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How can teachers build mathematically powerful students who can solve real-life problems, communicate their understanding to others, and perform well on local and state assessments?

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The animation is already done for you; just copy and paste the slide into your existing presentation. 5 Steps to A Balanced Mathematics Program Step 1: Math Review and Mental Math Step 2: Problem Solving Step 3: Conceptual Understanding Step 4: Mastery of Math Facts Step 5: Common Formative Assessments

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Build Build computational and procedural skills Develop Develop mathematical reasoning and problem-solving abilities Deepen Deepen conceptual understanding Demonstrate Demonstrate understanding in a variety of assessment formats

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https://www.youtube.com/watch?v=KdxEAt91D7k

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The animation is already done for you; just copy and paste the slide into your existing presentation. How can we help students develop number sense?

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The animation is already done for you; just copy and paste the slide into your existing presentation. Model different method for computing Ask students regularly to calculate mentally Have class discussions about strategies for computing Make estimation an integral part of computing Question students about how they reason numerically both when they make mistakes AND when they arrive at the correct answer Pose numerical problems that have more than one possible answer - Marylin Burns

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Number Sense Activity Dot Plates

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What patterns did you notice?

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The animation is already done for you; just copy and paste the slide into your existing presentation. Students with number sense naturally decompose numbers, use particular numbers as referents, solve problems using the relationships among operations and knowledge about the base-ten system, estimate a reasonable result for a problem, and have a disposition to make sense of numbers, problems, and results. Knowledge of the number system Patterns in the number system Sense of quantity Reasonable answer

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It is the key to understanding all math. As students build their number sense, mathematics takes on greater meaning. Mathematics becomes more about reaching understandings than following a rigid set of rules. With strong number sense, children become more apt to attempt problems and make sense of mathematics. It is the key to understanding all math. Jessica Shumway Number Sense Routines

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Reasoning with Fractions Reasoning with Whole Numbers Reasoning with Fractions https://www.mathreasoninginventory.com/Home/ReasoningFractions Reasoning with Whole Numbers https://www.mathreasoninginventory.com/Home/ReasoningWholeNumbers https://www.mathreasoninginventory.com/Home/ReasoningFractions https://www.mathreasoninginventory.com/Home/ReasoningWholeNumbers Snapshot of Students Misunderstanding (Math Solutions by Marilyn Burns) Jonathan

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Jo Boaler Professor Stanford University Jo Boaler Professor Stanford University Reasoning About Division – Teaching Channel https://www.teachingchannel.org/videos/common-core-teaching-division

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The animation is already done for you; just copy and paste the slide into your existing presentation. Build Ten Frame on Floor https://mathsolutions.wistia.com/medias/a47aut7kzw Ten –Frame and Dot Card Images https://mathsolutions.wistia.com/medias/09jhvdzx89 Leprechaun Traps: Addition within 100 (1 st Grade Class) https://www.teachingchannel.org/videos/grade-1-math Reasoning About Division – Teaching Channel https://www.teachingchannel.org/videos/common-core-teaching-division

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The animation is already done for you; just copy and paste the slide into your existing presentation. A systematic method to deal with student misconceptions using error analysis, specific feedback, and reflection. This step creates immediate gains in student learning. Mental math promotes number sense development and enhances math fact development.

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The animation is already done for you; just copy and paste the slide into your existing presentation. Repeated Reasoning multiple opportunities to practice the same skill 24 attempts to reach 80% (Marzano) Effective Feedback Specific and timely feedback is the single most powerful modification that enhances student achievement. (Hattie) Relational Thinking math interconnected concepts and ideas emphasizing reasonable answers, number sense, students making sense of the math

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Category Development Skills and concepts students should know but typically don’t Concepts and skills that are vital to success in their grade level Reinforce grade-level or course Priority Standards Front Load Upcoming Unit 2-5 problems from different categories minutes at the beginning of math period

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The animation is already done for you; just copy and paste the slide into your existing presentation. Student Collaboration Classroom environment that values students’ explanation of their understanding Key Statement Ideas Essential Understanding that we wants students to have Error Analysis Timely and Specific Feedback Focus based on students misconceptions Student Reflection Specific to error Stating what they know mathematically

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The animation is already done for you; just copy and paste the slide into your existing presentation. Daily Math Review 1 st Grade Set Up: Students sit on the rug close to the teacher. Students have a designated partner. Categories and problems based on number sense. Students have necessary manipulatives for categories. Students have a paper template to record work.

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Categories are completed one at a time using the following sequence: Teacher reads problems problem and then the student and teacher read the problem together. Students try the problem independently using available manipulatives and paper and pencil. Students turn to face their partners and discuss what they tried and what they think the answer is and record on their paper what they tried.

