raft examples math

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April 18, 2019 6-8-geometry

Printable raft writing surface area activity, grades 6–8, by: jeff todd.

Today I'm sharing a surface area activity I've used in middle school classrooms since the mid-90s. I have since developed it to become a RAFT writing assignment. In this article, you'll find free printable instructions and rubrics for scoring this toy company themed surface area activity!

Surface Area Activity That Incorporates The RAFT Writing Strategy

This surface area RAFT activity is perfect for middle school students learning about surface area of rectangular prisms. Students imagine that they are a marketing company president and are pitching to a toy company a design proposal for a box for shipping square toy blocks. They need to propose a shipping container for the toy blocks that is not too expensive (i.e., conserves surface area) and provides ample space for a powerful marketing message (i.e., has a large side to display the marketing message).

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Using the raft writing strategy in mathematics.

If you haven’t used the RAFT writing strategy in math before, let me introduce you to the format. RAFT stands for Role, Audience, Format, and Topic. With the RAFT writing strategy students are given a role in a real-life writing topic, a specific audience, a pre-defined format, and a specific topic.

Here is how this surface area activity works using a RAFT writing model:

Role—You are the President of a marketing company that is submitting a proposal to design the packaging for a product.

Audience—You are writing to the President of a toy company, who will make a decision on which proposal to accept.

Format—You are writing a business letter that includes an attachment showing your marketing design for the packaging of the product.

Topic—You are addressing two areas of concern about the package: the cost of the cardboard and the design of the main face (side) of the package.

The surface area activity is framed in this way: You are to create a design proposal for the packaging (a box) of ABC blocks (children’s toys) that will be used to display a set on the shelf of a store. The package contains 48 one-inch cubes. You must identify the dimensions of the box. The toy company wants to keep the cost of the cardboard used to make the packaging as low as possible, but would also like to have one face of the package designed to capture the customers’ attention.

Individual and Group Work

I have done this activity both as an individual and as a group activity. If it is used as group work, the surface area activity lends itself to having “departments.” There could an art department that designs the package, a writing department for writing the letter, a technical department calculating the dimensions of the package, and a manager to coordinate the group’s activities.

The scoring rubric for the RAFT activity includes criteria for students to communicate mathematically when writing the letter. Specifically, students can address the Standard for Mathematical Practice 3, which includes students constructing a viable argument as to why the toy company should use their design. These goals are also consistent with the ELA writing standards for grade 6–8, where students are required to write arguments to support claims with clear reasons and relevant evidence.

In Conclusion

If you would like to use this RAFT writing surface area activity in your class, click on the link below to download the instructions for students and the scoring rubric to grade their work.

R.A.F.T. Writing in MATH

• by Kelly Harmon
• Jan. 11, 2019, 1:46 p.m.

When I started using the  6+1 Traits of Writing  9 years ago, I loved the strategy of RAFT to get students focused on a specific message for a specific audience.  RAFT   stands for Role, Audience, Format, and Topic.  It really helped my students zone in on what was most important. Then as my instruction evolved, I found that RAFT was also an awesome strategy for writing in math.

In math, this strategy is great for getting students to think deeply about mathematical ideas. In RAFT, student construct an explanation or argument to a prompt. The prompt asks them to use their conceptual or procedural knowledge to address a prompt in a specific format for a specific audience and topic

Here are a few example prompts:

R: You are a big number.

A: Your audience is a smaller number.

F: The format is a letter.

T: The topic is "Ways we can become equal"

R: You are a math strategy for adding numbers (or multiplying)

A: Your audience is another strategy

F: The format is a debate

T: The topic of the debate is "How and why your strategy is better than the other strategy"

R: You are a square.

A: Your audience is a rectangle.

F: The format is a Venn Diagram.

T: The topic is "Ways you are the same and how you are different"

The response to the prompt will provide you and the student with data about the students' current understanding and reasoning about critical math concepts or procedures. Be sure to develop a rubric that includes the learning targets you are looking for students to demonstrate through the writing.

