# Adding Fractions with Common Denominators

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## Objective

SWBAT to add benchmark fractions using a number line and will express their developing understanding of quantities that are less than and greater than one whole.

#### Big Idea

Straightforward practice adding benchmark fractions on a number line!

## Opener

5 minutes

OPENER:

"Think (silently)  about how adding fractions on a number line will compare to adding whole numbers.  Think of a similarity, a difference, or both."

After a few minutes:

"Turn and share with a neighbor.  I will be coming around to listen to your ideas."

I am doing this to gather information and I want to encourage open discourse.  If students are corrected every time they say something they won’t feel free to speak.  So, I don't correct any of their thinking but I do provide them with sentence stems and vocabulary assistance.  This is an especially important support for ELL students.

Example sentence stems to facilitate student thinking.

I think that (adding fractions or adding whole numbers) is going to be (alike, different) because _____________.

I think one thing that is different between adding whole numbers and adding fractions is ______________ (e.g., that a whole number has digits written like this (child demonstrates) and a fraction has a number on top and on the bottom.)

After a few minutes, I randomly choose on 3-5 students to share their thoughts about how adding fractions might be different or similar to adding whole numbers.  I may also deliberately pick a child with an especially clear thought or a misconception that I know other students share.

## Direct Instruction and Guided Practice

20 minutes

GUIDED PRACTICE

I use simple number lines such as the ones on Guided Practice Examples of Number Lines to show two addition problems, 1 + 2 = 3 and 1/4 + 2/4 = 3/4.

"The denominator stands for equal parts that make up one whole unit or group. As the number of pieces that make up one whole remain the same, the denominator remains unchanged when we are adding.   In addition (and subtraction) we are working with the numerator, the number of those equal pieces that are represented."

I go through several examples, briefly but clearly.  Consider writing out the complete equations and letting them look at them and think before then going through the steps.  This is helpful to whole to part thinkers.

 2/4 + 2/4 = 4/4 1/3 + 1/3 = 2/3 1/8 + 3/8 = 4/8.

• "What did you notice about the numerator?"
• "What did you notice about the denominator?"
• "Is the sum greater than one whole?  How do you know?"
• "Is the sum less than one whole?  How do you know?"
• ** "Which is larger?  5/4 or 2/3?"  (What I'm looking for here is that 5/4 is larger because it is larger than one whole, whereas 2/3 is less than one whole.  The comparison does not need to go beyond recognition of fractions that are less than, equal to, or greater than one whole."

Then I draw number lines. I explicitly make the tick marks and count the spaces.  I ask the students to assist me as I  label the fractional part represented by each line. Then I ask students to model the addition problem with me.  After we've done 5 to 7 of those, I have them do 5 to 7 more on their own as I watch.

 1/2 + 1/2 = 1/2 + 2/2 = 1/2 + 3/2 = 1/6 + 4/6 = 1/3 + 3/3= 2/3 + 2/3 = 4/8 + 6/8 = 2/4 + 3/4 = 1/8 + 5/8 =

When I cross the "one whole" mark I ask questions at least half of the time instead of just stating it.  "Is 3/2 larger or smaller than one whole?  How do you know?"

## Independent Practice

30 minutes

While the fine motor task of drawing out a number line adds a layer of complexity for the students, in this lesson I have (most of them) draw their own number lines because I do firmly believe (and research has shown) that we learn things in a different, more entrenched way when we have to write them out by hand.

I have them draw out number lines to show these addition equations:

 1/4 + 1/4 = 4/4 + 2/4 = 1/4 + 1/4 + 1/4 = 1/3 + 1/3 + 1/3 = 3/3 + 1/3 = 3/3 + 3/3 = 1/2 + 1/2 = 2/2 + ½ = 2/2 + 2/2 = 3/2 + 1/2 = Create your own.

I use this time to confer with students and nudge them to the next level of thinking on an individual basis.  This student demonstrates a thorough understanding addition of fractions with common denominators.  The next step for her will be to put this in written form.

This student also understands how to add fractions with common denominators and can show it on a number line.  I admire his creative use of English to try and explain that for which he does not yet have English words.

## Wrap-up

5 minutes

To close this lesson, I ask students to write a few sentences in their math journal.  They may respond to one or more of these prompts:

• Why doesn't the denominator change when you are adding fractions?