4.2.4 An Algorithm Using Partial Quotients

​An Algorithm Using Partial Quotients

4.2.4 Guided Instruction

Open Ended

What do you notice?

What do you wonder?

​Craters on the Moon

Have you ever wondered why the moon is covered in giant craters, or shallow holes?

The craters are created by meteors that collide with the moon on a daily basis.

The moon’s atmosphere is not strong, like Earth’s atmosphere, and allows for about 100 small meteors to hit the moon every day.

Since they plan to send more astronauts to the moon, NASA wants to be sure that the space suits will remain intact.

To check for safety, they tasked scientist Bill Cooke with testing the impact of a meteor on the moon.


Cooke simulated, or modeled, the impact by shooting marbles into soil at 16,000 miles per hour to watch them explode!

Scientist Bill Cooke then compared the marble explosions to the flashes of light seen in a meteor explosion on the moon.

Categorize

Options (4)

Divide the total number by four

Gradually put the same number of marbles into four groups until none are left

Multiply the numbers of marbles by the four directions, or groups

Divide the marbles in half, then put one marble in the other two groups

He shot the same number of marbles into four different directions.

If he is given a large quantity of marbles, how might he equally divide them among the four directions?

Strategies That Will Work

Strategies That Will Not Work

Kayla wanted to break up her division problem into partial quotients.

Here is her work.

Where did the highlighted numbers come from?

Match

Match each expression with the group of expressions with the same value

• $$480\div30$$

• $$390\ \div\ 30$$

• $$256\div4$$

• $$216\div4$$

• $$\left(300\ \div\ 30\right)+\left(180\div30\right)$$

• $$\left(300\div30\right)+\left(90\div30\right)$$

• $$\left(200\div4\right)+\left(40\div4\right)+\left(16\div4\right)$$

• $$\left(200\div4\right)+\left(16\div4\right)$$

Categorize

Options (4)

$$480\div15=32$$  

$$32\times15=480$$  

$$15\div480=32$$  

$$480\times15=32$$  

There are 480 dancers who make groups of 15. How many groups are there?

Expression that DO represent this

Expressions that DO NOT represent this

There are 480 dancers who make groups of 30. How many groups are there?