I love this strategy because it gets kids to think and develop new ideas. Learning happens when we are in a productive struggle and RAFT will take your students there!

A Guide to the R.A.F.T. Writing Strategy Across Content Areas

Why is RAFT writing one of the most effective writing strategies, particularly across all content areas and subjects? Before we share how it enables fluency and purpose, incorporates the elements of effective writing, provides students with a choice that is on grade level, and engages students to explain what they know and elaborate, let’s first talk about how different writing styles contribute to learning and understanding.

How Writing Pulls Back the Curtain

Heard often in classrooms: “I know the answer but I can’t explain it!” The problem here is a student who suffers from messy thinking and the simple answer to clearing that confusion might be writing.

Research has proven that writing crystallizes cloudy thinking, yet teachers often miss opportunities to provide students a venue for becoming aware of what they know and do not know. Another missed opportunity arises from a misunderstanding of types of writers.

What many mistake as writer’s block is actually a block in thinking.

Dianne Boehm simplifies this concept in her book Mozartians, Beethovians, and the Art of Teaching Writing . She describes writers as either Mozartians or Beethovians:

• Beethovians are discoverers who discover what they think during the writing process. They actually generate their ideas as they write. These writers are very messy writers who write in a non-directed way. This writing almost always needs a great deal of revision.
• Mozartians , by contrast, are planners. They mentally compose before they ever put pen to paper, working in a linear way focusing on what comes next. As they write they tend to recall what they know and organize that information as they write. Their revision process isn’t nearly as broad because they have mentally composed, revised, and edited throughout the composition process. 

Either type of writer is using writing in a way that contributes to learning and understanding.

Effective Writing in the Classroom

Regardless of which type of writer you or your students are, the implications are the same. Writing is the ideal vehicle for getting at what students understand and don’t understand. Junior Teague wrote that “nothing is so simple that it cannot be misunderstood.” All teachers have an amusing personal anecdote that illustrates the truth of this statement. The stories lose their humor, however, when we are honest about how much misinformation escapes our notice . Students are gifted at staying below the radar of our formative assessments, but writing pulls back the curtain.

Writing can help content area teachers in their efforts to provide students with opportunities to connect prior knowledge. It provides an ideal vehicle for summarizing strategies that benefit both the student and the teacher with shared insights to understanding. Writing helps students organize their thinking, create new knowledge, and make tentative ideas become permanent ones.

R.A.F.T.: The Best Writing Strategy For All Content Areas

Of course, there are numerous writing strategies to choose from.  However, in my opinion, the best writing strategy is the R.A.F.T. strategy.

Effective writing enables students to write fluently and purposefully for an audience. R.A.F.T. can help you identify and incorporate the elements of effective writing . The R.A.F.T. strategy engages students in explaining what they know about a topic and then elaborating. In addition, it provides students with a choice that is on grade level.

What is the R.A.F.T. Strategy?

The R.A.F.T. stands for:

• Helps the writer decide on point of view and voice.
• Reminds the writer that he must communicate ideas to someone else.
• Helps the writer determine content and style. 
• Helps the writer organize ideas and employ the conventions of format, such as  letters, interviews, and story problems. 
• Helps the writer focus on main ideas. 

R.A.F.T. Procedure: 

• Think about the concepts or processes that you want students to learn as they read a selected passage. Consider how writing in an interesting way may enhance students’ understanding of the topic. 
• Brainstorm possible roles students could assume in their writing.
• Decide who the audience would be as well as the format for writing.
• After students have finished reading, identify the role, audience, format, and topic (RAFT) for the writing. Assign the same role for all students or let them choose from several different roles.

