# Frequently Asked Questions about Implementing TTA

TTA has been designed specifically for underprepared beginning algebra students who are concurrently enrolled in a 9^{th} grade algebra course. The curriculum is designed for students who are studying algebra but require additional support with the foundations of algebraic thinking. Teachers and school administrators typically select students for placement in a TTA class based on some combination of middle school grades, state test scores, and recommendations from middle school teachers. There are schools that are using the materials in other interesting and productive ways, including as part of the regular middle school pre-algebra curriculum and as part of summer school courses, though TTA was specifically designed for the 9^{th} grade context.

TTA is *not* designed for students who are well-prepared for 9^{th} grade algebra. Many TTA ideas may be interesting and useful for well-prepared 9^{th} graders (such as area models or mobile puzzles), and these ideas can be productively included in a standard Algebra 1 curriculum. But these students are not the intended audience of the TTA curriculum and are likely to require more challenging content in their mathematics courses.

TTA is also *not* designed to remediate major gaps in critical arithmetic content. TTA students should be able to add single-digit numbers in their head, should be familiar with single-digit multiplication facts (even if they don't know them all by heart), and should have some prior exposure to arithmetic with fractions and the coordinate plane. Though the needs of students with interrupted formal education vary widely, these students may not be prepared for a TTA course and an Algebra 1 course taught concurrently in 9^{th} grade. While many of the ideas in TTA may be helpful (especially Mental Mathematics and the treatment of numbers, operations, and word problems), students with major mathematical deficiencies likely need more targeted support with basic arithmetic operations.

TTA was designed as an algebra support course with the expectation that students are learning about traditional algebra topics in the same year in their primary 9^{th} grade mathematics course. TTA presents another way to think about many essential algebra topics with the expectation that an Algebra 1 (or Integrated Mathematics 1) course that students are also taking is covering the requisite standards. For example in TTA, work with placing fractions on the number line builds toward understanding proportional relationships, which builds toward understanding the slope of a line drawn through two points. And TTA students do create equations for lines by generalizing their process of testing whether various points have a specific slope with a given point. But focused work on an algorithmic formula for slope (e.g., *m* = (*y*_{2} – *y*_{1})/(*x*_{2} – *x*_{1})) or specific forms of equations for lines (e.g., point-slope form, or slope-intercept form) are assumed to be addressed in their primary first-year high school mathematics class.

Each TTA lesson includes three levels of built-in differentiation: (1) the green-labeled Important Stuff problems, which every student should complete; (2) the white-labeled Stuff to Make You Think problems, which are extensions designed to engage faster students in relevant mathematical problems that may take more time and thinking to solve; and (3) the pink-labeled Tough Stuff extension problems, which add an additional level of challenge. The mathematical Explorations included in each unit also feature built-in differentiation with extension problems in pink-labeled Further Exploration sections.

There are also Additional Practice problems included at the end of each lesson that are at approximately the same level as the Important Stuff problems and are intended to be accessible for all students. These can be used for formative assessment or with students who need more time to master a particular concept. There are also Unit Additional Practice problems at the end of each unit that are similar to the problems on the Unit Assessment. These can be used similarly to the in-lesson Additional Practice problems and also help students prepare for the Unit Assessment.

Additionally, teachers may find the free puzzle apps available at solveme.edc.org helpful in differentiation. These mathematical puzzle apps were inspired by TTA and can be played on iPads or in a browser on a tablet or computer. Each app includes multiple levels of challenge available to the user as well as information pages that describe how to play, build, and teach with these puzzles.

TTA is designed as a full-year course that meets 5 days a week for approximately 45 minutes a day. In this context, three of the twelve units should be completed each quarter. Both lessons and Explorations are designed to take approximately one day each, and each unit includes 5-8 lessons and 1-2 Explorations. The teaching guide for each lesson and Exploration includes a "Lesson at a Glance" section with proposed timing. This pacing expects that all students complete the Important Stuff content but not necessarily the Additional Practice, Stuff to Make You Think, Tough Stuff, or Further Exploration exercises provided for differentiation.

TTA was designed so that students *won't* need calculators. This isn't a strict rule (except in the case of Mental Mathematics or pages that explicitly say not to use calculators), but the problems were carefully crafted to encourage use of mental mathematics strategies, and using calculators will make that a missed opportunity for building number sense and confidence. Number line subtraction, for example, focuses on jumping to multiples of ten, and area models break up numbers by place value. In problems with numbers that have more than one non-zero digit, the authors were careful to keep the computations manageable without a calculator throughout the course.

