Connecting Fractions and Decimals: How? When? Why?

My colleague and I were going through your scope and sequence scheduling for fourth grade. How do you transition from fractions into decimals? We are trying to create that aha moment with a majority of our lessons and trying to make it relevant for the students as to why they need to use certain tools in math. For whatever reason we are struggling with a legitimate reason as to why it’s good to use decimals over fractions in some cases and what kind of activity to tie in with that concept. What can we show or give the students that would make it clear this is why we need decimals sometimes as opposed to fractions and vice versa? If you have any thoughts I would love to hear them and thank you for your time.

 

Tim S.

Wisconsin

Wow! You’re making me think!

 

Fractions and decimals are often taught as separate units instead of connected ideas. However, you can’t give meaning to decimals without understanding fractions. I purposefully use the terms common fractions and decimal fractions to distinguish between the two while also serving as a reminder that they are both fractions.

Transitioning from Fractions to Decimals

 

I begin with common fractions. We make fractional units, draw pictures of fractional units explore equivalency, and compute. We then connect common fractions to decimal fractions using familiar models. Begin with a page of pre-sectioned rectangles similar to the fraction kit strips.

 

 

As you can see there are 10 on that page. However, 5 per page would be a better option if you have them write as much as I do.

Flow:

 

  1. The students color in a different number of sections on each “strip.” They do not need to color in a specific order.

 

  1. Students label each shaded representation using a common fraction.
  1. Introduce decimal fraction notation as an equivalent way to name the shaded region.

.3                                     .6

  1. Students write the number-word.

three-tenths                      six-tenths

 

Note: The number word is the same for both common and decimal fractions.

  1. Repeat steps 2-4 for the unshaded regions.
  1. Students write a set of equations for each.
  1. Students could also write 4 additional equations.
  1. When I asked my colleague Dr. Jill Perry (Rowan University) to write a guest blog about when and why it’s good to use decimals over fractions, she suggested another way to record.

Love it! Why didn’t I think of that?

 

In other words, we are able to make many connections through this activity. We examine patterns and relationships.

I then change the whole to:

 

 

and repeat the steps outlined above.

We end with connecting tenths and hundredths.

 

 

The students shade in half of each whole.

 

Students then label in a variety of ways:

Note: I was taught that zeroes at the end of a decimal number “don’t matter.” You can add and remove as needed. It is important that students understand that .5 (five-tenths) and .50 (fifty-hundredths) are equivalent. However, .50 is made up of smaller pieces (units). The zeroes do make a difference in relation to the unit fraction pieces used.

 

 

A more detailed description of this sequence is available in Creating Fraction and Decimal AHAs.

When and why use common fractions over decimal fractions or vice versa

 

I’m afraid I haven’t really thought deeply about it until I read your questions. Maybe it’s not choosing one or the other but understanding and using the connection between the two. Building comfort with moving between the two. Students can then choose the most appropriate version based on the context.

 

When thinking of decimal fractions, I immediately think of money, time-keeping in races (e.g., track, swimming, skiing, skating, etc.), technology uses (entering numbers into computers and calculators and using to compute, analyze, etc.), and the patterns of our base 10 system.

 

Money: I don’t believe that students understand the meaning of the currency symbols. They read the symbols $ (dollar) and ¢ (cent) but do they connect them to the wholes that they represent? How often do we see decimal points used with the cent symbol? Do students understand that the whole is a cent or penny? Therefore, .25¢ would be a fourth of a cent or penny. We don’t have fractions of a penny in our currency. Do students understand that when using the decimal point with the dollar sign we are representing parts or a fraction of a dollar? The dollar is the whole.

I don’t think they do. Fractions help with this.

 

Positional Number System: Because we have a positional, base 10 number system, positions within the system represent a power of 10. The digit placement gives value to the digit. Decimals are used within the system to represent fractional amounts. When students get to middle school and have worked with positive and negative exponents the patterns become more clear.

We build the foundation for this in the elementary grades by developing the concept that the place to the immediate left is 10 times greater and to the immediate right is one-tenth the size. Because of this we are able to represent smaller and smaller fractional units quickly and we can quickly move from tenths to hundredths to thousandths, ten thousandths, and hundred thousandths, etc.

 

Algebra: In algebra we tend to use common fractions within expressions and equations instead of decimal fractions.

 

 

Context helps I think. Being able to comfortably move between the two based on context is important.

 

What do you think? I’d love to hear what you come up with. I hope you’ll share.

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