R.A.F.T. Scoring Rubric: 

Table of Contents – R.A.F.T Writing Examples

• 1st Grade – ELA
• 2nd Grade Math – Money
• 2nd Grade Science – Plants
• 3rd Grade ELA – Charlotte’s Web
• 3rd Grade ELA – Character Perspective
• 5th Grade Math – Decimals
• 4th Grade Science – Astronomy
• 6th Grade Math – Geometry
• 7th Grade Science – Invasive Species
• 8th Grade Social Studies – Taxation
• 9th Grade ELA – Inferencing
• 9th Grade ELA – Anaylzying Viewpoints
• 10th Grade Science – Anaylzying Viewpoints
• Subject Area: Social Studies
• Subject Area: Science
• Subject Area: Math
• Subject Area: ELA

1 st Grade RAFT Example for English/Language Arts: How to Write a “How To” Paragraph

2 nd Grade RAFT Example for Math: How Do People Pay for Things

2 nd Grade RAFT Example for Science: Lesson on Living Things: Plants

3 rd Grade RAFT Example for English/Language Arts: Charlotte’s Web

• Role: You will assume the role of Wilbur or Charlotte.
• Audience: The audience is “himself” or “herself.”
• Format: In reading this story, we discussed the unusual friendship between a pig named Wilbur and a barn spider named Charlotte. When Wilbur was in danger of being slaughtered by the farmer, Charlotte writes messages praising Wilbur, such as “Some Pig” in her web to persuade the farmer to let him live. The format you will use is a personal journal or diary. Assume or pretend that your chosen character talked things over in his or her head, as the action of the story played out. What was he or she thinking? How did it feel? What did he or she think that the farmer should do? How can you describe these things? When you assume the role of Wilbur or Charlotte, you will be using words to describe how you feel—you will become the character.
• Topic: The actions taken to save Wilbur from slaughter.
• Writing Task: Write a response in which you assume the role of Wilbur or Charlotte. You must decide what you think he or she was thinking and feeling, and then describe it in detail. Use specific references to the text. You should have at least four or more references to the text and at least three quotations. Your response should be at least five paragraphs long.

3 rd Grade RAFT Writing Example for ELA: Character Perspective

5th Grade RAFT Example for Math: Decimal

4th Grade RAFT Example for Science: Astronomy

6 th Grade RAFT Example for Geometry Lesson: Types of Angles

7 th Grade RAFT Writing Example for Science: Invasive Species

8 th Grade RAFT Writing Example for Social Studies: Taxation Without Representation

9 th Grade RAFT Example Lesson on Inference Using John Steinbeck’s, “The Pearl”

• Role: You will assume the role of Juana, wife of Kino in John Steinbeck’s, The Pearl.
• Audience: The audience is “herself.”
• Format: In reading the novel, we considered the “Song of Evil” and the “Song of the Family;” now, you are to create Juana’s “Song to Herself.” The format you will use is a personal journal or diary. Assume or pretend that Juana communicated with herself, talked things over in her head, as the action of the story played out. What was she thinking? How did it feel? What did she think her family should do? Now, how can you describe these things? When you assume the role of Juana, you will be using words to describe how you feel—you will be singing the “Song of Herself.”
• Topic : The time you will use is during the action of The Pearl and speculation on what happened afterward—what did the family do after they threw the “pearl of the world” back into the ocean?
• The Writing Task: Write a response in which you assume the role of Juana, wife of Kino in John Steinbeck’s The Pearl. You must decide what you think she was thinking and feeling, and then describe it in detail. Use specific references to the text. You should have at least seven references to the text and at least three quotations. You must also specifically mention all four of the essential questions, which is cake because Juana is an indigenous female in a sexist and racist culture that was neither fair nor just because those in power—including her husband—used it over the powerless, a group of which she is a member. Your response should be at least two typed double-spaced pages in 12 point font.

9 th Grade RAFT Example for ELA: Analyzing Viewpoints Lesson

Writing Task: There are many views on the use of alcohol and tobacco. They range from those vehemently against it to those who believe there should be no laws regulating it. It is important to be able to see and understand viewpoints different than our own. Although understanding does not mean agreeing, seeing the other side allows us to have a deeper understanding of the complexity of these social issues. Based on the US Health Department video we watched to complete your graphic organizer showing the research findings about short and long term consequences of alcohol and tobacco use, complete two of the following R.A.F.T. assignments. Choose one from A and B, and one from C and D. You will be graded based on the rubric displayed on the front board. Please look over the rubric before you begin.This will give you a clear picture of my expectations for this activity. Your R.A.F.T. will be due tomorrow as you enter the classroom.

