# Series: Connecting Math to Real-World Tasks

Math.4.NF.B.3a

Common core State Standards

• Math:  Math
• NF:  Number & Operations--Fractions
• B:  Build fractions from unit fractions
• 3a:
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
<br />
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.

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Math.4.NF.B.3c

Common core State Standards

• Math:  Math
• NF:  Number & Operations--Fractions
• B:  Build fractions from unit fractions
• 3c:
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
<br />
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.

Lesson Objective: Use fractions to solve a real-world problem about chocolate bars
Grade 4 / Math / Modeling
Math.4.NF.B.3a | Math.4.NF.B.3c

#### Thought starters

1. What do students do before getting the task?
2. How does Ms. Linares make sure students understand the problem?
3. What do you notice about how Ms. Linares balances time for both individual and group work?
I had never heard of the three phase lesson structure. I can't wait to use it in my class. This year we are focusing on math tasks and formative assessment. I love how this structure helps students problem solve by giving them time to think, write a plan, share, guide each other, record key points, and reread the problem with solution, and celebrate at the end. Awesome job! Thank you for uploading the video!
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Great lesson idea and strategies.
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Excellent instructional strategies used by teacher
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As a reading specialist it was interesting to see Ms. Linares using many of the engagement strategies that are suggested/endorsed for literacy work. It goes to prove that when students are engaged they are more willing to work. It appears that in this classroom students are very used to the structures and routines of explaining their thinking and helping each other. In many instances students may be able to get to the answer, but can't explain how they did it. This video gave so many examples of this and through the work the students were also working on Speaking and Listening skills throughout the lesson. It was necessary to listen to the speaker to understand or clarify their own thinking. The children were respectful and polite as their peers worked through the challenge. It was also nice to see the teacher encourage students to do the heavy lifting and help others. The teacher could have given an explanation and done the work, but by encouraging the students to move forward as mathematicians they were able to work it out. Fractions are a difficult concept for many children to understand and to attach the application of the concept to a word problem with support and scaffolding worked very well. Needless to say when math is connected to candy attention was high. Add to this all of the positive feedback the children and teacher left with smiles.
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I noticed that your background knowledge was helpful for the students! :)
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#### Transcripts

• Launching a Fractions Task Transcript

Teacher: What do you know about whole numbers and fractions? I'll give you a couple of

Teacher: What do you know about whole numbers and fractions? I'll give you a couple of seconds to think. What do you know about whole numbers and fractions?

The strategies that I've gained through the [Bodel 00:00:14] training, I've been implementing in my classroom. It allows students to attack a task in three parts: the before, the during, and the after. I use it also as a diagnostic tool. I use it when I'm teaching so I can see right away the students that are getting it, students who are still struggling, students that might need additional support outside that specific lesson time.

Okay. Let's do a whip around. Once you're going to share with your group what you know about whole numbers and fractions and then whip around to two, thees, and fours. Okay, ready once? Get your idea ready, your thought ready, and share.

Class: I know that whole numbers are ...

Teacher: I activated students' prior background knowledge by asking them what they already knew about whole numbers and fractions. Who's the speaker in this group?

Class: A fraction is part of...[crosstalk 00:01:27][inaudible 00:01:27]

Teacher: You're correct. The three-phase lecture structure really plans it well. Okay, what are my students are going to do before I give the task. I have to make a connection. Let's start first with making a connection. We all love chocolate right?

All kids, they love chocolate so it's like a hanger, a hook for them to hook into the task. This is a visual. Just to make a connection. This is a visual of our chocolate bar task. The task involves students, ask students to think of ten mini chocolate bars that are two inches long. They had to arrange them in a train.

Class: How long will a train of ten bars be if [inaudible 00:02:15] with a one-fourth space between them?

Teacher: We read the problem. We read the task and we annotate it. We might circle key words, underline specific numbers and talk about it as a class. [inaudible 00:02:27] Tell us, what does train mean in this task?

Male: In this task it means that the mini snickers are lined up in a row.

Teacher: So they're talking about train like a row? Now is when I start probing them with questions, specific questions to see where they're going. Think time. What is going to be your plan? Think of a strategy. What strategy will you use to help you solve this problem? Pencils down, right now you're thinking ...