This is an important question that should be discussed with curriculum planners at your school (other TTA teachers, department heads, etc.) prior to the start of the school year. There certainly are schools using TTA in creative ways to supplement their algebra courses, but we recommend carefully considering the integration of the materials. Critically helpful to this kind of planning is to have a clear understanding of the scope and sequence of TTA, which is unlike a traditional pre-algebra or algebra course. Page 14 of the Series Overview includes a mapping of typical Pre-Algebra and Algebra I topics with the units of TTA that may be useful in this process.

TTA is intended for use in an approximately 45-minute class period while students are concurrently enrolled in a traditional 45-minute Algebra 1 course. Contexts that are similar (such as a single 90-minute block), can be modified to match this intended approach as well as possible (such as by teaching TTA for 45 minutes and teaching from a traditional algebra text for the other half of the period). Contexts that are significantly different (such as one 45-minute period for both algebra 1 and TTA) will require more planning ahead of time, and decisions should be made based on the goals of the school's implementation. The authors of TTA have seen successful implementations in a variety of 'off-label' contexts including using TTA as a stand-alone pre-algebra course and using TTA alongside an integrated math 1 course. One factor that stands out as especially important to success, at least anecdotally, is high fidelity to the philosophy of the materials. Teachers can achieve this by carefully reading the provided materials including the Series Overview, the Teacher Guides, and if you have a copy, the Making Sense of Algebra teacher professional book.

TTA was written to be usable alongside *any* Algebra 1 course, so it is not directly aligned with *any* specific text. It is expected that the two courses will cover some ideas (such as graphing) at different times. This is not significantly different from students' experiences with other topics taught across multiple courses (such as learning quadratics at a different time in mathematics class than in physics or learning about some part of history at a different time in a social studies class than in English). TTA follows its own coherent trajectory that builds over the course of the year, and while it may seem appealing to reorder the units of TTA so as to align with the traditional algebra course, the TTA authors and researchers *highly recommend* that teachers follow TTA as written so students experience a coherent building of the conceptual ideas of algebra.

TTA offers a number of features to support students still developing English reading skills including:

**visual representations**that support mathematical problem-solving, understanding, and communication (for example, mobile puzzles)**hands-on activities**such as explorations and games that let students engage with the mathematics and practice sharing their thinking**dialogues**, which model how to talk about mathematics and can be read aloud, allowing practice with understanding mathematical explanations

For students who are learning English, consider sometimes grouping them with other students who speak the same language, letting them write (and perform or record) dialogues of students solving problems in their own language, and/or having them translate the provided Thinking Out Loud dialogues into their own language. You can also support students using strategies that help them make sense of written directions or help them produce language to share their thinking. For example, you could display a sentence starter that would begin an explanation and have each student use sentence starter to open their response.

When leading Mental Mathematics with English Language Learner (ELL) students, consider both writing and saying each prompt and then letting students both write and/or say their response. The goal of Mental Mathematics with this population is to let students gain the same mathematical skills from the activity as their peers while they learn the relevant English, so use writing as a tool only as much as it is needed to do the activity, and then back off the writing to make the Mental Mathematics more mental as soon as students are ready.

Many additional resources have been developed to support work with students in mathematics classes who are also developing proficiency in English. For example:

- Mathematical Thinking and Communication: Access for English Learners is a book that shares perspectives and strategies about the use of diagramming in mathematics as a thinking and communication tool. It includes an overview of several instructional strategies that can be used during mathematics lessons to support language access, language production, and problem-solving.
- Strategies to Improve All Studentsâ€™ Mathematics Learning and Achievement is a compilation of short essays based on work at EDC, which includes a section with strategies for ELLs in the mathematics classroom.
- Stanford University's Understanding Language: Language, Literacy, and Learning in the Content Areas offers events, papers, teaching resources, and videos about the role of language in the Common Core State Standards. Be sure to also check out:
- TODOS: Mathematics for ALL is an educator community that advocates for equity and high quality mathematics education for all students—in particular, Latina/o students

The authors of TTA encourage a focus on student participation, engagement, effort, and perseverance over more quantitative measures of student success. Knowing that schools commonly require quantitative measures of success, we recommend using the Unit Assessment for summative evaluation once students have mastered the content of each lesson in the unit and both you and your students are pleased with their performance on the Unit Additional Practice pages included in the student materials (these are similar to the problems on the Unit Assessment).

