Partial Quotients with Minecraft Lesson

Partial Quotients with Minecraft

In the activity you were asked to help the village prepare their supplies for the buyers

4 carrots can be sold for $1

But 8 carrots can be sold for $2

You can create different ways to bundle the carrots.

76 carrots

Fill in the Blanks

Multiple Choice

The carrots have to be sold in bundles of 4... are these in bundles of 4???

• Yes

• No

Multiple Select

Which chests have 76 carrots and are bundled into multiples of 4?

How many groups of 4?

8 Carrots

This is 2 groups of 4.

For each group of 4 they sell for $1

2 groups of 4 = 2x$1 = $2

Multiple Choice

How many groups of 4 are in 20 carrots?

• 12

• 3

• 5

• 6

Multiple Choice

How many groups of 4 carrots are in this chest?

• 3

• 4

• 5

• 20

Partial Quotients

To divide you can pull out groups and count the number of groups.

But... it might be faster to do it in larger groups!

You have 320 carrots ÷ 4

What is 320 divided by 4?

You can do 4 + 4 + 4 + 4 + ..... + 4 = 320

or....

If you know 8 carrots is 2 groups...

If you know 16 carrots is 4 groups of 4...

If you know 20 carrots is 5 groups of 4...

Multiple Select

How can you write 320 carrots in groups of 4?

• 320 = 4 + 8 + 20 + 20 + 20 + 20 + 8 + 200 + 8 + 12

• 320 = 80 + 80 + 4 + 16 + 40 + 100

• 320 = 100 + 100 + 100 + 20

• 320 = 75 + 25 + 100 + 8 + 12 + 100

What is 320 ÷ 4?

How many groups of 4 is this?

320 =

4 + 8 + 20 + 20 + 20 + 20 + 8 + 200 + 8 + 12

What is 320 ÷ 4?

1 + 2 + 5 + 5 + 5 + 5 + 2 + 50 + 2 + 3

320 =

4 + 8 + 20 + 20 + 20 + 20 + 8 + 200 + 8 + 12

What is 320 ÷ 4 = 80 groups of 4

1 + 2 + 5 + 5 + 5 + 5 + 2 + 50 + 2 + 3

320 =

4 + 8 + 20 + 20 + 20 + 20 + 8 + 200 + 8 + 12

There are 66 bales of hay. How can we divide this by 6 by using partial quotients?

Divide by 6

Multiple Select

How many groups of 6 are in 66 bales of hay? Which expression shows adding groups of 6?

• 66 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6

• 66 = 12 + 12 + 12 + 12 + 12 + 6

• 66 = 60 + 6

• 66 = 50 + 1 + 6

66 ÷ 6

How many groups of 6 are in 66?

66 Bales of Hay

= 30 + 30 + 6

66 ÷ 6

= 5 groups + 5 groups + 1 group = 11 groups

All of these are in groups that are multiples of 12.

How many porkchops?

60 + 36 + 48 + 12 + 12 + 24 +24 + 12 + 24 + 36 + 48 + 24 + 60 + 12 + 12 + 36 + 24 + 60 + 12 + 24

How many porkchops?

60 + 36 + 48 + 12 + 12 + 24 +24 + 12 + 24 + 36 + 48 + 24 + 60 + 12 + 12 + 36 + 24 + 60 + 12 + 24

Think groups of 12....

60 + 36 + 48 + 12 + 12 + 24 +24 + 12 + 24 + 36 + 48 + 24 + 60 + 12 + 12 + 36 + 24 + 60 + 12 + 24

Think groups of 12....

5 + 3 + 4 + 1 + 1 + 2 +2 + 1 + 2 + 3 + 4 + 2 + 5 + 1 + 1 + 3 + 2 + 5 + 1 + 2 GROUPS

50 groups of 12

5 + 3 + 4 + 1 + 1 + 2 +2 + 1 + 2 + 3 + 4 + 2 + 5 + 1 + 1 + 3 + 2 + 5 + 1 + 2 GROUPS

50 x 12 = 600

5 + 3 + 4 + 1 + 1 + 2 +2 + 1 + 2 + 3 + 4 + 2 + 5 + 1 + 1 + 3 + 2 + 5 + 1 + 2 GROUPS

Dividing by Partial Quotients

600 ÷ 12

How many groups of twelve?