At first, I just let them try it. I observe what is going on and then once I give them some clarification, then I step in with specific questions about what they're doing.I heard different ideas. I heard from multiplication. I heard adding. I heard drawing. Remember, there's multiple ways to do this. There's different ways. We don't all think the same way. Right below your understanding the task, there's a plan. Now put it in words. Quickly, I'm going to give you about a minute and a half-two minutes. Now put it into words.

In group discussions, students know we do a round robin. So that allows equal opportunity for all students to share as well.Be respectful Listeners. Hear their mathematical thinking. [inaudible 00:03:43] Begin.

Class: [crosstalk 00:03:43]

Male: Maybe I'm going to add them or multiply them to know what is the answer and then I will justify my answer.

Teacher: The students were engaged into the lesson. There were a lot of conversations and part of doing mathematics is the conversations. They need to be involved. It's not about just adding computation numbers but also explaining what is it that they're doing. Does that connect to the task itself?

I want to hear from Malorie right now. Malorie came up with an idea but she's struggling to put it down on paper. So she's going to share her plan and let's see if we can help her out.How did you start making whole?

Teacher: Oh. So how many fourths will make up one full inch?

Malorie: Four. Wait, yeah.

Teacher: Okay. So she said how many fourths make up one whole inch?

Class: Four

Teacher: Four fourths. She wanted to represent that. So go ahead and let's help her represent. She said to add them. Okay, let's try it Malorie. Let's try it. What I thought would be easier for them, some students were being challenged. Go ahead and put it there. One-fourth. We're guiding you. What should she put next?

Class: Plus four.

Teacher: They're guiding you, see? So one-fourth. Okay, that's one-fourth, plus, help her out.

Class: Plus one-fourth

Teacher: It was challenging for them to realize well, if I take my fractions, can I make whole numbers from these fractions? That was the challenging part, making that transition from those fractions to whole numbers and coming up with the grand total of this chocolate bar train. How many spaces did Malorie ... Remember how many fourths did she add?

Class: Nine.

Teacher: Nine. Is that the same as what [Gylie 00:05:42] got here?

Class: Yes.

Teacher: So you ended up with two and one-fourth inches. What are the key points that they want to remember? Maybe something they learned. Something they knew already, a connection or something they struggled with as well.

Male: I struggled to add all the inches because they add the one-fourth and four of them. I thought it equaled just one whole until I looked at the problem and it said one-fourth inch. That's when I finally kind of got it but I struggled adding all of it until Malorie shared and I got the answer.

Teacher: So Malorie's explanation helped you where you were struggling, Awesome! See Malorie, you helped her out there. So good job [inaudible 00:06:37] Good job at sharing your struggle with us. We want students to become independent problem solvers and through that three phase lesson structure, it is enabling them to do so. In a complete sentence, ready? Get your thoughts. How long will the train of ten bars be if they're lined up in a row with a one-fourth inch space between them? Ready, go.

Class: The train will be twenty-two and one-fourth inches long.

Teacher: Awesome job you guys. Let's go on a roller coaster before we wrap it up. Ready? One, two, three.

Class: (Making train sound)

Class: (Clapping sound)

Teacher: All right boys and girls. Thank you.

Math

### Connecting Math To Real-World Tasks

#### School Details

Orange Grove Elementary School
3525 West County 16 1/2 St
Somerton AZ 85350
Population: 357

Data Provided By:

#### Teachers

Patty Linares

Teaching Practice

### Three Ways to Encourage Student Collaboration

All Grades / All Subjects / Collaboration

Teaching Practice

### Five Ways to Start Your Lessons

All Grades / All Subjects / Planning

Teaching Practice

### Three Ways to Practice Goal Setting with Your Students

All Grades / All Subjects / Engagement

Lesson Idea

### New Teacher Coaching Cycle: Looking Closely at Text

Grades 9-12 / ELA / Tch DIY

TCHERS' VOICE

Differentiation

TCHERS' VOICE

Class Culture

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Lesson Planning

TCHERS' VOICE

### Move Over Debate, It’s Time to Deliberate

Educating for Democracy