Series Connecting Math to Real-World Tasks: Understanding Fractions through Real-World Tasks

Math.Practice.MP4

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP4:  Model with mathematics.

    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Download Common Core State Standards (PDF 1.2 MB)

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Math.3.NF.A.1

Common core State Standards

  • Math:  Math
  • 3:  Grade 3
  • NF:  Numbers & Operations--Fractions
  • A:  Develop understanding of fractions as numbers
  • 1: 
    Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.


    Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

Download Common Core State Standards (PDF 1.2 MB)

|
Math.3.NF.A.2a

Common core State Standards

  • Math:  Math
  • 3:  Grade 3
  • NF:  Numbers & Operations--Fractions
  • A:  Develop understanding of fractions as numbers
  • 2a: 
    Understand a fraction as a number on the number line; represent fractions on a number line diagram.


    a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.


    b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.


    Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

Download Common Core State Standards (PDF 1.2 MB)

Understanding Fractions through Real-World Tasks

Lesson Objective: Solve a real-world problem about fractions of watermelons
Grade 3 / Math / Modeling
6 MIN
Math.Practice.MP4 | Math.3.NF.A.1 | Math.3.NF.A.2a

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Discussion and Supporting Materials

Thought starters

  1. Why is it helpful to begin by activating students' prior knowledge?
  2. How does Ms. Franco encourage students to push each other's thinking?
  3. When does Ms. Franco listen actively without evaluation?
  4. Why is this important?

10 Comments

  • Private message to Kacie Mechler
I noticed the students were speaking more than the teacher. The students had to think about how they were going to attack the problem before they did it. The teacher did a lot of listening and evaluating her students as the worked. I think I would incorporate the part of the students reflecting and discussing the problem after they found the answer.
Recommended (0)
  • Private message to Beth Schlauch
Ms. Franco has obviously taught the students vocabulary relating to the task/lesson. She uses both mathematical vocabulary and words the kids know from everyday conversation to re-emphasize her instructions and expectations. I also like the way she gives clear tasks and goals, then monitors their work and thinking as partners and groups.
Recommended (0)
  • Private message to Lauren Gaspard
We feel as though her pacing sets kids up to have time to process what is asked and students can better explain their thinking when they share. She gave real world examples to hook her students into the lesson, we noticed they were more confident in answering the more abstract questions after the hook.
Recommended (0)
  • Private message to Anny Vang
Having students discuss and explain their mathematical thinking really encourages independent thoughts. I agree with Ms. Franco when she says students don't have to get the right answer the same way as the teacher does but just as long as they get the correct answer.
Recommended (0)
  • Private message to Araceli Valtierra
There was a lot of student discussion and students really explained their mathematical thinking. Students were given enough time to work together and by themselves to find the solution to the given problem.
Recommended (0)

Transcripts

  • Understanding Fractions through Real-World Tasks Transcript

    Speaker 1: Yesterday we were talking about where can we find math? Where do we

    Understanding Fractions through Real-World Tasks Transcript

    Speaker 1: Yesterday we were talking about where can we find math? Where do we see math? Do I see it in my reading? Do I see it where I'm walking home? Do I see it when I go to the grocery store? Where do I see math?

    We started with activating their prior knowledge.

    What do you know about fractions? Alec, can you tell me what you know about fractions?

    Alec: Fractions are parts of one whole.

    Speaker 1: How many of you agree with Alec that fractions are part of a whole? Show me thumbs ups if know. Okay, give him a round of applause. Thank you, Alec. Good idea. Thank you for sharing that.

    The test today was that Jack had eaten two thirds of a watermelon, so then Suzy came and got another watermelon the same size as Jack. Then her's was partitioned, divided. She cut it into six equal parts.

    Group: If she wants to eat the same amount as Jake, how many pieces should Suzy eat?

    Speaker 1: Okay. Our mystery hero is to read it one more time. I want you to keep on thinking about what is that task about. Who is there? What do you know? What is it that is unknown? Here we go.

    I like to spark their thinking. What I try to do is bring something that they already know.

    We have two watermelons. Now I want for you to think about what is your plan. We already have the known. We already have the unknown. How am I going to attack this problem? What should I do? What tools do I need to use in order for me to solve this task.

    [inaudible 00:01:58] You're going to discuss about how you are going to attack this task. In other words, what is your plan? How are you going to solve this task? I'm going to go around listening, and then we're going to wrap it up. Go ahead and go.

    I usually ask so many questions, but for this particular lesson, okay, I'm going to let you ... I'm going to see how you guys work by yourselves. I'm going to be listening for questions because they have to be coaching their partners. They have to be asking them questions.

    Group: [crosstalk 00:02:29]

    Speaker 1: It's a lot of talking in the classroom.

    Thank you for sharing your information[crosstalk 00:02:45]. Can you tell me what you did right here? What is that?

    Speaker 2: That is my pie chart and I partition it into equal parts. From the diagram that I did first I noted that Jake just cut them into bigger pieces and Suzy cuts it into small. I know that that is equal.

    Speaker 1: I know that he knows how to do his representations of the different fractions.

    Speaker 2: I already get one strategy and I tried another one. I remember that four sixths was the fraction.

    Speaker 1: Okay, can I ask you something? What does that "N" represent? I see an "N" right there. What does that representation of the letter "N"?

    Speaker 2: The "N" represents the unknown because if you do not have the answer, you can put a letter, whatever letter, and then you can figure out the answer.

    Speaker 1: Okay. Thank you so much for sharing.

    It's like, "Oh, wow." You came up with your own idea. It doesn't have to be the same one as mine. You don't have to use mine. As long as we come up with the same answers.

    Where do you think this number[inaudible 00:04:06] could go into? Where could it go? Yes?

    Speaker 2: Check answer.

    Speaker 1: Check your answer. This is bumping it up higher to make a whole. Even though your denominators are totally different.

    Then I can evaluate my students as they're working, and then evaluate myself, too. Did I support them enough?

    How many of you already found out the unknown for Suzy? Even though Isaac did it over here, but we didn't say whether we agree with him or disagree with him. Show me. Thumbs up if you agree with Isaac. Suzy got four sixths. Is that correct? Four sixths.

    Speaker 2: It is correct.

    Speaker 1: Think about Jake and Suzy's task. Think about what you did, how you attack this task, and how you justify your answer. Okay, you have one minute. You're going to talk to your neighbor. You're going to tell your neighbor, summarizing everything that you have done. Okay, ready? I'm going to walk around and listen to you.

    As I'm looking at them, it's like, "Yes. They got it." They understood tasks. They know that they're working on fractions and not addition and subtraction. They understand the task by understanding the words, the vocabulary that comes in. Embracing what they know, their knowledge.

    Okay. Thank you, boys and girls. You worked very, very hard. Thank you for sharing with your neighbors. We will continue with fractions. Show me thumbs ups, and tell yourself, "Awesome job." "Awesome job." Thank you. We're going to close up.

School Details

Orange Grove Elementary School
3525 West County 16 1/2 Street
Somerton AZ 85350
Population: 343

Data Provided By:

greatschools

Teachers

Maria Franco

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