10 th Grade RAFT Writing Example for Biology: Photosynthesis

Subject Area Examples

Social studies.

English/Language Arts

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Don Marlett

These are such good examples that I can use in my classroom. Love it.

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Ms. George's Class

Teaching While Using Marzano's Strategies

March 5 by admin

How I Successfully Used the RAFT Strategy

RAFT strategy?  What is that?  It is a strategy that can be used in any subject area.  RAFT stands for Role/Audience/Format/Topic, and writing from this aspect will provide students the opportunity to write from a perceptive that shows a better understanding and a higher level in their writing (Blackburn 56).  I read about this strategy while reading Rigor Is Not a Four-Letter Word by Barbara R. Blackburn.  I immediately used this strategy in the fall with my career exploration classes, and students were engaged and able to complete the task. I used this strategy again with my spring career exploration classes, and students were eager to begin this strategy.  The RAFT strategy is a great strategy to assess the student’s knowledge of the lesson you taught.

                Last fall, I instructed the whole class that they were to prepare a brochure on the topic of stress and how to relieve stress for high school students.  Their role was a high school counselor developing a  brochure for 8 th -9 th grade students.  I showed them a model of what was expected and a rubric.  Students had two class periods to complete the tasks and were allowed to use articles and worksheets we used for the topic of stress.  This strategy worked well. The information was correct and informative.  One negative was the design of the brochure.  I work at an art school, and many of the artists are perfectionists.  Although they were given two days and encouraged to work on it at home, they did not finish the artwork. 

                This semester, I deleted the artwork for the RAFT strategy.  Last week, I posted five RAFT worksheets around the classroom.  Students were instructed to write a 75-word speech or letter about work ethic skills.  They were given a rubric for this assignment and discussed the expectations for this assignment in a think-pair-share mode.  I gave students three minutes to walk around the classroom and decide on their RAFT assignment.  I was impressed and shocked by the engagement of the students.  Students quickly chose an assignment and began writing.  Students were discussing which RAFT was better and they started working.  Each class was given 15 minutes to write and instructed to finish it over the weekend. 

I walked around the room to observe students working, and most of the students chose to be the parent or teacher.  The students were adding the 7 As of work ethic skills (attitude, attendance, appearance, ambition, acceptance, appreciation, and accountability) and explaining each skill.  According to Blackburn, “when students are asked to write for a genuine purpose and audience, they tend to complete the assignment more effectively” (56).  I witnessed passion when they were writing because they decided their role and what they wanted to express when writing about the 7 As.   In each class, I gave the opportunity for four-five students to read their RAFT aloud.  I was impressed by how they wrote from their roles. Not only did I provide rigor to the assignment, but also differentiation instruction.  Students chose the area where they were strong and were able to produce successful pieces.  Also, students were writing more than 75 words because they knew they would write more and elaborate on the topic. 

                In conclusion, the RAFT strategy provides rigor and differential instruction because students are able to show what they know and write to an authentic audience.  This strategy can be used for every subject, including math.  I saw a math teacher making copies of a RAFT form for her class. My students appeared to be more engaged and eager to write from a different perspective.  I asked my students if they had ever completed a RAFT, and they quickly said no and continued to work on their assignment.  It’s those moments that make me passionate about students learning and teaching. 

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RAFT Assignments & Rubrics to Engage Students in Learning

The RAFT method is an approach to engaging students, designing assignments and rubrics, and providing opportunities for students to customize learning to their own learning styles.

The RAFT method is an approach to projects that is designed for engaging students, creating assignments and rubrics, and providing opportunities for students to customize learning to their own learning styles. It is student-directed differentiation at its best, and yet can be held to a rigorous evaluation standard. Here is how it works.

