Master Fractions

HELP YOUR STUDENTS MASTER THE FOUNDATIONAL MATH TOPICS THEY NEED FOR SUCCESS IN ALGEBRA AND BEYOND

The problem with fractions, and more broadly rational numbers, is pervasive. And has huge implications for all of our students.

“Students who complete Algebra II are more than twice as likely to graduate from college compared to students with less mathematical preparation.”
National Mathematics Advisory Panel
2008

Woot Math is research-backed with support from prominent organizations such as the Department of Education / Institute of Education Sciences, National Science Foundation, and the Bill and Melinda Gates Foundation. And Woot Math has been acknowledged as one of the leaders in utilizing research to help students be successful.

Woot Math was originally designed for middle school students who are struggling to learn key concepts like fractions that are preventing them from being ready for Algebra. If you are a math teacher, you know fractions are a challenge for students. But it isn’t just for the middle grades. Woot Math is used in conjunction with the core curriculum as early as 3rd grade. And used in intervention and remediation for middle and even high school students.

We work with leading researchers

In fact, a recent study funded by the National Science Foundation showed a 2X improvement in learning outcomes when students use Woot Math compared to when they do not.

Woot Math works with leading researchers to bring the best of learning sciences and mathematics education to life in fun and engaging ways to help students succeed. We are used across the world with great success. In fact, a recent study funded by the National Science Foundation showed a 2X improvement in learning outcomes when students use Woot Math compared to when they do not.

This study was a randomized crossover trial (Woot Math was blinded to this study), and run by researchers from the University of Colorado and University of Minnesota. It included 23 teachers (4th and 5th grade) from 8 schools and 2 districts.

The crossover trial involved a pre assessment, Woot Math or Business as Usual for 10 instructional hours, followed by a mid assessment. The groups then swap treatments, and end with a post assessment.

Diagram of Random Crossover Trial design

The results show that students learned more when Woot Math was added to classroom instruction than they did from “Business as Usual” instruction. The gains seen were 29% from pre-mid and 38% from mid-post assessment.

Assessment Gains from Random Crossover Trial

How are these types of outcomes achieved? Woot Math provides short-form video and fun problem-solving to explore and build conceptual understanding of the most challenging topics our students face. It isn’t skill-and-drill, but instead is focused on truly helping students understand the reason behind how rational numbers work.

In addition to the short videos, Woot Math includes multiple layers of scaffolded help, including review levels, quick tips, extra video instruction, and foundational levels. The scaffolded help goes beyond just assessing right/wrong, and also includes real-time analysis of each student’s work to address their specific struggling points – tailoring the content to meet each student’s personal needs.

Hamburger Drawing

Many adults also need help with fractions.

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s (as reported by the New York Times)

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.

https://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html

Why is Algebra such a stumbling block?

What is keeping our students from succeeding? Fractions, of course. We know that our students are struggling to master these key concepts. We also know that it is critical that they do so.

stumbling block
Why is Algebra such a stumbling block for our students? What is keeping them from succeeding? Fractions, of course. As stated in this seminal paper:
“Understanding fractions is crucial for mathematics learning…
It is also predictive for students’ mathematical achievement years later.”

– Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Torbeyns, Schneider, Xin, and Siegler, 2015
So what is the solution? At Woot Math, we know that all students, regardless of their ability or their grade level, can master fractions and rational numbers. Thanks to pioneers such as Carol Dweck and Jo Boaler, the message is getting out that there is no “math gene”. In fact, the research shows that all students can complete the Calculus sequence. But in order to do that, it takes time, perseverance, and perhaps above all, confidence to do so. This is where a great tutor, whether it be in-person or technology based (such as Woot Math) can help.

Key features of Woot math

digital manipulatives

Digital Manipulatives

Students are able to interact and connect multiple representations, a critical bridge to fluency with rational numbers.

adaptive engine

Adaptive Engine

Our adaptive technology is able to go beyond right or wrong and address each student's actual work. This enables us to deliver personalized instruction.

fraction models

Multiple Models

Help build effective mental models. Multiple representations of concepts and engaging, hands-on interactions deepen number sense.

instructional video

Instuctional Video

Inline, instructional video introduces the students to new concepts, and, when they are struggling, gives additional, scaffolded instruction.

Actionable data

Actionable Data

Quickly assess screenshots of student work to gain insight into areas of struggle and success. Woot Math gives you the data you need, when you need it.

engaging for students

Engaging for Students

Designed for middle school students. 95% of students have found Woot Math helpful, and would recommend Woot Math to another student.

