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**Finding Multiplication Combinations and Factors using arrays**

ALL ABOUT ARRAYS Finding Multiplication Combinations and Factors using arrays By: T. Logue

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**Learning Goals What am I learning today? Why am I learning this?**

Writing multiplication equations that describe dot arrangements Using arrays to model multiplication Identify multiplication combinations and finding factors Why am I learning this? To help me understand numbers and factors of numbers How do I know when I am being successful? I can build an array for a given number. I know how to find the factors of a given number

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Guiding Questions How do you know if all possible arrays have been found for a given number? What number relationships are evident when all possible arrays have been found?

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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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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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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 Go to elmo with tiles. Then back to pp for drawing array

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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:**

x = Can you write an equation for 24 with more than 2 factors? Can you break apart the factor 8? factor factor Turn and talk, then share in glass mode

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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 board and label the dimensions. Then write the equation in your spiral. See if you can write one with more than 2 factors! You will have about 10 minutes for this activity. Timer

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Dimensions When you labeled the dimensions of your array, you were actually naming multiplication combinations for the number. What are some combinations we found for rectangles made with 24 tiles? Get in glass mode list equations, click to turn and talk, click to list factors in order Did we find all the possible arrays? How do we know? Now we need to list these factors in order from smallest to greatest

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Listing Factors Factors of 24:

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Discussion We just found all the factors of 24. What are some multiples of 24? What are some ways we can remember which are multiples and which are factors? Turn and talk: Go to chart paper 2 columns multiple and factor

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**Remember this F is for Factors, and there are just a few.**

M is for Multiples, and there are many millions of those. We will talk more about multiples later…

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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. (10 columns). Think of a number that might work. Guess and check with tiles. Be sure to draw and label your array on the white boards! 10 Minutes & Share! Work with partner.

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Discussion What number did you come up with that would fit the clue (10 tiles wide)? What do these numbers have in common?

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Each day, the Stone Printing Company prints 25 sales flyers for each of its 10 customers. How many total sales flyers does the Stone Printing Company print each day? 2,500 50 250 10

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**Let’s Review Learning Goals**

Our goals were: Writing multiplication equations that describe dot arrangements Using arrays to model multiplication Identify multiplication combinations and finding factors What did you learn today about these goals? How do you know that you were successful today? (“ I know how to….” or “I can …..” What do you still have questions about?

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Guiding Questions How do you know if all possible arrays have been found for a given number? What number relationships are evident when all possible arrays have been found?

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Independent Work: Pages 1 and 2. You will figure out the numbers using the clues provided, and draw arrays to represent the numbers. Use your tiles and grid paper!

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