Fractions and Expressions

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Students will be able to draw a picture and write an equation to solve a problem.

Big Idea

Students will develop comprehensive understanding and flexible skills by using concrete manipulatives and pictorial representations of a mathematical situation.


15 minutes

Fraction Pad

Whole group instructions 

To begin I check to make sure students have the math background needed in order to be successful in this lesson.  I also need to determine my students' range and depth of strategies. I ask students, "how else can you solve word problems more efficiently?"  

Some students say math models and and looking for "clue" words.  

I remind students of their "clue" words but warn them that in some math equations keywords can indicate different operations. You need to check that your decision makes sense by looking at the context of the problem. 

The "clue" words are displayed on my math vocabulary wall. At this point of the year, I expect my students to know:

  • Add 
  • Altogether
  • In all
  • Compare
  • Difference
  • Equal
  • Equal groups
  • Subtract
  • Less than
  • More than
  • Greater than
  • Fewer
  • Sum

 I ask students, "What should you do if you find more than one keyword listed in a word problem?"  Students say they should re-read the math problem to make sure they understand exactly what the problem is asking them to do.

To confirm their thinking and narrow down any misconceptions, I review the given word problem to assess what they know so far. I also ask some critical thinking questions that are "Common Core" aligned. Fractions and Word Problems.docx

For example:

"How can you solve this problem in different ways?" (Or prove your work, using another way.)

"How can mathematical models help you understand the problem" Show and explain your thinking.  

I want students to realize that they are using decomposing and composing skills, along with other math facts to help them solve problems.  As students respond to the given questions, I use their responses to adjust the difficulty of this lesson.  Doing this helps me meet my students where they are in their learning.

 Mathematical Practices:

 MP.2. Reason abstractly and quantitatively.

 MP.3. Construct viable arguments and critique the reasoning of others.

 MP.4. Model with mathematics.

 MP.5. Use appropriate tools strategically.

 MP.7. Look for and make use of structure

 MP. 8. Look for and express regularity in repeated reasoning.



Interactive Learning!

10 minutes

Interactive Learning

I encourage students to take notes throughout the lesson. I give extra points for students who have a well kept math journal.

In this interactive activity students learn to use multiple problem solving skills to solve real world problems using fractions. Technology is a great way to engage students and should be incorporated as much as possible.  It is important for students to experience new concepts in many different ways.  Technology and real-world scenarios allow students to stay focused and connect with how the problem is being solved, instead of just using basic computational steps.  

Probing Questions:

How did you reach that conclusion?

Can you make a model to show that?

Why is that true?

Students are explaining their own thinking and thinking of other methods with accurate vocabulary as to why their solution is correct.


Guided and Modeling

20 minutes

 I invite students to the carpet to discuss and work our way through a mathematical model.

 I start off by pointing out keywords that help us decide which operation and mathematical models to use to make sense of and solve problems.  

I ask students to think about how far you ride your bike when you go bike riding. 

Responses are around a few miles, blocks, or a ½ a block.  I'm going to use biking around the neighborhood to create a "real world" context for students.


Mike rode his bike ¾ of a mile on Tuesday, 3/4 of a mile on Thursday, and 2/4 of a mile on Saturday.  How far did he ride his bike in all?

After giving students time to read the problem, I ask (1) "What keywords will help determine how to solve the problem?, (2) What are the given numbers? (3) Can drawings be used to help solve this problem? If so, how? (4) What are the steps you would use to solve this problem, and (5) What math skills are you using to solve the given problem? I take time to collect this information, and post it where students can see it.

Some students are not able to explain how to solve this problem.  So, I ask them to turn and talk to their neighbor. Talking with a partner in a pair-share gives them the space to discuss and develop their thinking of how to solve their equations.  Additional Problems.docx 

Independent Closing

20 minutes

Now that students have a better understanding of what they are expected to do. I ask them to move into their assigned seats.  I want to assess students' knowledge so far.  I probe their thinking by asking them what skills they noticed in the different math problems being used repeatedly? (they say math, division and subtraction) if not I briefly explain how the given math skills are used. I ask students to explain how the mathematical model helped them solve the equation.  (By using a mathematical model it assists me in understanding the problem) Assessment 

While students are responding to the given set of questions, I jot down any misconceptions and the names of students who appear to still be having difficulty understanding this concept.  I use their response to re-teach in a small group setting. This helps me meet the needs of all students.

I encourage students to use their own problem solving methods. However, I want them to choose one problem from their given assignment to write in their math journal.  I ask them to explain in detail/drawing how they solved their problem. I tell them that the math entry can be used when they need additional help solving word problems later on.


Student Sample