R – ROLE The R stands for ROLE. The students determine the role they wish to take in the presentation of the project. For instance, in a nursing program, students could speak from the perspective of the patient, nurse, doctor, family member, hospital administration, or community at large. In a fifth grade science classroom, students could speak from the perspective of the frog, pond, scientist observing the frog, wildlife federation, or community where the pond is. The ROLE of the learner is entirely up to each learner.

A – AUDIENCE The A stands for AUDIENCE. The students choose the audience to whom they are presenting. In many cases, the options for audiences could be similar to the ones available for the role.

F – FORMAT The F stands for FORMAT. This is the format in which the assignment is presented. Students have the freedom to choose if they wish to write a research paper, do a presentation, create a short video, Prezi, or power point, do a play, facilitate a debate, create a gallery photo display, or any other presentation type that they can come up with. Freedom in format liberates the student in how to present their work.

T – TOPIC The T stands for TOPIC. Several topics are chosen by the teacher and presented to the students to choose from. Given the many options in each of the 4 categories R.A.F.T. student generated projects will be widely diverse even if the topics are limited.

A teacher may get overwhelmed with the amount of options that students have. To make things easier, a teacher can simply choose to give students options in one of the four factors, instead of all four. For instance, the teacher could choose the role, the audience, and the topic, and let the students choose the format of their presentations.

Invariably the question from teachers is “How do I measure the success of the students equitably when there are so many project options?”  The easiest way to achieve this is to use a standardized rubric that fits all project options and holds all students to the same rigor in assignment production. There are a wide variety of categories that can be used for the rubric that will apply to any project, such as the introduction, focus, grammar and mechanics, sequencing and completeness, communication, word choice, communication, audience awareness, communication, APA Style, discipline inclusion, and conclusion.

While it can require a mental shift for the teacher, allowing students freedom in creating their projects can increase student engagement and allow them to connect with the material in the way that works best for them personally.

Sample Rubric for RAFT Projects

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RAFT Writing

I first heard of RAFT writing several years ago as a strategy for students to show their content knowledge beyond just writing reports.  Most of the suggestions for use have been in upper grades classrooms, especially in middle school and high school.  It’s also a common format for writing in content areas to have students demonstrate their understanding of the topic that has been learned- often as a product at the end of the unit. RAFT Writing has students respond when the Role, Audience, Format, and Topic are laid out for students to do their writing, often showcasing their content knowledge.  It’s also a great tool to help teachers write prompts for those content areas.

Over the years, however, I’ve used RAFT as a writing strategy for analyzing prompts in elementary school with students as young as first grade.  RAFT has allowed me to give students experience and exposure with various writing types, build in creative writing into our writing centers, and give students a tool to use for state testing to analyze the prompts their given and respond appropriately.

RAFT is an acronym identifying the four aspects of a writing prompt:

R- Role (who is the character/narrator and their point of view)

A- audience (who is the writing for), f- format (what type of writing is expected), t- topic (what you are writing about).

Examples of RAFT in content areas could be: ~Write an article as if you were a water droplet going through the water cycle.

~Write a story as a water droplet going through the water cycle.

~Pretend you are a child in 1774 in what will eventually be America. Describe what your life is like.

RAFT Writing is commonly used as essay responses at the end of units to measure students’ content knowledge.  It’s also used in more open ended ways allowing for differentiation; the role and audience may be the only pieces given and students are able to choose the format and specific topic.  Or, students are given the topic and format, but can choose their role and the audience.  This is most often done in intermediate classrooms and higher as the focus is on the subject and content that has been taught, and not on the writing itself.

I’ve used RAFT as a strategy in other ways in my elementary classroom, and with other classes and groups of students, with good success.

RAFT Writing in the Primary Grades

I have used RAFT Writing with students as young as first grade as a way of building creative writing. In first grade I introduce it by explaining each of the components.  We then generate, together, several different items for each component. We generally do about 4-6 and often use students in the class or people in the school as the role and audience. This helps make the task relevant to students. We then roll a dice to choose which item from each category we’ll use.  We do a shared writing of it together, the first time. Then, we select another for the students to complete independently.  After students are familiar with RAFT and how it can be used to generate a writing task, I use my RAFT Writing cards as an option during our centers to build students’ creative writing.

