Math Expressions

1. Math Expressions Fourth Grade Informational Meeting

2. Math Expressions - Philosophy Math Expressions was developed to meet the national need for a balanced program that can: • Focus on understanding and on skill • Use an approach that emphasizes in-depth, sustained learning of core grade-level concepts (rather than a spiral curriculum) • Expand the types of word problems to include those solved by students in other countries • Use math drawings made by students and research-based visual representations to support student understanding and class discussion • Find and use computational algorithms that relate easily to common U.S. algorithms but that can also be used more easily by students • Start at the students’ level and continually elicit their thinking, but provide visual and linguistic supports that all children understand • Bring all children to fluency in the core elementary computational topics while still incorporating important parts of other mathematical topics

3. Math Expressions - Goals Students will exhibit… • Conceptual understanding—Comprehension of mathematical concepts, operations, and relations • Procedural fluency—Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately • Strategic competence—Ability to formulate, represent, and solve mathematical problems • Adaptive reasoning—Capacity for logical thought, reflection, explanation, and justification • Productive disposition—Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

4. Common Core State Standards Instruction in 4th grade focuses on four critical areas: • Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; • Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; • Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

5. Content Standards • Operations and Algebraic Thinking • Use the four operations with whole numbers to solve problems. • Gain familiarity with factors and multiples. • Generate and analyze patterns. • Number and Operations in Base Ten • Generalize place value understanding for multidigitwhole numbers. • Use place value understanding and properties of operations to perform multi-digit arithmetic. • Number and Operations—Fractions • Extend understanding of fraction equivalence and ordering. • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. • Understand decimal notation for fractions, and compare decimal fractions. • Measurement and Data • Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. • Represent and interpret data. • Geometric measurement: understand concepts of angle and measure angles. • Geometry • Draw and identify lines and angles, and classify • shapes by properties of their lines and angles.

6. Practice Standards • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

7. Math Expressions – The Units • Place Value and MultidigitAddition and Subtraction • Multiplication with Whole Numbers • Division with Whole Numbers • Equations and Word Problems • Measurement • Fraction Concepts and Operations • Fractions and Decimals • Geometry

8. Math Instruction with Math Expressions Differences • Digs deeper into concepts • Requires children to understand their thinking • Requires children to verbalize their thinking • Follows the Common Core Standards • More assessment • Differentiated instruction is built into the program • More opportunity for practice • More opportunity for practice and review

9. From the Concrete to the Abstract. Students gain an in-depth understanding of the concepts when they are grounded in a foundation that is concrete before they are asked to work in the abstract. For example multiplication:

10. Understanding Concepts With Pictures • Math drawings, focused on reasoning, help students to attach meaning to new concepts • Pictures and models: • Provide support for students as they shift their understanding of concepts from the concrete to the abstract • Help students ‘put to words’ the methods they used • Provide a ‘proof’ for their solutions • Create a fluent and deep understanding of the material

11. Math Talk – Student Communication • Math Talk- The student doing the talking is the one doing the learning!! • Students: • Explain their thinking and the methods they used • Prove their answer with pictures and numerical models • Classmates: • Ask questions for clarification • Offer different solution methods

12. Problem Solving • The ability to solve problems is a key feature of successful math students. • A goal Math Expressions is to help students become reflective and resourceful problem solvers • To solve problems an algebraic approached is used. Students must: • Understand what the problem is asking, • Represent the situation with pictures or numbers • Solve the situation, • Then check for reasonableness. • The students solve an ambitious range of problem types

13. Problem Types – Fourth Grade

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21. What’s with Puzzled Penguin? • Students gain an in-depth multi-facetted understanding of a concept when they analyze problems for correctness.

22. Vocabulary • More intense • Math word walls • Glossaries

23. What if my child does not understand? Through daily formative assessments, teachers are picking up on difficulties students are having. • Leveled Activity Cards • Concepts are taught for a length of time • Fluency Check • Soar to Success

24. What if my child needs a challenge? • Challenge Center • Leveled Activity Cards • Destination Math • Math journal writing prompts

25. What are the expectations for my child? • Path to Fluency • Fluently multiply and divide within 100 • Fluently add and subtract multi-digit numbers • Homework- Students should have homework at the end of each lesson. This gives them the opportunity to practice the skills taught and practiced in class. • Remembering sheets- Provides practice of concepts previously taught • Math Talk (Communication)- Students should be able to talk about and explain concepts. If they can explain a concept they are more likely to understand it.

26. What should I be doing at home? • Build fluency by practicing basics facts with your child nightly • Use “Math Talk” questions (How do you know? Are you sure? Why?) to prompt student explanations • Complete the homework with your child if needed • Check the homework after your child has completed it for accuracy • Contact your child’s teacher if you have any questions • Have your child play the online math games at home

27. Resources • Parent Letters • Math Expressions – Website • www-k6.thinkcentral.com • Student Activity Journal • Your Child’s Teacher

28. What questions do you have? • Please fill out the survey • Thank-you!!!