left box students write-- "My Total ___"; "Partner's Total ___"; "Difference ___".

Students take turns rolling the die. First student to roll, draws the corresponding number of circles at the top of the second box. If a student rolls 2, then 2 circles are drawn. The circles represent groups. Now, the second student rolls and draws circles. For the next round of rolls, the first student rolls again and now draws the corresponding number of stars in each of the circles. If a student rolls 6, then 6 stars are drawn in each of the circles. Then the second student follows the same procedure. Once both students have drawn circles and stars in their rectangles, they will determine how many stars are in their own rectangle and write an equation to represent the multiplication fact. For example, 2 x 6 = 12 stars. The goal is to draw circles and stars in each of the rectangles.

Once all the rectangles are filled, students determine the total number of stars they have drawn and will record the number in the upper left corner box where "My Total" is written. Then they write their partner's total. Finally, the students find the difference between the total number of stars each drew and record the number in the upper left corner box. Students use the back of the paper to calculate the sum of their seven products and the difference between the number of stars the students drew. As you can see this is a "mathematically rich" game! When you feel your students are ready to move on to other combinations, provide them with a cube marked with 4,5,6,7,8,9.

**Hopefully, you have found some helpful information for introducing multiplication. Now let me share a game I created that provides practice for multiplication/division facts.**

**Last month I created multiplication and division word problem task cards for Valentine's Day. This inspired me to design more cards but with a St. Patrick's Day theme. This new batch is aligned with 3rd grade standards so the focus is on multiplication and division**

**facts, particularly the more difficult ones. In addition, I put together a board game,**

*Pot of Gold Adventure*, in which students race to win the leprechaun's pot of gold at the end of the rainbow. However, in order to move around the board, the players must correctly solve a word problem task card requiring a multiplication or division fact. Below is a task card sample along with the game board.

**Read the Teaching Tips below to learn the best ways to use this product.**

**Try out a sample of these task cards for FREE!**

**Thanks for visiting my blog today! I know how busy teachers are so I hope I provided you with valuable teaching treasure that will benefit you and your students. If you like the adorable shamrock on my St. Patrick's Day product covers, check out Clip Factory by Teacher's Take-out.**

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