RAFT Writing as a Test Prep Strategy

I also really like using RAFT as a test prep strategy.  On the state tests, students are given an on-the-spot prompt to respond to.  Often, it’s in response to reading, and students are expected to respond from a range of genres.  In my experience, students struggle to identify the proper genre to respond to or miss out on other key pieces of information, such as writing from a character’s perspective.  With my third graders, it’s so important to me that they have a strategy to “attack” a difficult task that is given to them.  RAFT is a strategy that can make them break down the prompt and help them feel ready to respond successfully.

We do our main writing work during our writers workshop four days a week. However, one day a week, we do specific RAFT practice. I begin the year doing various narrative writing tasks with RAFT, though I introduce it with examples of all 3 genres. I want my students to be successful with it so I don’t typically do much of the other genres until we have explicitly done them together. However, I will occasionally do something like a how-to, or something opinion based that I know they have strong feelings about. Our weekly RAFT practice gives my students an opportunity to work through the genres in a more spiral way than we typically do during writers workshop. It also allows me to continue to do focused lessons on specific strategies I want to see in their writing.  This pre-writing step has made a world of difference for my students as they tackle the demands of state testing writing prompts!

After I’ve introduced and practiced RAFT with my students, we begin analyzing prompts. Using the strategy to think through and plan writing with the acronym is why it’s so effective and useful. This easy form is one I use when I begin having students independently analyze their writing prompts.  I have students identify each area of RAFT and then I work to correct any misconceptions.  You can download the free page by clicking the image below.

I also offer a variety of free RAFT writing resources in my free library. As we practice RAFT throughout the year, we move on to students writing based on the the prompt information. These printables and templates have us up and working with a prompt in just a few quick seconds. I have 5 ready to print digital RAFT prompts ready to go!

You can download each of them from my Free Library. To access it, sign up for my newsletter. After confirmation, you’ll receive an email with the link and password to access each of the files for yourself.

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RAFT is such a useful writing strategy that can be incorporated in so many different ways in the classroom.  In addition to our writing block, I also use digital prompt writing and journals to give students much needed practice responding to prompts on a regular basis.  You can read more about that by clicking the link below.

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I'd done it often in 4th grade, but not with much success in 2 nd. They have so much trouble, it seems, with " role" ( writing from that perspective) . I do love the format and the creativity it allows.

I started with silly ones like kindergartener. They were so excited to write with incorrect spelling and backwards letters. I let them do it once, but then they got it! Maybe it's also a developmental shift for them right about that age.

Cute idea! (You know that this is Debi, don't you, not Kelley? I can't figure out how to get her name off the account.)

Yes, I just figured you were on the wrong account 🙂

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RAFT examples for math

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RAFTs – Differentiated for Learner Success

by John McCarthy | May 5, 2014 | Differentiated Instruction , strategies , Writing | 1 comment

In the previous two articles, we explored RAFTs (Role, Audience, Format, and Topic + Strong Verb) as an instructional strategy , and how to use RAFTs for coaching writers on writing . RAFTs can ignite engagement and context for learning. Planned with forethought, students can explore a need or problem that exists in the world beyond the classroom walls. An important consideration is: How do I differentiate RAFTs to support my diverse learners? The solution is simple, yet has layers of possibilities when implemented based on an understanding of your students.

Interests are activated by giving students several options to choose from. Take this even further by having a blank option—allowing for students to craft their own RAFTs based on the topic–a great way to foster Student Voice.

Readiness : Differentiating RAFTs based on Readiness requires the most planning, which results in worthwhile learner experiences. Sometimes students have different levels of a skill or concept. One to two prompts are crafted to match the academic level of each group of students. Having more than one prompts encourages student interests because they have choices. Prompts are assigned based on formative assessment data . The learners, individually or in groups, work at the RAFTs that will stretch them appropriately.

• RAFTing the Writing Rapids
• RAFTs: Coaching Writing Tips

Very motivational.