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Class solves the problem together The students star work that is correct on their paper and circle and fix work that is incorrect or incomplete. Students turn back to their partner and participate in reflection by sharing how they did on the problem. The class says they key statement for the problem together 2 times.

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The animation is already done for you; just copy and paste the slide into your existing presentation. Teacher-directed Student-directed Group answer “Pass the Pen” method Speedy (end of cycle when most students have mastered)

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Advanced Student: Give the option of helping others Provide individualized bonus problem Solve problems multiple ways Struggling Student: Peer collaboration Oral response in reflection Pictorial reflection work Small group/individual help teacher Survival Box Survival Box

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The animation is already done for you; just copy and paste the slide into your existing presentation. Ten problems (max.) 2 to 4 per category Correct quiz with students increases student engagement &responsibility Collect data to inform decisions 90% students get 100% on category to take it off DMR

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Mini-Math Workout for the Brain Students need regular opportunities to develop effective computation strategies that are base on number sense. Helping student use number strategies is an effective way to develop number sense. Students need daily practice to develop and retain strong number sense and effective computational skills. Mental Math

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The animation is already done for you; just copy and paste the slide into your existing presentation. Teacher says a string of numbers and operations ( – 3 x 2) Students think, then write the answer Teacher repeats the string of operations Students check their work mentally The whole class tells the answer chorally Teacher asks 3 students to tell how they thought of the answer Do 2-3 problems Mental math problems should be related to the same theme. Stay with theme 2 weeks Mental Math Steps

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Mental Math Themes one more/less than given number counting by 2, 5, 10 Anchors of 5 and 10 Doubles, fact families, number facts math vocabulary measurement (time, money, calendar, inches, feet, etc. Start with one more than 5 (6); double that number (12) think what is one less than that number (11) Start with a dozen; subtract half.... number operations fractional operations and concepts math vocabulary exponents square roots percent-decimal-fraction Start with square root of 144 (12); add square root of 81 (21); divide by 7 (3) cube the result (27)....

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Mental Math Table Assignment 1.Choose 3 different mental math themes and write problems for each. 2.Share with group 3.Nominate 1 to share with larger group

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Daily Math Review and Mental Math Reinforce prior learning of math skills Provide daily practice for mathematical computation problems Promote mathematical reasoning and develop number sense Includes specific feedback, error analysis, and student reflection

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The animation is already done for you; just copy and paste the slide into your existing presentation. Start with concepts students should know but don’t Critical areas for students success

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The animation is already done for you; just copy and paste the slide into your existing presentation. Daily Math Review Complete Cycle 5Reflection Starters: 1. Next time I will 2. I didn’t understand # because 3. To help me solve this, I knew 4. I need to remember__ because_ 5. I learned that Category: Fractions on a Number Line (3.NF.2a) Category: Subtracting with regrouping with a zero (3.NBT.2) Category: Subtracting with two regroupings (3.NBT.2) Misconception: Students do not understand where a fraction is represented on a 0-1 number line; knowing equal parts on a number line Misconception: Students do not always know how and when to regroup multi-digit numbers. (1 regrouping with a zero) Misconception: Students do not always know how and when to regroup multi-digit numbers. (2 regroupings) 9 Questions: Questions: Which shape on the number line represents ½? 2. Which shape on the number line represents ¼? 3. Which shape on the number line represents 3/4? 4. Which shape on the number line represents 2/4? 5. Which shape on the number line represents 4/4? Key Statement: Fractions on a number line have equal parts. Key Statement: Sometimes you need to regroup when solving a subtraction problem. Key Statement: Sometimes you need to regroup more than once when solving a subtraction problem.

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The animation is already done for you; just copy and paste the slide into your existing presentation. Daily Math Review Assessment 90% of the students need to get 100% on a category to “retire” the category. 2 – 4 questions per category. (3.NF.2a)(3.NF.2a) Questions: a zero (3.NBT.2) Questions: (3,NBT.2) Questions: Category: Subtracting with two regroupings Category: Subtracting with regrouping with Which shape on the number line represents ½? Which shape on the number line represents 3/8? Which shape on the number line represents 5/8? Category: Fractions on a Number Line

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The animation is already done for you; just copy and paste the slide into your existing presentation. Daily Math Review AssessmentName:Name:Date Fractions on a Number Line Which shape on the number line represents ½? 2.Which shape on the number line represents 3/8? 3.Which shape on the number line represents 5/8? Subtraction: 1 Regrouping and a Zero = = = Subtraction: 2 Regroupings = = =

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New Albany, Indiana % proficient % proficient (increase of over 800 students passing) Special Education Students % proficient % proficient Example of cohort of students over 4 years: 4 th grade % proficient 5 th grade % proficient 6 th grade % proficient 7 th grade % proficient

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