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ALL ABOUT ARRAYS Finding Multiplication Combinations and Factors using arrays Featuring: Amanda Bean’s Amazing Dream By: T. Logue

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Guiding Questions How can building arrays help you find all the multiplication combinations for a number?

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Array Arrays are different ways that we can organize a total number of things using rows and columns. Rows go across. Columns go up and down. Here we see 2 rows and 3 columns: 2 ROWS 3 COLUMNS

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**Using arrays can help us find all the factors for a given number.**

Quick Check: Remember, factors are all the numbers you can multiply together to get a certain product. Here is an array: This array is 2 x rows, 6 columns. 12 total cookies. So we know that two of the factors for 12 are 2 and 6. Could you arrange these 12 cookies into another type of array?

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Building Arrays Now we are going to build arrays to help us think about numbers. We are going to use tiles for this activity. Yippee!!! If I wanted to build an array with 24 tiles, I might use the combination of 8 x 3. First with tiles, then by drawing it Watch Me elmo

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**Marked Array (Grid Paper)**

3 columns Dimensions Here is an array for the number 24 using the factors 8 and 3. 8 rows

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**Unmarked Array (no grid paper)**

Dimensions 3 columns Here is an unmarked array for the number 24, still using 8 x 3. Sometimes we can’t use grid paper to draw the array because the numbers are too large…like, say, 580!! In that case we can use rectangles like these to make an unmarked array—and label the dimensions. 8 rows

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**Writing An Equation My equation would look like this:**

8 x 3 = 24 Can you write an equation for 24 with more than 2 factors?

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Your turn! Using your tiles, you will work with your partner to build other arrays that have a total of 24 tiles. For each array you build, draw the array on your grid paper and label the dimensions. Then write the equation. See if you can write one with more than 2 factors! You will have about 10 minutes for this activity.

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Dimensions When you labeled the dimensions of your array, you were actually naming multiplication combinations for the number. Wow you’re smart!! What multiplication combinations did we find for the number 24? Come on up and list them! Have several students use CPS chalkboard to write their combinations on the slide

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**Listing Factors IN ORDER**

When you list factors for a number, you want to put them in a certain order. Always start with the number 1, and end with the number you are factoring. For example, lets find the multiplication combinations for the number 16. Use CPS Chalkboard to write directly onto this slide as you list the combinations for the number 16

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**Let’s practice some more**

OOPS! Should find all the combinations (factors) for the number 15 Can you suggest a way to arrange these cookies into an array? What multiplication combinations can you come up with? Find them all, and then list those factors in order!

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**Now use your tiles & the clue to solve this problem!**

CLUE: This number of tiles will make a rectangle that is 10 tiles wide. Think of a number that might work. Guess and check with tiles. Be sure to draw and label your array! 10 Minutes & Share!

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**Let’s Review Our Guiding Question**

How can building arrays help you find all the multiplication combinations for a number? Take a few minutes to jot down your thoughts in your journal. We will share in a few minutes.

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Independent Work: Student Activity Book P You will figure out the numbers using the clues provided, and draw arrays to represent the numbers. Use your tiles and grid paper! Verify page

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