1 group = 12

2 groups = 24

3 groups = 36

600 ÷ 12

What do you know? Remove groups of 12 until you can not remove any more groups!!

Keep track on the right hand side!

600 ÷ 12

Keep track on the right hand side!

600 ÷ 12

What multiples of 12 do you know??

600 ÷ 12

3 groups of 12 is 36. Pull out (subtract) this amount.

600 ÷ 12

564 remaining... what can you pull out (subtract)?

600 ÷ 12

What about 5 groups of 12?

Subtract 60.

600 ÷ 12

How much you pull out (subtract) is YOUR choice!

Your choice... how many groups of 12 do you subtract from 504?

600 ÷ 12

504 is big... I want to do this faster so I need more groups!

600 ÷ 12

Keep going... now choose!

600 ÷ 12

Still 264 to divide up...

600 ÷ 12

Still 264 to divide up...

600 ÷ 12

Need more room? Start a new column.

Keep going ... new column.

How many groups of 12 are in 144?

600 ÷ 12

At least 10 more groups!

Subtract 12x10

600 ÷ 12

Only 24 left! I know this one!!!

This is a final 2 groups of 12.

600 ÷ 12

Zero! Perfect! Divided evenly.

600 ÷ 12

Add up how many groups you pulled out

Add them up!

600 ÷ 12

50 total groups of 12!

600 ÷ 12 = 50

Use partial quotients

What is

1505 ÷ 7?

How many groups of 7 do you think it is?

Use partial quotients

What is

1505 ÷ 7?

Use partial quotients

What is

1505 ÷ 7?

Use partial quotients

What is

1505 ÷ 7?

Use partial quotients

What is

1505 ÷ 7?

This is slow going...

What is

1505 ÷ 7?

Keep going

What is

1505 ÷ 7?

ALMOST THERE!

What is

1505 ÷ 7?

ZERO remainder!

What is

1505 ÷ 7?

Add up the quotients

= 215

There are 215 groups of 7 in 1505

What is

1505 ÷ 7?

Multiple Choice

What is seen in the picture?

¿Qué se ve en la imagen?

• Partial Product

• Partial Quotient

• Partial Difference

• Partial Sum

Multiple Choice

What is the value of the missing partial quotient?

• 50

• 400

• 40

• 30

Multiple Choice

What's going to go on the right side of the chart?

• 3, 6, 9, 12, 15, 18

• 3, 6, 9, 12, 15, 30

• 3, 4, 5, 6, 7, 8

• 30, 60, 90, 120, 150, 300

Multiple Choice

Using partial quotients to divide, what number is missing?

• 1 x 18

• 100 x 18

• 10 x 18

• 2 x 18

Multiple Choice

What number is missing?

• 180

• 18

• 100

• 10

Multiple Choice

How many groups of 18 are taken out?

• 1 x 18

• 2 x 18

• 5 x 18

• 10 x 18

Multiple Choice

What number is missing?

• 14

• 15

• 16

• 17

Multiple Choice

What is the total of the number of Partial Quotients you took out?

• 22

• 21

• 20

• 25

Multiple Choice

What is 412 divided by 18?

• 22

• 16 r 22

• 22 r 16

• 16

Multiple Choice

What number is missing?

• 87

• 10

• 870

Multiple Choice

What number is missing?

• 1

• 100

• 871

Multiple Choice

What is 871 divided by 87?

• 1 r 10

• 10 r 1

• 87

Multiple Choice

$$892\ \div26\ =$$  Divide using partial quotients.

• 24 r 8

• 35

• 34 r 8

• 32

Open Ended

Divide. Use partial quotients algorithm.