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## 3rd grade (Eureka Math/EngageNY)

### Unit 1: Lesson 1

Topic A: Multiplication and the meaning of the factors- Equal groups
- Equal groups
- Introduction to multiplication
- Multiplication as equal groups
- Understand equal groups as multiplication
- Multiplication as repeated addition
- Relate repeated addition to multiplication
- Understand multiplication using groups of objects
- Multiply using groups of objects
- Multiplication with arrays
- Understand multiplication with arrays
- Multiply with arrays

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# Multiplication as equal groups

CCSS.Math:

Sal uses arrays and repeated addition to visualize multiplication. Created by Sal Khan.

## Want to join the conversation?

- how do you multiply mills and thousands(0 votes)
- you can try converting the number so you only have to multiply the numbers with value example

12000*600 is the same as 1200000*6 then multiply what i'm trying to write is put the zeros behind the larger numbers but don't put numbers with value like 123456789......(35 votes)

- How to do you multiply hundreds and thousands?

For example 100x2000?(10 votes)- Multiply the numbers without the zeros at the end, then place the total number of zeros at the end of the result.

In your example, do 1x2=2, then place a total of 2+3=5 zeros at the end. So 100x2000 = 200,000.(3 votes)

- haw do i get to fourth grade?(5 votes)
- its how not haw so u have to wait one year bro(2 votes)

- did you know any thing times eleven is it twise

like 7 times 9 is 77(4 votes)- Yup, that’s right for single-digit numbers, but if you get to 10 or bigger it doesn’t work out. 10x11=110, not 1010. 11x11=121, not 1111.

Also, 7x9=63.

I hope this helps!(5 votes)

- I do know all my tables by heart but how do stick on to them(2 votes)
- Skip counting also helps. For example, I know 8x8=64 but if I forget how much 7x8 is, all I have to do is subtract 1 eight from 64.

Think about it: 8x8 is the same as 8 eights, so 7x8 is 7 eights. Therefore, 7x8 has 1 less eight than 8x8. So 7x8 is the same as 8x8 - 8, or 64 - 8. Which is 56.(2 votes)

- can you multiply fractions?(0 votes)
- Yes, you can! Here's an example if you want to know how: https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/v/multiplying-fractions(1 vote)

- who first used multiplication and in which country?(2 votes)
- The oldest known multiplication tables were used by the Babylonians about
**Iraq**4000 years ago . But he early**Egyptians**were the first to discover multiplication and to use it effectively as well as teach it to one another.

The modern method of multiplication based on the Hindu–Arabic numeral system was first described by**Brahmagupta**(598 - died after 665) was an**Indian**mathematician and astronomer.

Brahmagupta gave rules for addition, subtraction, multiplication and division.(6 votes)

- how much of this do we need to know?(2 votes)
- All of it. Someday you may need to use this, because we shouldn't depend on calculators.(2 votes)

- how would you multiply big numbers with out adding(2 votes)
- Multiply the number by how many times you see the same number appears.

Ex: 5+5+5+5+5+5+5=? 5*7=35(2 votes)

- hello everyone, can someone answer my question please, if multiplication is a repetition of addition , then how to explain 10 X 0.5? using a repetition concept(2 votes)
- (0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5) = (10 X 0.5)

But what about 0.5 x 0.5 using repetition? Well you'd have to jump through some hoops, like change the first decimal to a fraction, say 5/10 (doesn't matter what as long as it equals 0.5), which would allow you to re-write the equation as:

5/10 X 0.5 = (0.5 + 0.5 + 0.5 + 0.5 + 0.5)/10 = 2.5/10 = 0.25

Probably not helpful to think about multiplying decimals as repetition of addition. So I would say it's only useful when multiplying whole numbers.(2 votes)

## Video transcript

I have these three star patches,
I guess you could call them, right over here. And so I could say, if I had
one group of three star patches, how many star patches do I have? So I literally have one
group of three star patches. Well, that means that I
have three star patches. 1, 2, 3. This is my one group of three. Now let's make it a little
bit more interesting. Let's say that I had two groups. Let's say that I had
two groups of three. So that's one group, and
then here's a second group. Here's two groups of three. So how many total star
patches do I have now? Well, I have two
groups of three. Or another way of thinking
about it is this is 3 plus 3. This is equal to 3 plus
3, which is equal to 6. So we see 1 times 3--
one group of 3 is 3. Two groups of 3, which is
literally two 3's, is 6. Let's make it even
more interesting. Let's have three groups of 3. Now, what is this
going to be equal to? Well, it's three groups of 3. So I could write this as
three groups, 3 times 3. And how many of these star
patches do I now have? Well, this is going
to be 3 plus 3 plus 3. It's going to be
3 plus 3 plus 3. Notice I have three 3's. I have two 3's. I have one 3. So this is 3 plus 3
plus 3 is equal to 9. And you can count them. 1, 2, 3, 4, 5, 6, 7, 8, 9, or
you could just count by 3's. 3, 6, 9. And I think you see
where this is going. Let's keep incrementing it. Let's get four groups of 3. So let's think about
what 4 times 3 is. 1, 2, 3, and 4. This right over here
is four groups of 3. We could write this
down as 4 times 3, which is the same thing
as 3 plus 3 plus 3 plus 3. Notice I have four 3's. One 3, two 3's,
three 3's, four 3's. One 3, two 3's,
three 3's, four 3's. So we get 3, 6, 9, 12. So what I encourage
you to do now, now that the video is almost
over, is to keep going. I want you to figure out what
5 times 3 is, and 6 times 3, and 7 times 3, and 8 times 3,
and 9 times 3, and 10 times 3. And I'll give you a little hint. You don't always have to
draw the star patches, but it's nice to visualize it. We saw 4 times 3 is
literally four 3's. Well, 5 times 3 is
going to be five 3's. So 2, 3, 4, 5. Which is equal to
3, 6, 9, 12, 15. So I encourage you to think
about what all of these are after this video is done.