28 SUMMER LEARNING 931984—Summer Scholars: Mathematics Management Guide © | Teacher Created Materials 6 Overview Effective Mathematics Intervention Meeting the needs of students who struggle in mathematics can present a real challenge for teachers . Research recommends that teachers identify students who need additional support and establish procedures for effective instruction to help those students become successful in understanding mathematical procedures and skills (Gersten et al . 2009) . Russel Gersten et al . identify evidence-based recommendations designed specifically to reduce the number of students who struggle in mathematics (2009) . The following recommendations are the core foundation of an effective intervention program, and summer school is one form of intervention . Focus on whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. Researchers agree that students with difficulties in mathematics often lack proficiency in computational skills (Bryant et al . 2008; Gersten, Jordan, and Flojo 2005; Calhoon et al . 2016) . Quality computation instruction is important to ensure early mastery of these foundational skills (Miller et al . 2011) . While Summer Scholars includes lessons on each of the nationally emphasized mathematical domains, the majority of lessons focus on number sense and building conceptual and procedural knowledge . These skills are foundational to understanding mathematics at higher levels . Instruction should be explicit and systematic. This includes providing models of proficient problem-solving, verbalization of thought processes, guided practice, corrective feedback, and cumulative review . The student-centered gradual release of responsibility model (I Do, We Do, You Do) in Summer Scholars begins with the teacher modeling concepts and asking intentional questions to encourage students to share their thinking . This provides information about where students are and what support they will need . Each lesson component makes explicit connections among math ideas and representations . Solve word problems that are based on common underlying structures. Problem-solving is woven through each lesson in Summer Scholars . A blend of conceptual and procedural understanding is developed, connecting the meaning of operations with procedural skills . © | Teacher Created Materials 931984—Summer Scholars: Mathematics Management Guide 7 Overview Effective Mathematics Intervention (cont.) Allow students to work with visual representations of mathematical ideas. Students need experiences with concrete representations to make connections to pictorial and numerical representations (Vygotsky 1978) . Summer Scholars helps students move from concrete to pictorial to numerical/abstract representations by carefully scaffolding instruction for each student . Also, the detailed lesson plans develop teachers’ understanding of visual models, supporting their instructional use . Build fluent retrieval of basic arithmetic facts. Basic facts are naturally incorporated in Summer Scholars, and the math fluency games specifically address the reinforcement of basic facts and computational fluency . Monitor student progress. Progress monitoring is crucial to understand whether students are progressing . Without this information, teachers will not know how to structure ongoing support . Assessing student progress through formative assessments (such as the Quick Checks) not only guides instruction, but also helps develop ongoing support for students in the non-summer-school mathematics class . Include motivational strategies. Students who struggle often tend to become discouraged and give up . Giving these students more of the same instruction, such as drill sheets, does not meet their needs for achieving success in mathematics . The activities in Summer Scholars provide students with multiple experiences and opportunities to develop understanding and practice skills . Lessons are designed to scaffold student understanding and support student success . The digital games included in each level are motivational and fun to play while providing ongoing practice . In addition, teachers may provide other measures of reward for student accomplishments . Effective Mathematics Instruction for All Learners The Meadows Center for Preventing Educational Risks (2017) also includes the following practices for effective mathematics instruction: • Teach the “why” and “how” along with math rules and procedures . • Require students to show and explain their work . • Use technology when appropriate . • Differentiate instruction to meet students’ needs . • Use precise math language and vocabulary . To meet these needs, Summer Scholars lessons help teachers explain the reasoning behind many mathematical ideas . Students show and explain their work to partners and on activity sheets . Summer Scholars includes several pieces of technology to enhance students’ mathematical understandings (see pages 36–39 for more information) . Many differentiation options are provided to meet students’ needs (see page 29 for more information) . Math language and vocabulary activities are provided at the start of every lesson, and additional practice is included in the Mathematical Discourse Task Cards . The repeated practice of key math skills in Summer Scholars helps students gain confidence they need to be successful . © | Teacher Created Materials 931993—Summer Scholars: Teacher’s Guide 7 Day 1 Place Value Ones, Tens, and Hundreds I Do whole group small groups pairs independent 5 min 10 min 15 min 30 min 35 min 40 min 45 min 20 min 25 min 1. Provide each student with 10 connecting cubes. Say, “A candy company is packaging taffy. One of our connecting cubes is going to stand for one piece of taffy. As the pieces of candy come down the production line, they get packaged 10 at a time. Each package gets 10 pieces of taffy. Use your connecting cubes and connect 10 cubes together, making a package.” 2. Say, “If we have two packages, how many taffy pieces do we have?” Use two student packages as examples, and count by tens as a class to prove the answer. (20) “What about four packages?” (40) “Count by tens to 40 with a partner.” Allow students to count by tens to 40. Then, use four student packages as examples and count by tens as a class to prove the answer. 3. Say, “As the candy company gets packages of 10 taffy pieces, they load them into boxes that will go to the stores. Only 10 packages fit into a box. How many taffy pieces are in a box of 10 packages with 10 pieces each?” (100) Use 10 student packages to demonstrate, counting aloud by tens as a class to prove the answer. 4. Say, “The way these taffy pieces are packed is similar to the ways ones, tens, and hundreds are grouped in place value. Every time we have 10 taffy pieces, we make a package of 10. When we get 10 packages of 10 candies each, we make a box of 100. In place value, 10 ones make a ten, and 10 tens make a hundred.” 5. Say, “Let’s do another example.” Draw the following on the board or on chart paper. ________ ________ ________ hundreds tens ones 6. Say, “A store has ordered 132 pieces of taffy. We already have our model of a box of 100.” Display 10 student packages. Fill in the hundreds blank with 1. “But our store needs 132 pieces of candy. How many packages of 10 do we need to make 30?” (three) Use student examples to demonstrate, and fill in the tens blank. 7. Ask, “How many single pieces of taffy do we need?” (two) Use two connecting cubes to demonstrate and fill in the ones blank. Then say, “We say this number as one hundred thirty-two, and we write it like this: 132.” Summer School Rising Grades 1–8 Multiply the Math Learning Over the Summer and Add Up Achievement Gains Summer Scholars: Mathematics has been created specifically for summer learning. Students and teachers alike will appreciate its fresh spin on key mathematical concepts and strategies for problem-solving. It’s a bright new way to give learners opportunities to explore and engage in mathematical thinking and prepare for a successful school year ahead. • Teachers save prep and planning time with 25 scaffolded lessons, mathematical discourse, and hands-on STEAM activities. • Content-area readers are included in each kit to help students connect math concepts and skills to real-world applications. • Student growth is easy to track with pre- and post-assessments and progress monitoring. SUMMER SCHOLARS: MATHEMATICS STEAM Readers Digital Resources Management Guide Teacher’s Guide Student Guided Practice Book Nonfiction Books Scan this QR code to watch the Summer Scholar videos. SPANISH AVAILABLE
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