At Woot Math, our passion is to help all students be successful. As stated by Dr. Siegler, the ramifications for us not doing so are much too high.

“If you don't understand fractions, it's literally impossible for you to understand algebra, geometry, physics, statistics, chemistry.
It closes a lot of doors for children.”
Dr. Bob Siegler, Carnegie Mellon University
The Wall Street Journal, 2013

We invite you to try Woot Math with your students. Whether you are a teacher, a homeschool parent, or a tutor, we believe you will have a great experience. And more importantly, it will help your students master the key foundational topics that they need to be successful.

Sign up for the free tier

There is no obligation and it is entirely free. If you find that Woot Math works for your students, you can upgrade to the premium version at any time.

What happens when I end an assignment?

It is sometimes necessary to stop an assignment mid-stream and assign it later in the school year. In this case, what happens to the student data?

The answer is, it depends.

Adaptive Learning

For Adaptive Learning assignments, you can start and re-start assignments as much as you want, and students can pickup from where they left off. No problem!

Because Adaptive Learning units are a progression of content that is driven by our proprietary adaptive engine, Woot Math knows where the students are at any given time, and it will automatically allow them to resume when you re-assign an Adaptive Learning unit.

Imagine your students have started working on an assignment you gave to them (Ordering & Absolute Value, for example). Then, you decide you want to move on to a new topic, and end that assignment. Once you end it, it will be removed from their active assignments (any open assignments you’ve sent them will still be on their dashboard). Later in the year, when you want to circle back to Ordering & Absolute Value, just make the assignment again. Your students will then see it as an active assignment, and when they click into it, they’ll pick up exactly where they left off!

Formative Assessments (Quizzes, Homework/Classwork, Exit Tickets, etc)

The formative assessments that you assign your students are only active as long as the assignment is active, because these formative assessments are generally short-lived assignments that students do in-class. Once you end an assignment, the report is available and you can view the results. However, it isn’t possible to resume a formative assessment assignment. Note that you can always re-assign it. In that case, the students will start at the beginning again.

If you have any questions, please let us know, we are always happy to help!

Sequences and Modeling Formative Assessment

Sequences and Modeling Formative Assessment

Help students make connections between proportional thinking and sequences. This is a great way to set your students up for success with harder modeling tasks and Algebra. Students often first encounter this content through direct instruction and repeated practice. If this strategy didn't work for them, it's time for something new. In this week’s post we present a sequences and modeling formative assessment task designed to promote classroom conversation and discourse. Use it to get your students learning from each other and wrestling with problems that have multiple right answers.

Unit Conversions Warm Up

This review quiz/activity starts with a quick warm up. It is good to think about units and rates before diving into harder problems. The task asks, “A full gallon is 128 ounces, how many 8 ounce cups are there in a half gallon?”

Unit Conversions Formative Assessment

– Unit Conversions Formative Assessment –

This quick refresher on converting units helps prime students for the next two tasks. Unit conversions will help them model the number of ounces left and then the number of cups left per day.

– Milk Volume Conversion Task –

Evaluate the Reasoning of Others

Students experience how the modeling of the milk differs based on if the unit is ounces or cups. Then, the students are asked to evaluate the reasoning of two hypothetical students, Daria and Amir. Each are modeling the situation correctly but using different units. After doing the task, your student’s responses might look something like this,

– Evaluating Student Reasoning –

This task promotes productive conversations among your students. Ask your students students who answered A or B to elaborate on their good ideas of how to model the situation. It is important to assign competence to students who had some productive thinking. This will help them see they are on track, even if they didn’t recognize both of the correct answers. Hopefully, through a productive conversation, students will come to understand that both Amir and Daria are correct. They are just using different units to model the situation. We recommend you start this discussion with the “reveal answer” button deselected.

– Reveal Answer –

Sequences Formative Assessment

The final task is for the students to convert the recursive formulas into explicit ones.

– Recursive and Explicit Formulas –

Woot Math accepts equivalent answers and the correct answer can be either in the form f(n)=… or y= where n is the position in the sequence just like in the first two tasks. After students answer this question, review the answers to make comparisons. Ask them what they notice and what they wonder. How do the slopes of the two lines compare? If they represent the same situation, why does one have a slope of 8 and the other has a slope of 1? With your support, students can draw connections between the two models and the conversion factor between cups and ounces.
 
Get started by previewing the activity right now, or login to wootmath.com and search for Weekly Woot: Patterns and Sequences Rich Task in the Explore Content Gallery.
 
Visit our page on formative assessment for more on how to use these strategies in your classroom
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