1. Mathematics Lesson: Decimal Place Value with Base Ten-Expanded Form
5.NBT.3 Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g.,
= 3 x x x x (1/10) + 9 x (1/100) + 2 x (1/1000)
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols
to record the results of comparisons.

2. Essential Question and Vocabulary
How does the placement of the decimal impact the value of a number?
Thousandth: one part out of 1,000 equal parts of a whole; the position of the third digit to the right of the decimal point
Expanded Form – a way to write a number that shows the sum of the values of each digit in the number.

3. Chalk Talk-Equivalent Forms

4. Decimals Expanded Form
Expanded Form
Fourth Grade
showing multiplying by decimal representation of each
decimal place value or exponential form
showing multiplying by fractional representation of each
decimal place value
4.82
4(1) + 8(0.1) + 2(0.01)
4(1) + 8(1/10) + 2(1/100)
1.236
1(1) + 2(0.1) + 3(0.01) + 6(0.001)
1(1) + 2(1/10) + 3(1/100) + 6(1/1000)
57.49
5(10) + 7(1) + 4(0.1) + 9(0.01)
5(10) + 7(1) + 4(1/10) + 9(1/100)
236.45
2(100) + 3(10) + 6(1) + 4(0.1) + 5(0.01) Or
2(10^2) + 3(10) + 6(1) + 4(1/10) + 5(1/100)
2(100) + 3(10) + 6(1) + 4(1/10) + 5(1/100)
1.274
1(1) + 2(0.1) + 7(0.01) + 4(0.001)
1(1) + 2(1/10) + 7(1/100) + 4(1/1000)
5(100) + 7(10) + 6(1) + 3(0.01) + 7(0.001)
5(10^2) + 7(10) + 6(1) + 3(1/100) + 7(1/1000)
5(100) + 7(10) + 6(1) + 3(1/100) + 7(1/1000)

5. Compare the two numbers 1.236 and 1.274
1.236 < 1.274; I know is less than because they both have 1 one and 2 tenths, but has 3 hundredths and has 7 hundredths. 7 hundredths is greater than 3 hundredths, making larger than 1.236

6. Decimals Expanded Form Journal Prompt
1. Write each decimal number in expanded form two different ways.
2. Compare the decimals numbers using your knowledge of place value and expanded form. Explain your answer.

7. Answer for Decimal Expanded Form Prompt
= = 8(0.1) + 3(0.01) + 4(0.001) = 8(1/10) + 3(1/100) + 4(1/1000)
= = 8(0.1) + 3(0.01) + 2(0.001) = 8(1/10) + 3(1/100) + 2(1/1000)
>
I know is larger than because each number has a zero in the ones place, an eight in the tenths place and a three in the hundredths place. The only place value where these two numbers differ is the hundredths place. In 0.834, there are 4 thousandths and in there are 2 thousandths is greater than so is larger than