Eureka Math Parent Workshop Fifth Grade Presented By: Ms. Vereen Instructional Lead Teacher

What’s Your Child Learning in Fifth Grade Mathematics? In grade five, students will build their understanding of the place value system by working with decimals up to the hundredths place. Students will also add, subtract, and multiply fractions, including fractions with unlike denominators. They will continue to expand their geometry and measurement skills, learning the concept of volume and measuring the volume of a solid figure. Activities in these areas will include: Quickly and accurately multiplying multi-digit whole numbers Dividing numbers with up to four digits by two digit numbers Using exponents to express powers of 10 (in 102, 2 is the exponent) Reading, writing, and comparing decimals to the thousandths place Adding, subtracting, multiplying, and dividing decimals to the hundredths place

What’s Your Child Learning in Fifth Grade Mathematics? Writing and interpreting mathematical expressions using symbols such as parentheses. For example, “add 8 and 7, then multiply by 2” can be written as 2×(8+7). Adding and subtracting fractions with unlike denominators (bottom numbers) by converting them to fractions with matching denominators Multiplying fractions by whole numbers and other fractions Dividing fractions by whole numbers and whole numbers by fractions Analyzing and determining relationships between numerical patterns Measuring volume using multiplication and addition

Place Value Skills & Strategies Fourth Grade Fifth Grade Sixth Grade -Use place value understanding to round multi-digit whole numbers to any place -Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right -Compare two multi-digit numbers based on the meanings of the digits in each place, using the symbols > (more than), = (equal to), and < (less than) -Use place value understanding to round decimals to any place -Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1⁄10 of what it represents in the place to its left -Read, write, and compare decimals based on the meanings of the digits in the tenths, hundredths, and thousandths place, using the symbols >, =, and < -Understand that positive and negative numbers are used together to describe quantities having opposite directions or values -Understand a rational number (fraction, decimal, and percent) as a point on the number line -Understand ordering and absolute value of rational numbers

Place Value Skills & Strategies Students use place value understanding to figure out that, based on where the digits are located within the number, 0.115 is less than 0.151. Students recognize that a 5 in the thousandths place is only one tenth the value of a 5 in the hundredths place.

Fraction Skills & Strategies Fourth Grade Fifth Grade Sixth Grade -Break down a fraction into smaller fractions with the same denominator, or bottom number, in more than one way(3⁄8 = 1⁄8+1⁄8+1⁄8 = 2⁄8+ 1⁄8) -Explain why a fraction is equal to another fraction -Add and subtract mixed numbers (whole numbers mixed with fractions, such as 1 1⁄5) with the same denominators -Multiply a fraction by a whole number -Interpret a fraction as division of the numerator (the top number) by the denominator (the bottom number) -Add and subtract fractions with different denominators -Multiply a fraction by a whole number or another fraction -Divide fractions by whole numbers and whole numbers by fractions -Divide fractions by fractions using visual models and equations to show the problem

Fraction Skills & Strategies Understanding how to divide objects into equal shares prepares students for the division of fractions. Students will use pictures such as this to see that 4÷3 is the same as dividing 4 objects equally among 3 shares, or having 4 thirds (4⁄3).

What is Eureka Math? Math? A curriculum that connects math to the real world in ways that take the fear out of math and build student confidence. A presentation of math in a logical progression from Kindergarten through 12th grade. An approach that allows teachers to know what incoming students have already learned, as well as, ensures that students are prepared for what comes next.

What is Eureka Math? A way to dramatically reduce gaps in student learning, instill persistence in problem solving, and prepare students to understand advanced math. A cohesive method to the ultimate goal: students who are not merely literate, but fluent, in mathematics. A methodology that is unfamiliar to those of us who grew up memorizing math facts and formulas, Eureka teaches mathematics as a story to build students’ knowledge logically and thoroughly to achieve deep understanding.

Components of a Lesson: Lesson Study Components of a Lesson: Fluency Practice Application Problem Concept Development Student Debrief

