Grade 5 · Mathematics
Quarter 1 · Week 9 · TEKS
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This Grade 5 mathematics lesson focuses on understanding and representing the value of digits in decimal numbers through the thousandths place using expanded notation and numerals. Students will also learn to compare and order decimals to the thousandths place using comparison symbols (> , < , =). The lesson is grounded in TEKS standards and emphasizes place value understanding, mathematical reasoning, and real-world application.
Students should understand place value for whole numbers and decimals to the tenths and hundredths places, including reading and writing decimals and basic comparison of decimals to the hundredths place.
Decimals are numbers that show values less than one using places to the right of the decimal point. The first place to the right is the tenths place, the second is the hundredths, and the third is the thousandths. Each place represents a fraction of one: tenths are one part of ten, hundredths are one part of one hundred, and thousandths are one part of one thousand. For example, in the decimal 0.374, the digit 3 is in the tenths place and represents 3/10, the digit 7 is in the hundredths place and represents 7/100, and the digit 4 is in the thousandths place and represents 4/1000.
Expanded notation breaks down a number to show the value of each digit based on its place value. For decimals, this means writing each digit multiplied by its place value fraction. For example, the decimal 0.374 in expanded notation is (3 × 1/10) + (7 × 1/100) + (4 × 1/1000). This helps students see how each digit contributes to the overall number and understand the size of each part.
Students should practice writing decimals both as numerals (e.g., 0.374) and in expanded notation (e.g., 3 × 0.1 + 7 × 0.01 + 4 × 0.001). Using place value charts can help students place each digit correctly and understand its value. Visual models like decimal grids or base-ten blocks can reinforce these concepts by showing parts of a whole divided into tenths, hundredths, and thousandths.
To compare decimals to the thousandths, students look at each digit from left to right, starting with the tenths place. The first place where the digits differ determines which decimal is greater or smaller. For example, comparing 0.374 and 0.379, the digits in the tenths and hundredths places are the same, but the thousandths place digits 4 and 9 differ, so 0.379 > 0.374. Students use symbols > (greater than), < (less than), or = (equal to) to represent these comparisons. Ordering decimals means arranging them from smallest to largest or vice versa using the same digit-by-digit comparison method.
A common misconception is that a decimal with more digits to the right is always larger. For example, 0.4 is greater than 0.39 even though 0.39 has more digits. Another misconception is confusing place values, such as thinking the hundredths place is larger than the tenths place. Reinforce that place value decreases by a factor of ten as you move right from the decimal point. Use visual aids and expanded notation to clarify these points.
Write the decimal 0.526 in expanded notation.
The digit 5 is in the tenths place, so its value is 5 × 1/10 or 0.5. The digit 2 is in the hundredths place, so its value is 2 × 1/100 or 0.02. The digit 6 is in the thousandths place, so its value is 6 × 1/1000 or 0.006. Writing these together in expanded notation shows the value of each digit.
0.526 = (5 × 0.1) + (2 × 0.01) + (6 × 0.001)
Compare the decimals 0.374 and 0.379 using >, <, or =.
Look at each digit from left to right: tenths place is 3 for both, hundredths place is 7 for both, thousandths place is 4 and 9. Since 4 < 9, 0.374 < 0.379.
0.374 < 0.379
Begin by writing a decimal number such as 0.374 on the board. Ask students what each digit might represent and how the number is different from whole numbers.
Students share their ideas about the digits and their values. They may use prior knowledge about place value to guess the meaning of digits after the decimal point.
This activity activates prior knowledge about place value and introduces the concept of decimals through thousandths.
Provide students with decimal number cards and place value charts. Ask them to represent the value of each digit in decimals through the thousandths using expanded notation and numerals.
Students work in pairs or small groups to write decimals in expanded notation and explain the value of each digit using the place value chart.
Hands-on practice with place value charts and decimal cards helps students concretely understand the value of digits in decimals.
Model comparing two decimals to the thousandths place using examples on the board. Demonstrate how to use >, <, or = symbols to show the relationship.
Students observe the teacher’s demonstration and then practice comparing pairs of decimals using the symbols.
Explicit modeling helps students understand the process of comparing decimals digit by digit and using comparison symbols.
Present real-world problems involving decimals to the thousandths, such as measuring lengths or money amounts. Ask students to represent the decimals in expanded notation and compare them.
Students solve real-world problems by writing decimals in expanded notation and comparing them to decide which is greater or smaller.
Applying skills to real-world contexts deepens understanding and shows relevance of decimals in everyday life.
Give students a short quiz or exit ticket asking them to write decimals in expanded notation and compare pairs of decimals using symbols.
Students complete the assessment independently to demonstrate their understanding.
The evaluation confirms students’ mastery of representing decimal values and comparing decimals to the thousandths place.
Students work in pairs or small groups to write decimals in expanded notation and explain the value of each digit using the place value chart.
What digit is in the hundredths place in the decimal 0.483?
The digit in the hundredths place is 8.
Write the decimal 0.305 in expanded notation.
0.305 = (3 × 0.1) + (0 × 0.01) + (5 × 0.001)
Compare 0.482 and 0.428 using >, <, or =. Explain your answer.
0.482 > 0.428 because the tenths place digits are both 4, but the hundredths place 8 is greater than 2.
Order these decimals from smallest to largest: 0.367, 0.376, 0.363.
From smallest to largest: 0.363, 0.367, 0.376.
Write the decimal 0.709 in expanded notation and compare it to 0.79. Which is greater and why?
0.709 = (7 × 0.1) + (0 × 0.01) + (9 × 0.001). Comparing 0.709 and 0.79, 0.79 is greater because in the hundredths place 9 > 0 (0.79 has 9 in hundredths, 0.709 has 0).
Use place value charts and visual models to support understanding. Provide step-by-step guided practice with teacher support. Use simpler decimals focusing on tenths and hundredths before thousandths.
Use visual aids and gestures to explain place value. Provide vocabulary cards with definitions and examples. Use sentence frames to support explanations, e.g., 'The digit ___ is in the ___ place and means ___.'
Challenge students to write decimals in expanded notation including zeros in places. Have students create their own decimal comparison problems and explain their reasoning. Explore decimals beyond thousandths to ten-thousandths for extension.
Ask students to find examples of decimals in everyday life, such as prices or measurements, and write them in expanded notation. Have them compare two decimals they find and explain which is greater and why.
In this lesson, students learned to represent the value of digits in decimals through the thousandths place using expanded notation and numerals. They practiced comparing and ordering decimals to the thousandths place using the symbols >, <, and =. Through modeling, guided practice, and real-world problems, students developed a deeper understanding of decimal place value and how to communicate comparisons clearly and accurately.
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