Long Division- Partial Quotients

Here we go.... from multiplication to DIVISION!!

This is what our district has to say about division:

The student is expected to represent the quotient of up to a four-digit number divided by a one-digit number, with or without remainders, using strategies including arrays, area models, equations, and the standard algorithm.

Vocabulary
quotient, dividend, divisor, remainders, compatible numbers, convert 

Quotient is the answer to a division problem.
Dividend is the number being divided.
Divisor is the number doing the dividing.
Remainder is anything left over that doesn't divide evenly.

For example
73 divided by 9 = 8 with a remainder of 1
73 is my dividend, 9 is my divisor, 8 is my quotient, 1 is my remainder

To check this answer I would multiply my divisor (9) times my quotient (8) and then add my remainder (1) to see if I end up with my dividend (73)
9x8 = 72
72 +1 =73

I started off with the partial quotients method.

Here's a video that explains partial quotients.

2 digit by 2 digit multiplication standard method

We started our standard multiplication (2 digit by 2 digit) today!

Check out the pictures below to see how we did it.

Multiply the ones place.

Multiply the tens place.

Add up the partial products and you're done!

Here's another example. I circled the numbers as I multiplied them.

To help build up their math fluency I've been daily quizzes every day.

Once they pass the quiz, they go on to the next digit. Once they get all the way up to the multiples of twelve, I'll give them an ice cream cone!

2 digit by 2 digit multiplication

Most of my kiddos have mastery of 4 digit by 1 digit multiplication so it's time to move on to 2 digit by 2 digit multiplication.

In case you were wondering... here is my multiplication pack on TeachersPayTeachers

Just like with 4 digit by 1 digit, I start off with the partial products method, and then I move on to the standard algorithm.
However, the partial products method looks a bit different.
This time we can use an array.

48 x 26
I first decompose the numbers.
48 becomes 40 + 8
26 becomes 20 + 6

Then I draw my array.
I solve for the partial products.
20 x 40 = 800
20 x 8 = 160
6 x 40 = 240
6 x 8 = 48
Add up all the partial products and you get the total.

48 x 26 = 1,248

Then I ask myself, is this answer reasonable?

I know 48 is almost 50. 50 x 26 would give me 1,300.
That tells me my answer is reasonable.

Notice I bolded my vocab words:
decompose, array, partial products, total, reasonable

Here's my anchor chart.

Here is a visual I did with one class to show them that it is really an array!

Please ignore the other stuff on the white board. 

Multiplication

Here's a good video for the standard algorithm in multiplication.

We are doing multiplication!!! Not just any ol' multiplication but four digit by one digit multiplication.
I start off by teaching them the partial products method.
Here it is below:

This is called PARTIAL PRODUCTS.

I go through each place value and multiply. Then I add up all the products to come up with the final answer.

Akire showing off another example! 

Dylan here did it by himself. 

Dylan didn't have to show me all of the number sentences. I can see he got 360 by multiplying 60 x 6.

Here are some of the questions the district wants our kiddos to answer:

How does your knowledge of place value help you determine the product of 17 x 10? 17 x 100? How are those products similar? How are they different?

How does the value of the product change when you're multiplying by 100 rather than by 10?

Use three different methods to multiply 3,184 x 7.

Given mental math, partial products, and the algorithm, which strategy might you choose when multiplying 2,506 x 4? Explain your answer.