Decimals & Percents More Than Just Procedures Jennifer M North Morris Professional Development Specialist Math Coach

Essential Question What types of lessons and learning experiences can increase the conceptual understanding of percent and decimals for students?

Objectives Explore and engage in lessons which promote student thinking. Collaborate with other teachers to create a collection of learning experiences that will develop conceptual understanding.

Agenda: Decimals & Percents Day 1: What is Conceptual Understanding? Day 2: Where is the Decimal Fraction? Day 3: Parts of a Whole Day 4: Embracing Common Core

Move it!!

Introductions Someone You Look Up To Meet anyone (alive or passed) Inspirational Educator (not in this room) Take any of these people on vacation. Who? Where?

24 x 16

1.5 x 34

Number Talks Purpose: Develop conceptual understanding of mathematics Make sense of the math Learn from others Get students Thinking!!

Number Talks: Key Ideas Solve mentally (no paper) Find several ways to solve the task Silent thumbs up when finished Get possible answers Students share methods of solution Teacher visually demonstrates student thinking as instructed by the student

Number Talk Example o/e26276ebb66a448486c9/ o/e26276ebb66a448486c9/

Number Talks: Why?

Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

New Carpet! Ms Rouintree needs new carpet for her classroom. The room is a rectangle and measures 11.1 meters by 14.3 meters. How much carpeting does she need to order? Use numbers & a diagram

Conceptual Ideas

Applying Concepts

When do we divide by a decimal?

Dividing by Decimals Create a scenario. Solve with numbers and a diagram Prior Knowledge? How do we develop conceptual ideas?

Modeling: Circles I have one pizza and want to give 1/5 slices. How many people can I share with? 3 pizzas? What is the expression?

Modeling: Circles You have $1.50 and want to buy gumballs that cost $0.25. How many can you buy? $4.50? What is the expression?

Modeling: Circles 3.5 ÷ 0.5 How do you model? What is the Problem?

Modeling: Circles 5.4 ÷ 0.2 How do you model? What is the Problem?

Modeling: Circles 1.5 ÷ 0.25 How do you model? What is the Problem?

Where Would You Go From Here? Where do we need to go? How do we get there? Regularity?

Please divide: Show Work!!

Why Does this Work? 49.92/ / / / /0.156

Where Would You Go From Here? Where do we need to go? How do we get there? Regularity?

Conceptual Understanding Explore and engage in lessons which promote student thinking. Collaborate with other teachers to create a collection of lessons that will develop conceptual understanding.

Homework & Reflection Journal (?) of where we see/use percent & decimals everyday Reflection

Decimals & Percent More Than Just Procedures Jennifer M North Morris Professional Development Specialist Math Coach

Essential Question What types of lessons and learning experiences can increase the conceptual understanding of percents and decimals for students?

Objectives Explore and engage in lessons which promote student thinking. Collaborate with other teachers to create a collection of lessons that will develop conceptual understanding.

Agenda: Decimals & Percents Day 1: What is Conceptual Understanding? Day 2: Where is the Decimal Fraction? Modeling with Base Ten Blocks Day 3: Parts of a Whole Day 4: Embracing the Common Core

Count the Dots

4.5 ÷ 1.5

Number Talks: Examples

Line it Up!

Calculator Reset Press # Select 3 (All) Press = (Yes)

Line It Up!!! Press T Select 2 (Line0) Press `=

Introductions First educational memory First mathematics memory Favorite teacher Why teach? Why math?

Go to Your Corner!!!

Other Ideas for Random Numbers? Less than? Greater than? Odd/Even Math Facts Practice Chance! Choose Groups Other ideas…

Homework Journal (?) of where we see/use percent & decimals everyday Did you try anything new? Reflections

Ordering Decimals Which of the two numbers is larger? Be ready to explain your reasoning.

Rules for Size of Whole Numbers The number that has more digits is larger. If both numbers have the same number of digits or columns, start comparing from the left. The first one that has a higher digit is higher.