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Helping Multilingual Learners Thrive

RAFT (Role, Audience, Format, Topic) Assessment: Great way to assess Multilingual Learners

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Choice in writing and assessment can be motivating and builds in differentiation, so you don't have to create a bunch of assignments for each student to meet them where they are. One of the most versatile and creative writing strategies is the RAFT (Role, Audience, Format, Topic). As the teacher, you can provide parameters for this assignment connected to a goal or standard from your content area. This assignment/assessment leads students to understand the purpose for writing, the audience they are writing to, the varied formats of writing in everyday life, and the specific topic that will be their theme. It's fantastic for Multilingual Learners because they can delve deep into a topic without providing a language-heavy document. All students benefit from higher-order thinking, creatively stretching and focusing directly on how they need to write to address specific audiences.

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The following questions help students define with more depth the different aspects of the RAFT paper.

Role of the Writer: Who or what are you as the writer? An activist? A soldier? The President? Audience: To whom are you writing? A friend? Your teacher? Readers of a newspaper? Format: In what format are you writing? A letter? A poem? A speech? Topic and strong verb: What are you writing about? Why? What's the subject or the point?

Ways to teach RAFT explicitly, especially the first time you introduce it.

Project a completed RAFT example.

Describe each of the components of the RAFT: role, audience, format, and topic. (It may be helpful to have students in small groups create a large chart paper or a bulletin board for future reference).

On a projector, model how to write responses to the prompts and discuss the key elements as a class. Keep this as simple and concise as possible for newcomers to the language.

Have students practice responding to prompts individually or in small groups. At first, it may be best to have all students react to the same prompt so the class can learn from varied responses.

The RAFT strategy has been adapted for students from K-12 and beyond. I use RAFT in my college classroom. Thinking of these four different aspects pushes them to think more deeply. I have listed some strategies that are particularly useful for MLs.

MLs can review the RAFT concept and assignment orally first. Have students work in pairs to explain what is meant by role, audience, format, and topic.

In small groups, students can create anchor charts describing and illustrating each of the elements of RAFT.

Have students role-play explanations of the different aspects of RAFT assignment.

Allow students to create bi- or multi-lingual responses to the RAFT assignment.

Encourage less language-heavy formats such as brochures, slides, or posters for those at the beginning stages of proficiency.

Pair students together to create RAFT assignments with clear expectations for both students. Be mindful of the linguistic capabilities of both students for the final product.

Provide models of RAFTs for students to use as scaffolding for completing their own.

MLs who know the content or topic of the RAFT may be able to produce more depth within the RAFT, especially if they are encouraged to look up material in their primary language.

Sample RAFT for a math class!

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Rectangular Prism Formulas, Types and Real-world Examples

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A rectangular prism is a three-dimensional cuboid figure. In the same way that a triangular prism brings three connected lines to life in the real world, a rectangular prism takes the length and width of two-dimensional rectangles to the next level by adding height into the equation.

2 Types of Rectangular Prisms

Rectangular prism formulas, 9 common rectangular prism examples.

All rectangular prisms consist of eight vertices that are connected by 12 edges ending at right angles. However, there are some differences between these types of three-dimensional shapes.

Regular Right Rectangular Prism

Right rectangular prisms are the most common, with real-life examples including buildings , shoe boxes and pretty much any other three-dimensional object resembling a four-sided fish tank .

Oblique Rectangular Prism

An oblique rectangular prism is a special case that allows us to draw parallelograms in three dimensions. These shapes closely resemble a regular right rectangular prism that is tipped off its axis to lean sideways.

For prisms, all the sides extend upward from the base area before being capped with a top face like a flat roof on a large building. Use the following formula variations to solve for both volume and surface area.

Volume of a Rectangular Prism

You can find the volume of a rectangular prism by multiplying its length, width, and height:

Once you calculate the volume of a three-dimensional shape with rectangular bases and six faces, ensure the measurement is recorded in cubic units to accommodate the object's three dimensions (e.g., inches 3 or cm 3 ).

Volume of a Rectangular Prism Calculator

Surface area of a rectangular prism.

