Lesson 1 Introduction MGSE5.NBT.1 Understand Place Value

Lesson 1 Introduction Understand Place Value

MGSE5.NBT.1

Think It Through

How is place value related to the number 10?

We use a number system called base ten. This means that place value in any number is based on a pattern of tens.

Look at the following place-value models for whole numbers.

Thousands

1 thousand is 10 times 1 hundred

Hundreds

1 hundred is 10 times 1 ten

Tens

1 ten is 10 times 1 one

Ones 1 one

1,000

1

100 1

10 1

1 5 1,111

Think Place value in decimals is just like place value in whole numbers.

Look at the following place-value models for decimal numbers.

Ones

1 whole is 10 times 1 tenth

Tenths

1 tenth is 10 times 1 hundredth

Hundredths 1 hundredth

1

1

0.1

1

0.01

5 1.11

In a decimal number, a digit in one place has ten times the value

it would have in the place to its right.

310

310 310 310 310

thousands hundreds tens ones tenths hundredths

Circle all of the numbers in the equation below the chart.

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Lesson 1 Understand Place Value

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Think 1 hundredth is 10 times 1 thousandth.

If you break one hundredth into 10 equal parts, each part is 1 thousandth of the whole.

Look at the pattern in the chart.

3?110? 3?110? 3?110? 3?110? 3?110? 3?110? 3?110?

0.001 0.01 0.1 1 10 100 1,000 10,000

310 310 310 310 310 310 310

When you multiply a number by 10, the product is 10 times the number.

When the digit 1 moves one place to the left, its value is 10 times what it was.

When

the

digit

1

moves

one

place

to

the

right,

its

value

is

1 ?10?

what

it

was.

Look more closely at the first two numbers in the chart.

? One hundredth is 10 times one thousandth. 0.01 5 10 3 0.001

? One thousandth is one tenth of one hundredth. 0.001 5 0.01 4 10

To write the fraction one thousandth as a decimal, write a zero in the tenths and hundredths places and a 1 in the thousandths place to the right of the decimal point.

1 ?1?,0?0?0?

5

0.001

Reflect

1 In which number does the digit 5 have a greater value, 0.05 or 0.005? How many times as great is the value? Explain how you know.

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Lesson 1 Understand Place Value

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Lesson 1 Guided Instruction

Think About Place-Value Patterns

Let's Explore the Idea Let's explore place-value patterns

with another example using models. Each grid represents 1 whole.

A

B

C

2 Label models A, B, and C with a decimal to name the amount shaded. 3 The shaded region of Model B is how many times the shaded region of Model A?

The shaded region of Model C is how many times the shaded region of Model B?

4 Use the models above to complete the equations. 0.03 3 10 5 0.3 3 10 5 0.3 4 10 5 3.0 4 10 5

Now try these two problems.

5 Continue the 310 pattern to fill in the blanks.

0.003

0.03

0.3

300

6 Use the 410 pattern to fill in the blanks.

500

5

0.5

0.05

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Lesson 1 Understand Place Value

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Let's Talk About It

Now let's explore how 0.30 compares to 0.3.

7 Look at the models in problem 2 and the labels you wrote. Now shade some or all of the grids in the model below to show 30 hundredths. Each grid represents 1 whole.

Find the model on the previous page that has the same shading as the model you shaded above. What label did you give that model on the previous page? 8 Use the model you shaded in problem 7 to write a decimal for 30 hundredths. thirty hundredths 5 9 How do both shaded models show that 30 hundredths is the same as 3 tenths?

10 What equation can you write to represent "10 times 3 hundredths is 30 hundredths"?

Try It Another Way

11 Imagine a model shaded to show 0.001. How much would be shaded?

12 How would you shade a model to show ten thousandths?

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Lesson 1 Understand Place Value

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Lesson 1

Guided Practice

Connect Ideas About Place-Value Patterns

Talk through these problems as a class, then write your answers below.

13 Create Shade the models below to show how the value of 0.04 is related to the

value of 0.4. Then write a division equation to represent the relationship.

14 Analyze Kiran showed 0.08 with the model below.

What is wrong with Kiran's model? What can be done to her model to show 0.08?

15 Demonstrate A meter is one thousandth of a kilometer. Write an equation to

show the relationship between 7 meters and 0.007 kilometer.

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Lesson 1 Understand Place Value

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