Teaching for Understanding Division with Fractions Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee Math Teacher.

Slides:

Advertisements

Similar presentations

Teaching for Understanding: Fractions Dr. DeAnn Huinker, University of Wisconsin-Milwaukee Mathematics Teacher Leader (MTL) Seminar Milwaukee Public Schools.

Advertisements

Solving Fraction Equations by Multiplying

What is a reciprocal? How can I find the reciprocal of a number?

Division of Fractions: Balancing Conceptual and Procedural Knowledge Part 2 January 15, 2013 Common Core Leadership in Mathematics2 (CCLM) This material.

Visual Fraction Models

Multiplication & Division Problem Situations Something New?

Solving Linear Equations Rule 7 ‑ 1: We can perform any mathematical operation on one side of an equation, provided we perform the same operation on the.

Division of Fractions: Thinking More Deeply Nadine Bezuk and Steve Klass Session 502 CMC-N 2005.

Division of Fractions: Thinking More Deeply Division of Fractions: Thinking More Deeply Steve Klass National Council of Teachers of Mathematics Kansas.

Proper fractions The value of the numerator is less than the value of the denominator. Proper in this case does not mean correct or best.

Problem Solving, Protocols and Practice through the Ages Wisconsin Mathematics Council Wisconsin Mathematics Council 41 st Annual Conference 41 st Annual.

Chapter 3 Math Vocabulary

This material is based upon work supported by the National Science Foundation Grant No Building, Supporting, and Sustaining Professional Growth.

Reasoning with Rational Numbers (Fractions) DeAnn Huinker, Kevin McLeod, Bernard Rahming, Melissa Hedges, & Sharonda Harris, University of Wisconsin-Milwaukee.

Answers to page 74 #22-31.

Beginning the Journey into Algebra & Algebraic Thinking Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee Milwaukee.

Solving Equations by Adding and Subtracting: Vocabulary Solve: To solve an equation mean to find a solution to the equation. Isolate the variable: Get.

Activity 13.  Pick up a Notecard and write your NAME and PERIOD  Title Notecard: GOALS  Answer the following questions:  1. What do I want to improve.

Teaching for Understanding Division with Fractions Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee Math Teacher.

Solving Linear Equations Part I Presented by Mr. Laws 8 th Math/Algebra 1 JCMS.

Kevin McLeod Connie Laughlin Hank Kepner Beth Schefelker Mary Mooney Math Teacher Leader Meeting, April 5 th and 7 th The Milwaukee Mathematics Partnership.

Charting the Course for Mathematics Leadership Continuum of Professional Work in a Large Urban District DeAnn Huinker Kevin McLeod University of Wisconsin-Milwaukee.

NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number.

DeAnn Huinker, Melissa Hedges, Chris Guthrie, & Beth Schefelker

Division of Fractions Balancing Procedural and Conceptual Knowledge Tuesday December 6, 2011 Common Core Leadership in Mathematics (CCLM) Common Core Leadership.

Unit 2 – Week 4 Reasoning with Linear Equations and Inequalities Lesson 3 Students are introduced to the formal process of solving an equation: starting.

13.6 MATRIX SOLUTION OF A LINEAR SYSTEM.  Examine the matrix equation below.  How would you solve for X?  In order to solve this type of equation,

Properties of Multiplication The properties for multiplying whole numbers are also true for multiplying fractions and whole numbers. (only 1 new property)

Solving Equations Medina1 with Multiplication and Division.

Properties of Equality, Identity, and Operations September 11, 2014 Essential Question: Can I justify solving an equation using mathematical properties?

Big Ideas 3.4 Solving Equations Using Multiplication and Division

Day Problems Solve each equation. Check your answer. 1. x – 3 = 102. m – 3 = = a = k

Journey into Algebra: Describing Change Dr. Henry Kepner, Dr. Kevin McLeod, Dr. DeAnn Huinker, Mathematics Partnership (MMP) Math Teacher Leader (MTL)

Reasoning with Rational Numbers (Fractions)‏

Milwaukee Mathematics Partnership High School Labs Kevin McLeod and DeAnn Huinker University of Wisconsin-Milwaukee Designing High Quality Professional.

Dividing Fractions Using word Problems Absent Copy 1/22,23.

Capturing Growth in Teacher Mathematical Knowledge The Association of Mathematics Teacher Educators Eleventh Annual Conference 26 January 2007 Dr. DeAnn.

Using Subtraction, Addition, Multiplication and Division One Step Equations.

 A.4f Apply these skills to solve practical problems.  A.4b Justify steps used in solving equations.  Use a graphing calculator to check your solutions.

Ch 8 Equations and Inequalities

Solving One-Step and Two-Step Equations

Solve using mental math.

