CHANGE FOR YAKIMA—BTA LESSON?Carnegie Learning also offers print materials to help students master math concepts and skills. Our print materials our unique because they offer rich, multi-step problem solving activities that engage math students and show them that math is relevant to our daily lives. We also offer skills practice activities for students appropriate for skill development, remediation, etc.Learning By Doing PrinciplesCarnegie Learning believes that students develop math understanding and skills by taking an active role and responsibility for their own learning. With Carnegie Learning textbooks students become engaged in solving contextual math problems that strengthen their conceptual understanding of math topics. Rather than encouraging students to memorize procedures, we provide them opportunities to think and work together in small groups. Real-World ContextStudents work with their peers to solve real-world problem situations like using percents for leaving a tip in a restaurant or using a graph of an equation to determine the number of days it will take to build miles of highway. They become more engaged in learning mathematics when they see how it plays a significant role in everyday life. Mathematical DiscourseThroughout the student text icons prompt different forms of student communication. These icons may instruct students to work independently, work with groups, or share ideas with the class. Encouraging mathematical discourse provides opportunities for students to explain their thoughts and processes for solving math problems. A sample lesson from the Carnegie Learning® Student Algebra I Textbook is shown below. When a school implements Carnegie Learning textbooks, each teacher receives a textbook set that contains the following books. Teacher's Implementation Guide. The Teacher's Implementation Guide contains a lesson map for each student text lesson. The lesson map includes each lesson's objectives, key terms, NCTM standards, essential questions, warm up questions, open-ended questions, and closing activities. An image of each student text page, including answers, is provided in the Teacher's Implementation Guide. Teacher's Resources and Assessments. The Teacher's Resources and Assessments book contains five tests per chapter of the student text. The tests are a Pre-test, a Post-test, a Mid-Chapter Test, an End-of-Chapter test, and a Standardized Test Practice. The Teacher's Resources and Assessments book contains the assessments with answers in place and also includes answers in both the student assignments and student skills practice pages. Student-Centered ClassroomIn a student-centered classroom, the teacher facilitates learning and coaches students to master math concepts and procedures. Little time is spent on delivering lectures. Instead, teachers lead students in completing task-based lessons and fostering discourse where students share solutions to problems and explain their mathematical reasoning. Lesson MapThe teacher support materials help teachers guide instruction. The lesson map provides recommendations like how and when to group students for problem investigations, offers guiding questions to assess student understanding, and provides notes and tips regarding common student misconceptions and errors. It also provides suggestions for closing lessons, assigning follow-up activities, delivering assessments, and space to record teacher reflections. Task-Based LessonsThe lessons and activities are carefully designed to help teachers engage students in learning mathematics. The task-based lessons are organized by problem scenarios and investigations. For example, a problem scenario about tipping in a restaurant may be designed to help students use percents. The activities may require students to convert between fractions, decimals, and percents and consider mathematical relationships. The real world math tasks motivate students to learn and help them to consider how mathematics is a part of their daily lives. Custom TextbooksCarnegie Learning is prepared to rapidly and flexibly respond to individual state and district math requirements with custom textbooks. Carnegie Learning® Custom Math Curricula are currently available in Florida, Indiana, Georgia, Virginia, West Virginia, and the Hamilton County Schools in Chattanooga, Tennessee, among other states and districts.
The collaborative classroom is identified by discussion, with in-depth accountable talk and two-way interactions, whether among members of the whole class or small groups. It is a well-structured environment in which questioning and dialogue are valued and appropriate parameters are set so that active learning can occur. Careful planning by the teacher ensures that students can work together to attain individual and collective goals and to develop learning strategies. In the collaborative classroom, students are encouraged to take responsibility for their learning through monitoring and reflective self-evaluation. The collaborative classroom is one in which teachers spend more time in true academic interactions as they guide students to search for information and help students to share what they know. As facilitators, teachers have the opportunity to provide the correct amount of help to individual students by providing appropriate hints, probing questions, feedback, and help in clarifying thinking or the use of a particular strategy.
Each lesson opener is a short paragraph designed to motivate students to think about and discussthe usefulness and connections of mathematics in a variety of real-world contexts. These two- tothree-minute discussions prepare students to start the lesson.Real-world contexts confirm concrete examples of mathematics. The scenarios in the lessons helpstudents recognize and understand that the quantitative relationships seen in the real world are nodifferent than the quantitative relationships in mathematics. Some problems begin with a real-worldcontext to remind students that the quantitative relationships they already use can be formalizedmathematically. Other problems will use real-world situations as an application ofmathematical concepts.
Students will experience various hands-on activities that match or sort verbal descriptions, tables, andgraphs. These activities help develop skills recognizing and categorizing patterns in mathematics.
Research shows students learn best when they are actively engaged with a task. Often students only focus or mentally engage with a problem when they’re required to produce a “product” or “answer”. We offer a different approach to worked examples to help students better benefit from this mode of instruction. Many students need a model to know how to engage effectively with worked examples.Students need to be able to question their understanding, make connections with the steps, and ultimately self-explain (the progression of the steps and the fi nal outcome).This approach doesn’t allow students to skip over the example without interacting with it, thinking about it, and responding to the questions.This approach will help students develop the desired habits of mind for being conscientious about the importance of steps and their order.
Thumbs Up problems provide a framework that allows students the opportunity to analyze viable methods and problem-solving strategies.Questions are presented along with the student work to help students think deeper about the various strategies, and to focus on an analysis of correctresponses. One goal of these problems is to help students make inferences about correct responses. These types of problems will help studentsanalyze their own work for errors and correctness.This problem type is designed to foster flexibility and a student’s internal dialog about the mathematics and strategies used to solve problems.
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Who’s correct problems are an advanced form of correct vs. incorrect responses. In this problem type,students are not given who is correct. Students have to think more deeply about what the strategiesreally mean and whether the solutions made sense. Students will determine what is correct and what isincorrect, and then explain their reasoning. These types of problems will help students analyze their ownwork for errors and correctness.
Each lesson opener is a short paragraph designed to motivate students to think about and discuss the usefulness and connections of mathematics in a variety of real-world contexts. These two- to three-minute discussions prepare students to start the lesson.Algebra 1 Lesson 4.2 The Password Is…Operations!A Common Core Math Program
Algebra 1 Lesson 4.2 The Password Is…Operations!A Common Core Math Program
Algebra 1 Lesson 4.2 The Password Is…Operations!A Common Core Math Program
Algebra 1 Lesson 5.6 Checkmate!A Common Core Math Program
Research shows that only providing positive examples does not eliminate some of the things students may think; it is also efficient to show negative examples. From the incorrect responses, students learn to determine where the error in calculation is, why the method is an error, and also how to correct the method to correctly calculate the solution. These types of problems will help students analyze their own work for errors and correctness.Algebra 1 Lesson 7.2 Working the SystemA Common Core Math Program
Algebra 1 Lesson 5.4 Take Some Time to ReflectA Common Core Math Program
Questions require students to summarize and generalize their mathematical understandings and key concepts.Algebra 1 Lesson 4.5 Well, Maybe It Is a Function!A Common Core Math Program
Algebra 1 Lesson 4.3 The Power of Algebra Is a Curious ThingA Common Core Math Program
Algebra 1 Chapter 4 SequencesA Common Core Math Program