Rules for Size of Decimals

Cash for Gold!!! 1.74 g 0.07 g 0.3 g

How Far? 1.3 miles this morning 3.09 miles at lunch 0.82 miles this afternoon

Book Fair! I have $5 and buy a book that costs $2.25. Do I have enough for the poster?

Virtual Base Ten Blocks

4.5 ÷ 1.5

Walgreens I have $5 and need to split it evenly among 4 of us. How much do we get to spend?

Revisit Carpet Problem 3 m by 2.2 m

Revisit Carpet Problem 2.2 m x 2.3 m

Price Is Right, Anyone? =1qPBzKctgMk

Mini Price Is Right: You Just Won…maybe $20,000 What will you buy? You cannot go over!!

Who’s Closest? Contestant 1: $16, Contestant 2: $20,005.99

Homework & Reflection Find a lesson to share Create some math talk ideas & try one this week Reflection

Decimals & Percents More Than Just Procedures Jennifer M North Morris Professional Development Specialist Math Coach

3.6 x 2.4 On Grid Paper

Base Ten Blocks Why? When?

Multiplying Decimals? Why? When?

Represent 0.45 What is a decimal fraction?

Student Weaknesses Difficulty ordering decimals Relating decimals to drawn representations Relating decimals to fractions Explaining the need to “line up the decimals” for addition/subtraction. Lanchance & Confrey, 2002

Common Errors Treating decimals separately from fractions, ratios, & percent. Applying whole number rules Start by Counting Important source of information

Key Idea By building on their earlier understandings of whole number in the base ten systems and by building a strong sense of the ratios these decimal fractions express, children come to know what decimal fractions mean, gaining some sense of the power and elegance of the decimal systems along with a faculty for operating in it. Cohen, 2010

Find a number between 0.1 and 0.11

Line It Up!!

Number Lines

Homework & Reflection Find a lesson to share Create some math talk ideas & try one this week Reflection

Finding Your Place

Virtual Manipulatives

Essential Question What types of lessons and learning experiences can increase the conceptual understanding of percents and decimals for students?

Objectives Explore and engage in lessons which promote student thinking. Collaborate with other teachers to create a collection of lessons that will develop conceptual understanding.

Agenda: Decimals & Percents Day 1: What is Conceptual Understanding? Day 2: Where is the Decimal Fraction? Modeling with Base Ten Blocks Day 3: Parts of a Whole Day 4: Percent, Common Core, Lessons

20% of 40

20% of 65

Decimals & Percents More Than Just Procedures Jennifer M North Morris Professional Development Specialist Math Coach

Essential Question What types of lessons and learning experiences can increase the conceptual understanding of percents and decimals for students?

Objectives Explore and engage in lessons which promote student thinking. Collaborate with other teachers to create a collection of lessons that will develop conceptual understanding.

Agenda: Decimals & Percents Day 1: What is Conceptual Understanding? Day 2: Where is the Decimal Fraction? Modeling with Base Ten Blocks Day 3: Parts of a Whole Day 4: Percent, Common Core, Lessons

Homework & Reflection Reflections Materials Lessons to share

100 grids NCTM Illuminations: Grid & Percent It

Shade 2 % 35% ½ % 120%

400 People What does 1 square represent? What is 2% of the people? How many people are in ten squares? How many people in ½ square? What part of the square represents 200 people?

20% of First Grade’s 240 students Love gummy bears Use grid to represent 20% How many students like gummy bears?

Venn Diagrams Math Solutions

100 grids & Venn

Twenty-five acres of land are donated to a community, six acres of land must be used as a playground. Represent the situation. What percent of the land is to be used for the playground?

How Many Siblings?

Common Core

Where? Fractions? Decimals? Percent?

Highlight Fraction: Decimal: Percent:

Common Core: ¼,., P% Where? Domain? Essential Standards for grade level Questions

Predicting Candy