Solving Linear Equations with Justification of Properties.

Solving 1-Step Equations 2 An Equation is Like a Balance.

 A.4f Apply these skills to solve practical problems.  A.4b Justify steps used in solving equations.  Use a graphing calculator to check your solutions.

Lesson 2-3: Solving Equations by Multiplication and Division Algebra 1 CP Mrs. Mongold.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Using Properties to Reason through Tough Questions.

Solving Quadratic Equations. Find the quadratic equation if the solutions are 3 and -2. x = 3 x = -2 Make them equal zero. x – 3 = 0x + 2 = 0 (x – 3)(x.

Teacher Preparation and Professional Development: The Mathematical Knowledge Teachers Need University of Wisconsin–Milwaukee School of Education 18 th.

Part 2: Division of Fractions Balancing Procedural and Conceptual Knowledge Tuesday December 13, 2011 Common Core Leadership in Mathematics (CCLM) Common.

Proportional Reasoning: Looking At Student Work Learning About Student Thinking Identifying Next Steps MTL Meeting May 18 and 20, 2010 Facilitators Melissa.

Deepening Teacher Math Content Knowledge MMP Key Components of High Quality Professional Development DeAnn Huinker & Kevin McLeod University of Wisconsin-Milwaukee.

3. 3 Solving Equations Using Addition or Subtraction 3

Division with Fractions – Part 3 “Partitive Division Tools”

Division of Fractions Core Mathematics Partnership

Solving 1-Step Integer Equations

Ch 2.3 One Step (Multiplication & Division)

Teaching for Understanding Division with Fractions

Look for common factors.

IWBAT divide fractions and decimals.

Tuesday December 13, 2011 Common Core Leadership in Mathematics (CCLM)

Equations and Inequalities

Multiplying and Dividing Rational Expressions

Solving Division Equations

Fractions: Multiplying with mixed numbers

to the Work of the Mathematics Teacher Leader

Add Subtract Multiply Divide

Math-7 NOTES 1) 3x = 15 2) 4x = 16 Multiplication equations:

Add Subtract Multiply Divide

Presentation transcript:

Teaching for Understanding Division with Fractions Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee Math Teacher Leader (MTL) Seminar Milwaukee Public Schools June 2005 This material is based upon work supported by the National Science Foundation Grant No. EHR

Session Goals  Deepen conceptual understanding of division with fractions.  Examine “why” we can invert and multiply.

Popcorn Party Serving Size: 2 cups How many servings from:  8 cups of popcorn  5 cups of popcorn

Summarize  Write the equation for each situation (8 cups; 5 cups).  Identify the meaning of each number in the equations.

Summarize How many 2–cup servings? 8 ÷ 2 = 4 cups cup servings serving 5 ÷ 2 = 2 cups cup serving 1212 servings

What does the represent?  One-half of a cup of popcorn?  One-half of a serving?  Are you sure? 1212

Popcorn Party Serving Size: cup How many servings from:  1 cup of popcorn  4 cups  2 cups

Summarize How many 2–cup servings? 1 ÷ = 2 cup servings 4 ÷ = 8 cups servings 1212 cup serving 1212 cup serving

Task Popcorn Parties # 1 & # 2 æFacilitator æPaper Strip Demonstrator

Algorithm

Task Popcorn Parties # 1 & # 2  Facilitator poses one problem at a time.  Each individual silently solves it.  On facilitator’s cue: State answer.  Demonstrator models with paper strips.  Take turns to justify your reasoning.

Popcorn Party #1 Serving Size: cup of popcorn How many servings can be made from: 1 cup of popcorn 2 cups of popcorn 3 1/2 cups of popcorn 1414

Popcorn Party #2 Serving Size: cup of popcorn How many servings can be made from: 3/4 cup of popcorn 6 cups of popcorn 2 1/4 cups of popcorn 4 1/2 cups of popcorn 3434

Popcorn Party Serving Size: cup How many servings from 4 cups? 3434

Summarize How many 2–cup servings? 4 ÷ = cups 3434 cup serving

Discussion In reviewing these division situations and your solutions, what are you noticing?

Fraction Division Algorithm Photo Sequence from Session

7 X = 1 ?

a X = 1 ? Multiply by the inverse, which is also called the reciprocal.

a X = 1 a ≠ 0 Is this true for any number? What about zero? 1a1a

3434 X = 1 1 ?

7 ÷ 8 = How else can we write this?

12 24 = ? ? 1212

=

5 ÷ = 3434 Estimate Greater than 5? Equal to 5? Less than 5?

Summarize How many 2–cup servings? 5 ÷ = 3434 How else can we write this?

5 =

=

= cdcd 1 abab