5.5.2-Develop Estimating Quotients

What is place value?

The value of where a digit is in a number!​

​Judging by what number sits in a certain place in either a decimal or whole number, it is a certain value or percentage in relation to the power of ten.

Place Value

• Helps us to compare and order numbers.

• Helps us to understand the value of a digit depending on it's place within a larger number.

• Helps us to determine in which form a number is shown: standard, word form, expanded or model form.

Multiple Select

Understanding place value can help us to:

• compare numbers

• determine the value of a digit

• find the products of numbers

• know the different ways to show a number

Multiple Choice

Which of these numbers has a 4 in the ten thousands place?

• 42, 764, 891

• 3, 420, 412

• 14, 674, 924

• 6, 348, 242

Multiple Select

Check the numbers that could round to 5,000.

• 5, 532

• 4,729

• 5,008

• 4, 311

Multiple Choice

$$5\times2=$$  

• 10

• 8

Multiple Choice

So....... $$10\ \div2\ =$$  

• 2

• 20

• 12

• 5

Multiple Choice

9 x 8=

• 81

• 17

• 72

• 63

Multiple Choice

$$7\times7=$$  

• 64

• 63

• 48

• 49

Multiple Choice

$$4\times8=$$  

• 36

• 32

• 28

• 36

Multiple Choice

Find the quotient.

902 ÷ 4

• 205 R2

• 215 R5

• 225 R2

• 225 R5

Multiple Choice

What is the result of dividing 670 by 5?

• 134

• 135

• 136

• 137

Multiple Choice

Which of the following is a strategy for estimating quotients when dividing by two-digit divisors?

• Rounding the divisor and dividend to the nearest ten

• Multiplying the numbers instead of dividing

• Ignoring the place value of the numbers

• Adding the numbers together

THINK:

​If 21 X 10 =

and

if 21 X 20 =

and

if 21 X 30 =

Then, 21 X __ is about 504

Is that a reasonable result?

How could you help your partner without saying the answer?

​How does your model show how to estimate the number of robots in each box?

What number in each Model It shows the divisor? Are they the same or different?

Multiple Choice

Look back at the table in the MODEL IT! What is the total number of robots if there are 40 robots per box?

• 840

• 8400

• 820

• 800

​You want to choose numbers that are CLOSE or FAR from the dividend and divisor so that the estimated quotient is close to the actual quotient.

​If 50 ÷ 2 = 25 then 500 ÷ 20 = ____ So that means that there are ____ robots in each box.

​CIRCLE ONE

​342 is close to 350
and
38 is close to 35
and
10 x 35 is ___ , so 350 ÷ 35 =

SOLUTION: That means 342 ÷ 38 is close to __.

​Multiple of 10	​10	​20	30​	​40	​50
​23 x Multiple of 10	​230	​	​	​	​

​Solution: between __ and __.

Multiple Choice

In the problem $$47913\div77$$   what would you round the divisor to?

• 75

• 80

• 70

Multiple Choice

In the problem $$47913\div77$$   what would you round the DIVIDEND to in order to be compatible with your NEW divisor of 80?

• 48000

• 50000

• 45000

Multiple Choice

Now that you have made

$$47,913\div77$$  into the easier division problem of

$$48000\div80$$  

what would your estimated quotient be?

• 6

• 60

• 600

Multiple Choice

In the problem

$$34973\div68$$  

what would you round the divisor to?

• 70

• 65

• 60

Multiple Choice

In the problem

$$34973\div68$$  

what would you round the DIVIDEND to in order to be compatible with your NEW divisor of 70?

• 30000

• 34000

• 35000

Multiple Choice

Now that you have made

$$34973\div68$$  into the easier division problem of

$$35000\div70$$ what would your estimated quotient be?

• 5

• 50

• 500

Multiple Choice

In the problem

$$2798\div44$$   what would you round the divisor to?

• 50

• 40

• 45

Multiple Choice

In the problem

$$2798\div44$$   what would you round the DIVIDEND to in order to be compatible with your NEW divisor of 40?

• 2800

• 3000

• 2600

Multiple Choice

Now that you have made

$$2798\div44$$  into the easier division problem of

$$2800\div40$$

what would your estimated quotient be?

• 7

• 70

• 700

Open Ended

Explain IN DETAIL how you would estimate the quotient for $$27,397\div92$$  .

Poll

How do you feel about estimating quotients?

• I'm lost in space!

• Need more help...

• Almost there.

• I got this!

Open Ended

After learning about dividing multi-digit numbers and estimating quotients, what is one question you still have or something you would like to know more about?

Multiple Choice

What is the main purpose of estimating quotients when dividing multi-digit numbers by two-digit divisors?

• To make division easier and faster by using approximate values

• To always get the exact answer

• To avoid using multiplication

• To skip understanding place value