In this Grade 4 lesson from Saxon Math Intermediate 4, students explore the relationship between fractions and decimals, learning how place value determines the denominator in tenths and hundredths. Students practice converting between fraction and decimal notation, reading mixed numbers such as "twelve and twenty-five hundredths," and representing values like 0.07 and 2.07 using shaded grid models. Hands-on activities with a stopwatch further reinforce decimal reading and ordering skills in a real-world context.
Section 1
📘 Relating Fractions and Decimals
To name a decimal number, we name the numerator shown by the digits and then we name the denominator indicated by the number of decimal places.
Next, you'll practice converting between these forms and comparing their values using grids and real-world examples like stopwatch times.
Section 2
Relating Decimals and Fractions
Fractions and decimals are two ways to describe parts of a whole. In a decimal number, the denominator is not shown but is indicated by the number of decimal places. One decimal place represents tenths, and two decimal places represent hundredths, such as and .
For one decimal place: .
For two decimal places: .
When a zero is a placeholder: .
Think of the decimal point as a secret code for the denominator! One spot after the point means the denominator is 10, and two spots mean it's 100. You are just hiding the bottom number of the fraction in plain sight, which makes everything on the page look much cleaner and tidier. It’s a shortcut!
Section 3
Naming decimal numbers
To name a decimal number greater than 1, like , you mentally split it at the decimal point. First, name the whole-number part. Second, say the word 'and'. Third, name the fraction part by reading the digits and stating the place value (tenths, hundredths, etc.).
The number is read as 'ten and seventy-five hundredths'.
The number is read as 'six and four tenths'.
The number is read as 'eight and two hundredths'.
Reading decimals is like introducing a friend's family! First, you say the whole number's name, like 'twelve'. Then, you use 'and' as the bridge to the rest of the family. Finally, you introduce the decimal part, like 'twenty-five hundredths'. This simple, three-step introduction will make you sound like a math with every single time.
Section 4
Connecting decimals to money
A powerful way to understand decimals is to relate them to money. Think of a large square or one whole unit as one dollar. A column (one-tenth of the whole) is like a dime, and a single small square (one-hundredth) is like a penny. This makes decimal values tangible and easy to visualize.
represents one dime, which is of a dollar.
represents one penny, which is of a dollar.
dollars is three dollars, five dimes, and two pennies, or 'three and fifty-two hundredths' dollars.
Imagine your math grid is cash! A big square is a one dollar bill. Each column is a shiny dime (one-tenth), and each tiny square is a copper penny (one-hundredth). So, when you see a decimal like , you can picture two whole dollars, four dimes, and five pennies. Suddenly, decimals feel a lot less abstract!
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Section 1
📘 Relating Fractions and Decimals
To name a decimal number, we name the numerator shown by the digits and then we name the denominator indicated by the number of decimal places.
Next, you'll practice converting between these forms and comparing their values using grids and real-world examples like stopwatch times.
Section 2
Relating Decimals and Fractions
Fractions and decimals are two ways to describe parts of a whole. In a decimal number, the denominator is not shown but is indicated by the number of decimal places. One decimal place represents tenths, and two decimal places represent hundredths, such as and .
For one decimal place: .
For two decimal places: .
When a zero is a placeholder: .
Think of the decimal point as a secret code for the denominator! One spot after the point means the denominator is 10, and two spots mean it's 100. You are just hiding the bottom number of the fraction in plain sight, which makes everything on the page look much cleaner and tidier. It’s a shortcut!
Section 3
Naming decimal numbers
To name a decimal number greater than 1, like , you mentally split it at the decimal point. First, name the whole-number part. Second, say the word 'and'. Third, name the fraction part by reading the digits and stating the place value (tenths, hundredths, etc.).
The number is read as 'ten and seventy-five hundredths'.
The number is read as 'six and four tenths'.
The number is read as 'eight and two hundredths'.
Reading decimals is like introducing a friend's family! First, you say the whole number's name, like 'twelve'. Then, you use 'and' as the bridge to the rest of the family. Finally, you introduce the decimal part, like 'twenty-five hundredths'. This simple, three-step introduction will make you sound like a math with every single time.
Section 4
Connecting decimals to money
A powerful way to understand decimals is to relate them to money. Think of a large square or one whole unit as one dollar. A column (one-tenth of the whole) is like a dime, and a single small square (one-hundredth) is like a penny. This makes decimal values tangible and easy to visualize.
represents one dime, which is of a dollar.
represents one penny, which is of a dollar.
dollars is three dollars, five dimes, and two pennies, or 'three and fifty-two hundredths' dollars.
Imagine your math grid is cash! A big square is a one dollar bill. Each column is a shiny dime (one-tenth), and each tiny square is a copper penny (one-hundredth). So, when you see a decimal like , you can picture two whole dollars, four dimes, and five pennies. Suddenly, decimals feel a lot less abstract!
Book overview
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Continue this chapter