3-5 Math Night: Place Value Presented by: Hand out: 3-5 Q & A Math 3-5 Help at home Index card: write questions/comments- these will help inform our next steps, such as the November evening, classroom supports, etc.. Also, I will be taking questions from the K-2 night and tonights night and writing a newletter to share on K-5 Math that can answer some of your questions. Also- I have received emails expressing interest in our math opportunities…Perennial Math Presented by: Beth Finkelstein, K-5 Math Staff Developer Joanne Lombardi, Third Grade Teacher Laura Pelin, Third Grade Teacher Kate Alix, Fourth Grade Teacher Tricia Galloway, Fifth Grade Teacher Maureen Haberstroh, 2-4 TSP Teacher

Pelham Public Schools K-2 Math Presentation Agenda Common Core State Standards (CCSS) Math in Focus 3-5 Fluency Development Developing Understanding: Place Value Place Value in Math in Focus 3-5 Hands-on Exploration in the Hall Presented by: B. Finkelstein,A. Imperioli, A.Schaps, J.Denet, C. Cavalli

Common Core State Standards (CCSS) In the past, states had different standards for what students needed to know and be able to do in math and ELA. CCSS was developed to provide strong, shared expectations among different states of student learning. CCSS provide clear, consistent guidelines for what students should know and be able to do at each grade level in math and English Language Arts. The Singapore Syllabus was an important resource for the developers of the CCSS for mathematics.

Standards for Mathematics Mathematical Content Standards for Mathematical Practice Skills and knowledge the students will learn each year Different for each grade level Skills build upon each other each year Habits of mind that students should develop to foster mathematical understanding and expertise Span all grade levels Eureka Math Modules and Math in Focus address both the Standards for Mathematical Content and the Standards for Mathematical Practice.

Components of a Math in Focus Lesson Teach/Learn Guided Practice Let's Practice Workbook Homework Think Central: Online Access *Note: There are many problems for practice during a lesson through the Guided Practice, Let's Practice and the Workbook. Students will not always be assigned all of the problems to complete in the Workbook. Components of a Math in Focus Lesson: Whole Group, Guided Practice: Small Group/Partner Work, Independent Practice, Assessment Teach/Learn: This is a connection to previous learning or a real-life application problem to set the context for the day’s learning. This involves direct instruction with the teacher modeling mathematical concepts using manipulatives, engaging students in a discussion, and having students share their thinking and strategies. Guided Practice: The teacher continues to support students while they work on problems in a large group, small group, or with a partner. Students may be using manipulatives, trying out problems on a dry erase board, working in a math journal or playing a game to reinforce the concept. Let's Practice: This is where students will have the opportunity to practice the skills independently or with a partner. At this time the teacher will walk around and give guidance and assess student understanding. Workbook: Students will work independently in their workbook to practice the skills from the lesson.* Homework: Homework is meant for students to practice the learning from the day. Homework might be assigned as pages from the Workbook or from additional black-line worksheets that accompany the program. *Note: There are many problems for practice during a lesson through the Guided Practice, Let's Practice and the Workbook. Students will not always be assigned all of the problems to complete in the Workbook.

How are we addressing a new program starting in Grades 3-5? 2014 Summer Work: Mapped out the sequence of lessons and included lessons from prior grades to fill gaps Pre-Test: Each chapter has a pre-test that identifies knowledge of skills needed for the new chapter. Includes links to prior grade’s lessons if needed. Experience with Concrete-Representational-Abstract to build understanding.

Pedagogy of Math in Focus For students to develop a deeper understanding of the mathematics, we do not just want to show them the steps or algorithm to memorize. We want them to first have a concrete experience with manipulatives so they can see what is happening (Concrete). Then they take that experience and interpret their understanding and communicate their understanding through a visual representation (Pictorial). This might be drawing a picture or symbols. At the early level this might be drawing circles to represent a quantity. As students progress and the numbers get larger they begin to use symbols (e.g. a line to represent a group of 10, or circles with 1, 10, 100,… to represent the place value chips. ) As students progress through these stages, the teacher continues to show them the abstract symbols (the equation or algorithm). This way, students can begin to see the connections and have a deeper understanding of what is happening when they use the algorithm. (Good example: Adding with regrouping…Use base 10 blocks for students to see what happens when you have more than 9 ones…you can regroup and take a 10 rod. This is what happens when we put the little one above the 10s column). file:///H:/My%20Documents/013-014%20Math%20Staff%20Development/2014-2015%20September%20Info/Building%20Mathematical%20Understanding.pdf

