📊🤔 Explore A - Lesson 3.1 Multiplication as Repeated Addition

Part 1

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What patterns can you see?

What is an addition equation you could write for the second sentence "2 triangles have 6 sides"?

Answer:  3 + 3 = 6

What is an addition equation you could write for the fifth sentence "5 triangles have 15 sides"?

Answer: 3 + 3 + 3 + 3 + 3 = 15

This is repeated addition. 

Repeated addition is using the same addend multiple times.  

For the second equation 3 + 3 = 6; 3 is an addend two times.

For the fifth equation 3 + 3 + 3 + 3 + 3 = 15; 3 is an addend 5 times.

Part 2

How would you determine how many sides 9 triangles have?

Answer:  3 + 3 + 3 + 3 + 3 + 3  + 3 + 3 + 3 + 3.

How would you determine how many sides 100 triangles have?

Did you add 3 one hundred times?  How would you calculate that? 

Skip counting by 3's, making a table, or is there another way?

Part 3

Repeated addition is adding the same number multiple times.  This leads to the concept of multiplication.  

Multiplication is the operation of repeated addition of the same number.

Changing the equations from part 1 into multiplication equations yields the following:

$3+3=6$  is equivalent to  $2\times3=6$.

$2\times3=6$  This is read as "two times three equals six".

This means 2 groups of 3, or 2 addends of 3.

$3+3+3+3+3=15$ is equivalent to $5\times3=15$.

$5\times3=15$ This is read as "five times three equals fifteen".

This means 5 groups of 3, or 5 addends of 3.

The picture below shows the rest of the equations transformed.

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Part 4

What multiplication equation would represent the number of sides 9 triangles have?

$9\times3=?$ (You find the answer!)

What multiplication equation would represent the number of sides 100 triangles have?

$100\times3=?$ (You find the answer!)