Teacher Guide: Decimal Place Value

@ Learning Objective 5-10 min lesson

Students will: Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right. Students will read, write, and represent decimals in standard form, word form, and expanded form.

Why this matters for FAST: Understanding decimal place value is foundational for all decimal operations. Students must identify digit values, convert between forms, and understand how moving a digit changes its value by a factor of 10.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Place value chart
Base-ten blocks (optional)
Decimal number cards
Colored pencils

! Common Misconceptions to Address

Misconception #1: More Digits = Larger Number

Students think 0.125 > 0.5 because 125 is greater than 5. They ignore the place value and compare as if they were whole numbers.

How to Address:

"Look at the tenths place first. 0.5 has 5 tenths, while 0.125 has only 1 tenth. Since 5 tenths > 1 tenth, we know 0.5 > 0.125. Always compare place by place, starting from the left!"

Misconception #2: Confusing Decimal Place Names

Students say "one hundred twenty-five thousandths" when reading 0.125, but write it as 0.00125 because they think of "thousands" as the whole number place.

How to Address:

"Notice the -ths ending! Tenths, hundredths, thousandths are to the RIGHT of the decimal. Tens, hundreds, thousands are to the LEFT. The decimal names have 'ths' because they're parts of a whole."

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Review whole number place value. Ask: "In the number 555, what is the value of each 5?" (500, 50, and 5). Establish that each place is 10 times greater than the place to its right.

2

Introduce Decimal Place Value (2 min)

SAY THIS:

"Just like whole numbers, decimals follow the same pattern - each place is 10 times smaller as we move to the right. After the ones place, we have tenths (1/10), hundredths (1/100), and thousandths (1/1000)."

Place Value Chart

4

7

.

3

8

5

47.385 = "forty-seven and three hundred eighty-five thousandths"

3

Teach Expanded Form (2 min)

Show how each digit can be written as its value:

SAY THIS:

"47.385 = 40 + 7 + 0.3 + 0.08 + 0.005. We can also write this as: (4 x 10) + (7 x 1) + (3 x 0.1) + (8 x 0.01) + (5 x 0.001)"

4

Demonstrate How Digit Value Changes (2 min)

Show that moving a digit one place left multiplies its value by 10, and moving right divides by 10.

The 3 in 47.385 is in the tenths place = 0.3
If we move it one place left (ones), 3 = 3 (10 times greater)
If we move it one place right (hundredths), 3 = 0.03 (10 times smaller)

5

Guided Practice (2-3 min)

Work through these together:

Write 12.056 in word form
Write 5.409 in expanded form
What is the value of the 6 in 3.126?
How does the value of 4 change from 0.4 to 0.04?

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"In the number 8.247, what is the value of the digit 4?"

A) 4 B) 0.4 C) 0.04 D) 0.004

Correct answer: C) 0.04 (4 is in the hundredths place)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Decimal place value Value of a decimal digit Convert decimals between standard and expanded form Decimal number names Equivalent decimals

^ Differentiation & Extension

For struggling students: Use base-ten blocks or money (dimes = tenths, pennies = hundredths) to make decimal place value concrete. Focus on tenths and hundredths before introducing thousandths.

For advanced students: Extend to ten-thousandths and hundred-thousandths. Challenge them to explain why 0.30 = 0.300 = 0.3 using place value concepts.

For home: Send Parent Activity sheet. Families can explore decimals using money and measurements.