We are teaching FLUENCY and UNDERSTANDING Students work on developing fluency with counting and math fact practice each day: Flashmasters, Fluency Drills We teach strategies for mental computation We build understanding of concepts and provide opportunities for application We teach strategies for problem solving We all believe that students need to be fluent. They need to know their basic facts. They should be able to think 8 x 7 and immediately know 56! Just as they need to know 9 + 7 =16. We know this is necessary so it does not slow students down when working with larger numbers and solving problems. We want them to think about the problems, not figuring out basic facts. That being said, there is a time for teaching mental math strategies, so students can compute more complex numbers mentally and of course, we want them to understand place value and operations, so they can visualize and think about what is happening in a problem as a they solve it. We do not want our students to be the person at the dinner table when the check comes that they pass it to another person, saying “I’m not good at math”. After all, dealing with a check is basic computation, but so many people have only learned rote rules, they cannot apply it to situations in life.

Focus on Place Value Place value is the value of each digit depending on its place, or position, in a number. Tonight, we are going to emphasize the importance of Place Value. Grades 3-5 all started with their first chapter on Place Value. Let’s look at how we can think about place value in operations. As I show you some examples, think about how each emphasizes the value of the digits.

Traditional Algorithm with Regrouping: I’m sure this looks familiar to most of you. It is how most of us would have been taught to do multiplication. We learned the steps of the algorithm and we followed them. I remember being in a math education class and being asked why I put the 3 up there. Many people responded, because that is what you are supposed to do, but few could explain clearly what it meant. We want to teach students to understand what this all means.

Decompose Numbers: Take apart 34 + 52 Think of 52 as 50 +2 34 + 5 tens, or fifty, is 84. 82 + 2 ones is 86.

Rectangular Array Apply Place Value: This is rectangular array. It is showing 213 x 4. You can see the 2 hundreds are shown 4 times. The 1 ten is shown 4 times. The 3 ones are shown 4 times. We can think about the place of each digit and what happens when we multiply each digit value by 4.

67 x 45 Area Model Using Place Value: This is an Area Model. It is similar in that the number 67 is thought of as 6 tens or 60 and 7 ones. The number 45 is seen as 4 tens or 40 and 5 ones. The value of each digit is multiplied and then the products are added.

Think: 60 + 7 40 + 5 Multiplying Using the Place Value of Each Digit Decomposing Factors: Think: 60 + 7 40 + 5 This is less of a visual model, but here one is still using the value of each digit to multiply.

Let’s look at the progression of teaching place value with Math in Focus in grades 3-5 We are going to look at what your children are doing in their 3-5 classes as they get started this year with place value. The end goal is an efficient way for students to work with numbers. They start to work in second grade with regrouping ten ones to make a ten as they will learn to add numbers such as 28 + 7. In third grade, they will work regularly with the standard algorithm we are familiar with. The difference is we will take time to get there to be sure we build understanding, so that our children don’t just follow rote rules, but rather have a good visual model in their minds of what is happening as they eventually use the algorithm. We are building understanding and models that will help with whole numbers and their work with fractions.

Place Value Chart with Base Ten Blocks Place Value Chart with Place Value Disks

Grade 3

Grade 3

Grade 3

Grade 4

Grade 4

Grade 4 Add Multi-Digit Numbers with Regrouping Algorithm with Place Value Understanding:

Grade 4

Grade 4

Grade 5 5 x 100 means 5 groups of 1 hundred, so 5 x 100 = 5 hundreds or 500 11 x 100 means 11 groups of 1 hundred, so 11 x 100 = 11 hundreds or 1, 100 5 x 1,000 means 5 groups of 1 thousand, so 5 x 1,000 = 5 thousands or 5,000 11 x 1,000 means 11 groups of 1 thousand, so 11 x 1,000 = 11 thousands or 11,000

Grade 5

Grade 5

Grade 3: How can you help your child with mathematics? Pelham Public Schools K-2 Math Presentation Grade 3: How can you help your child with mathematics? Read the parent letter sent home from the classroom to learn about the concepts being taught in the upcoming chapter. Resist the urge to “show” your child how to do the math. Instead, encourage thinking and persistence. Have him/her look at a sample problem or ask “What do you remember from class?”, “What do you think this means…?” or “What do you think you should do first?” Play math games with your child. For example, “I’m thinking of two numbers whose product is between 20 and 30. How many pairs can you think of that would satisfy this problem?” Have your child explain the solutions. How does he or she know that all the number pairs have been identified? Encourage your child to write or describe numbers in different ways. For example, what are some different ways to make 1450? 1450 = 1 thousand, 4 hundreds, 5 tens, and 0 ones, or 1000 + 450, 14 hundreds and 50 ones, 13 hundreds + 15 tens, etc. Use everyday objects to allow your child to explore the concept of fractions. For example, use measuring cups to have students demonstrate how many ⁄1 3’s are in a whole, how many ⁄1 4 cups you need to make 1 1⁄4 cups, and how many times you have to refill a ½ cup measure to make 1½ cups. Encourage your child to stick with it whenever a problem seems difficult. This will help your child see that everyone can learn math. Praise your child when he or she makes an effort and share in the excitement when he or she solves a problem or understands something for the first time. From: Council of the Great City Schools: Parent Roadmaps to the Common Core Standards- Mathematics Presented by: B. Finkelstein,A. Imperioli, A.Schaps, J.Denet, C. Cavalli

Grade 4: How can you help your child with mathematics? Pelham Public Schools K-2 Math Presentation Grade 4: How can you help your child with mathematics? Read the parent letter sent home from the classroom to learn about the concepts being taught in the upcoming chapter. Resist the urge to “show” your child how to do the math. Instead, encourage thinking and persistence. Have him/her look at a sample problem or ask “What do you remember from class?”, “What do you think this means…?” or “What do you think you should do first?” Use everyday objects to allow your child to explore the concept of fractions. For example, use measuring cups so students see how many times you have to refill a 1⁄4 cup to equal a 1⁄2 cup or how many 1⁄3’s are in two cups. Have students describe two fractions that are equal using a measuring cup (filling a 1⁄4 measuring cup twice is the same as filling one 1⁄2 measuring cup). Have your child write or describe fractions in different ways. For example, what are some different ways to make 3⁄4 ? Answers could include 1⁄4+1⁄4+1⁄4 or 3x1⁄4. Ask your child create and describe equal fractions. For example, have students take a sheet of paper, fold the paper in half, and then unfold and shade 1⁄2. Then have students take the same sheet of paper and fold the paper in a half again. Unfold the paper and have students discuss the number of parts that are now shaded. Encourage your child to talk about ways to show that 1⁄2 =2⁄4. (Students may continue this process creating other equal fractions.) Encourage your child to stick with it whenever a problem seems difficult. This will help your child see that everyone can learn math. Praise your child when he or she makes an effort and share in the excitement when he or she solves a problem or understands something for the first time. From: Council of the Great City Schools: Parent Roadmaps to the Common Core Standards- Mathematics Presented by: B. Finkelstein,A. Imperioli, A.Schaps, J.Denet, C. Cavalli

Grade 5: How can you help your child with mathematics? Pelham Public Schools K-2 Math Presentation Grade 5: How can you help your child with mathematics? Read the parent letter sent home from the classroom to learn about the concepts being taught in the upcoming chapter. Resist the urge to “show” your child how to do the math. Instead, encourage thinking and persistence. Have him/her look at a sample problem or ask “What do you remember from class?”, “What do you think this means…?” or “What do you think you should do first?” Use everyday objects to allow your child to explore the concept of fractions. For example, have your child divide a candy bar (or a healthy snack) between three people. Ask, “How much does each person receive?” (Each person would receive 1⁄3). Suppose there are three candy bars that you plan to share with two friends. Have your child describe the amount that each person will receive. Have your child explain how to write fractions in different ways. For example, what are some different ways to write 4⁄3 ? He or she could answer 4÷3, 1 1⁄3, 2⁄3 + 2⁄3, 2 x 2⁄3, 8⁄6, 4 x 1⁄3 , etc. Ask your child to give you a fraction equal to a decimal. For example, what are two fractions that can be used to represent 0.6? Answers could include 6⁄10, 60⁄100, 12⁄20 , or 3⁄5. Encourage your child to stick with it whenever a problem seems difficult. This will help your child see that everyone can learn math. Praise your child when he or she makes an effort and share in the excitement when he or she solves a problem or understands something for the first time. From: Council of the Great City Schools: Parent Roadmaps to the Common Core Standards- Mathematics Presented by: B. Finkelstein,A. Imperioli, A.Schaps, J.Denet, C. Cavalli

Explore in the Hall Place Value Riddles Multi-Digit Addition and Subtraction with Manipulatives Problem of the Lesson