TTA is meant to be a chance for students who have struggled with math to regain their footing in the subject as they enter into the abstract world of high school mathematics. Is it common for this population to have high anxiety and low confidence in mathematics, and just as a business person doesn't invest in ventures they expect to fail, your students may be apprehensive about investing time and energy in mathematics if their experiences haven't felt successful in the past. TTA is designed to encourage students to give math another try and to help them experience the joy of persevering through the challenges posed by the subject and feel real success. Keep these issues and goals in mind as you design your grading practices.

There are free interactive puzzle apps available at solveme.edc.org that are based on three TTA puzzle-types: Mobile puzzles, Who Am I? puzzles, and MysteryGrid puzzles. Each app includes a collection of built-in puzzles of varying difficulty as well as community-built puzzles made by other app users. Students can create accounts to save their process and user-built puzzles. And teachers can use puzzle numbers, difficulty levels, badges, or trophies as benchmarks for success. More information about playing, building, and teaching with these puzzles is included in the Information section of each app.

Build a supportive classroom culture. TTA is designed for collaboration: the lessons and Explorations are intended for use in pairs or small groups of students, Mental Mathematics is done together as a class, the Thinking Out Loud dialogues model productive mathematical discourse, the in-text Discuss and Write What You Think prompts encourage students to engage in mathematical discourse with each other, and discussion prompts in the Teacher Guide provide support for teachers in leading whole-group discussions. Teachers should support collaboration by utilizing these features of the curriculum, promoting group work, setting clear expectations for respectful behavior, and modeling constructive feedback.

Help students develop a sense of responsibility for their own success. While students' lack of preparation is likely not their own fault, they are the ones who must do the work of getting their mathematical proficiency back on track. The TTA curriculum helps students to build their sense of agency in mathematics; instead of just being consumers of problems given to them by their teachers and/or textbook, TTA students also create their own mathematical puzzles, write their own mathematical dialogues, and ask their own questions about word problem contexts. TTA teachers have the job of helping students build their sense of responsibility. Set clear expectations for effort and periodically ask students to reflect on how well they've met these expectations and, if necessary, what they will change in order to better meet them in the future.

At the bottom of the Table of Contents of the TTA Series Overview booklet, there is information about how to access the online TTA resources available on the publisher's website, including printable and projectable classroom resources and assessments and also projectable student materials, which can be displayed with or without the answers. There are TTA videos publicly available on transitiontoalgebra.com, and there are related free puzzle apps at solveme.edc.org.

Open the Answer Key (available by logging into the publisher's website, as described on the Table of Contents of the TTA Series Overview booklet) in Adobe Acrobat. Then, click the Answer Key On/Off toggle button at the top of any page to see either a blank copy of the student pages or a copy with the answers.

Note that this process *only* works in Adobe Acrobat (which is free from Adobe) and that this file is *not printable* for copyright reasons.

This is a challenging situation that requires some extra work on the part of the teacher to ensure a smooth integration for the new student(s). Here are some ideas: you might use the Unit Additional Practice pages from the units you have already covered to assess student deficiencies and select targeted units and/or lessons for student(s) to work on in order to help bring them up to speed; you might also look though the unit that your class is currently working on (or working on next) with an eye for what content the new student(s) are likely to need support with (for example, if an upcoming unit includes a puzzle-type that a new student has not encountered before, you might have them look back at the lesson—perhaps in a prior unit—where that puzzle was first introduced).

Honesty with students is always best, but it's not necessary to dwell on their lack of mathematical preparation; that's often *not* their fault, but they are likely to believe and receive regular messages that it is. TTA is designed to show students how algebra works. While students' traditional mathematics course will teach them the formulas and procedures, TTA will teach them the logic behind these methods and help students make sense of what they are learning in their other class. TTA also helps clarify common misunderstandings about arithmetic and shows how the same ideas that apply with numerical calculations also apply with algebraic manipulations. So for example, students review how fractions work and then apply that to rational expressions and slope. Similarly, they review the properties of multiplication with numbers and then extend those ideas to distribution and other manipulations with polynomials.