Lesson Study: Fluency Practice Daily, substantial, sustained, and supported by the lesson structure 8-12 minutes of easy-to-administer activities Energetic activities that allow students to see measureable progress Promotes automaticity – allows students to reserve their cognitive energy for higher-level thinking Support conceptual understanding and application as well as the mathematical practices (CLICK TO ADVANCE to BULLETs Every lesson starts w/ fluency Time to practice & review – daily basis (we all know that students who don’t have their basic facts down use a lot of their energy before they’ve even gotten to the heart of a problem – we want to free up their brains. ) (CLICK TO ADVANCE THIRD BULLET) The fluency activities in A Story of Units are generally daily, high-paced and energetic, getting students’ adrenaline flowing, and creating daily opportunities to celebrate improvement. From the beginning of the year, students see their accuracy and speed measurably increase both as individuals and as a class. Like opening a basketball practice with team drills and exercises, both personal and group improvements are exciting and prepare the players for the application in the game setting. (CLICK TO ADVANCE FOURTH BULLET) Fluency promotes automaticity, a critical capacity that allows students to reserve their cognitive resources for higher-level thinking. (CLICK TO ADVANCE FIFTH BULLET) By encouraging students to recognize patterns and make connections within the lessons, the fluency exercises in A Story of Units support the other two components of rigor as well as the Standards for Mathematical Practice.

Lesson Study: Fluency Practice Fluency activities serve a variety of purposes: Maintenance: Staying sharp on previously learned skills Preparation: Targeted practice for the current lesson Anticipation: Building skills to prepare students for the in-depth work of future lessons In fluency work, all students are actively engaged with familiar content. This provides a daily opportunity for continuous improvement and individual success.

Lesson Study: Application Problems Application problems are either after the fluency exercises and before the conceptual development or after the conceptual development and before the student debrief Application problems are commonly 7-12 minutes The Read, Draw, Write (RDW) process is modeled and encouraged through daily problem solving Application problems can be powerful formative assessments Students problem solve independently, choosing appropriate strategies and skills, even when not prompted by their teacher

Lesson Study: Concept Development Constitutes the major portion of instruction and generally comprises at least 20 minutes of the total lesson time.  Builds toward new learning through intentional sequencing within the lesson and across the module. Often utilizes the deliberate progression from concrete to pictorial to abstract, which compliments and supports an increasingly complex understanding of concepts. Accompanied by thoughtfully sequenced problem sets and reproducible student sheets.

Lesson Study: Student Debrief Encourages students to articulate the focus of the lesson and the learning that has occurred. Promotes mathematical conversation with and among students. Allows student work to be shared and analyzed. Closes the lesson with daily informal assessment known as Exit Tickets. Language Journal entry Exit ticket Most important – stdts held accountable, teachers get valuable feeback Tchrs can use exit tkt responses to plan could be refresher the next morning if not enough time, or repeat exact question again to see if stdts remember Did you learn what we meant for you to? You can change numbers and repeat questions… Like the other lesson components, the Student Debrief section includes sample dialogue or suggested lists of questions to invite the reflection and active processing of the totality of the lesson experience.  The purpose of these talking points is to guide teachers’ planning for eliciting the level of student thinking necessary to achieve this.  Rather than ask all of the questions provided, teachers should use those that resonate most as they consider what will best support students in reaching self-articulation of the focus from the lesson’s multiple perspectives. Rather than stating the objective of the lesson at its beginning, we wait until the dynamic action of the lesson has taken place.  Students then reflect back on it to analyze the learning that occurred, articulate the focus of the lesson, and make connections between parts of the lesson, concepts, strategies, and tools on their own.  We recognize or introduce key vocabulary by helping students appropriately name the learning they describe. Sharing and analyzing high quality work gives teachers the opportunity to model and then demand authentic student work and dialogue. Conversation constitutes a primary medium through which learning occurs in the Student Debrief.  Teachers can prepare students by establishing routines for talking early in the year.  For example, “pair-sharing” is an invaluable structure to build for this and other components of the lesson.  During the debrief, teachers should circulate as students share, noting which partnerships are bearing fruit, and which need support.  They might join struggling communicators for a moment to give them sentence stems.  Regardless of the scaffolding techniques that a teacher decides to use, all students should emerge clear enough on the lesson’s focus to either give a good example or make a statement about it. “Exit Tickets” close the Student Debrief component of each lesson.  These short, formative assessments are meant to provide quick glimpses of the day’s major learning for students and teachers.  Through this routine, students grow accustomed to showing accountability for each day’s learning and produce valuable data for the teacher that becomes an indispensable planning tool.

Helping Your Child Learn Outside of School 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, 4x1⁄3 , 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.

Partnering with Your Child’s Teacher Don’t be afraid to reach out to your child’s teacher—you are an important part of your child’s education. Ask to see a sample of your child’s work or bring a sample with you. Ask the teacher questions like: Is my child at the level where he/she should be at this point of the school year? Where is my child excelling? What do you think is giving my child the most trouble? How can I help my child improve in this area? What can I do to help my child with upcoming work?