Remember that the total surface area includes all the faces of the prism. There are six rectangular faces, so you must account for the lateral surface area of the sides with the addition of top and bottom faces. This is illustrated mathematically as:

Surface Area of a Rectangular Prism Calculator

Once you know what to look for, you'll start noticing rectangular prisms everywhere. Here are some everyday items that typically qualify as rectangular prisms.

• Apartment buildings
• Picture frames
• Protein bars
• Reams of paper
• Refrigerators
• Tissue boxes

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B.S. in Mathematics, 2024-2025 Catalog

Four Year Degree Worksheet for: B.S. in Mathematics - CSULB Catalog (24-25)

This degree worksheet is intended to help you develop a balanced course schedule while completing your degree within 4 years. The same sequence of courses (with fewer courses each semester) is also recommended for students completing their degree in 5 or 6 years. The listed schedule of courses is a sample path to the degree and one of several possible ways of completing the degree requirements.

This worksheet is not intended to replace academic advising with your assigned advisor. Students should consult with their assigned advisor to determine the appropriate sequence of required courses and electives based on their academic goals.

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Major-Specific Degree Requirements are listed as an " MSDR " in the notes column. These courses must be completed in order to declare your major. All students must have a GPA of 2.5 or higher in the STEM MSDR suite. For more information, please see: Major-Specific Degree Requirements for CSULB Students .

Pre-Mathematics first-time freshmen must complete MATH 122 and MATH 123 with a cumulative GPA of 2.5 or higher.

Additional Notes

Students should take the Graduate Writing Assessment Requirement Placement Examination (GPE) after Year 1.

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Drill with worksheets and flashcards is boring! Games engage young minds and enhance memory.

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Kindergarten||Mathematical Practices|||K.NBT.1. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.||Common Core Mathematics||Kindergarten||Number And Operations In Base Ten||Work With Numbers 11-19 To Gain Foundations For Place Value|||K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||K.OA.5. Fluently add and subtract within 5.||Common Core Mathematics||Kindergarten||Operations And Algebraic Thinking||Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 1||Mathematical Practices|||1.OA.3. Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction|||1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 ? 8 by finding the number that makes 10 when added to 8.||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction|||1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 ? 4 = 13 ? 3 ? 1 = 10 ? 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 ? 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Add And Subtract Within 20|||1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 ? 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Work With Addition And Subtraction Equations|||1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? ? 3, 6 + 6 = ?.||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Work With Addition And Subtraction Equations|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 2||Mathematical Practices|||2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.6. Add up to four two-digit numbers using strategies based on place value and properties of operations.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.8. Mentally add 10 or 100 to a given number 100?900, and mentally subtract 10 or 100 from a given number 100?900.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations.3||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.||Common Core Mathematics||Grade 2||Operations And Algebraic Thinking||Add And Subtract Within 20|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 3||Mathematical Practices|||3.OA.5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 ? 4 = 24 is known, then 4 ? 6 = 24 is also known. (Commutative property of multiplication.) 3 ? 5 ? 2 can be found by 3 ? 5 = 15, then 15 ? 2 = 30, or by 5 ? 2 = 10, then 3 ? 10 = 30. (Associative property of multiplication.) Knowing that 8 ? 5 = 40 and 8 ? 2 = 16, one can find 8 ? 7 as 8 ? (5 + 2) = (8 ? 5) + (8 ? 2) = 40 + 16 = 56. (Distributive property.)||Common Core Mathematics||Grade 3||Operations And Algebraic Thinking||Understand Properties Of Multiplication And The Relationship Between Multiplication And Division

2.0 Students understand and describe simple additions and subtractions.||CA Mathematics||Grade Kindergarten||01. Number Sense|||1.0 Students use number sentences with operational symbols and expressions to solve problem.||CA Mathematics||Grade 1||02. Algebra and Functions|||1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction.||CA Mathematics||Grade 2||02. Algebra and Functions|||1.1 Use the commutative and associative rules to simplify mental calculations and to check results.||CA Mathematics||Grade 2||02. Algebra and Functions||1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction.