Decimals & PercentsMore 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?
ObjectivesExplore 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
http://www.schooltube.com/video/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?
$4.50?
What is the expression?
Modeling: Circles
3.5 ÷ 0.5
How do you model?
What is the Problem?
Modeling: Circles
5.4 ÷ 0.2
How do you model?
What is the Problem?
Modeling: Circles
1.5 ÷ 0.25
How do you model?
What is the Problem?
Where Would You Go From Here?Where do we need to go?
How do we get there?
Regularity?
Please divide: Show Work!!
Why Does this Work?
49.92/15.6
499.2/156
4992/1560
4.992/1.56
0.4992/0.156
Where Would You Go From Here?Where do we need to go?
How do we get there?
Regularity?
Conceptual UnderstandingExplore and engage in lessons which promote student thinking.
Collaborate with other teachers to create a collection of lessons that will develop conceptual understanding.
Homework ?#$@?!& ReflectionJournal (?) of where we see/use percent & decimals everyday
Reflection
Decimals & PercentMore 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?
ObjectivesExplore 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
50-50 Chance!
Choose Groups
Other ideas…
Homework ?#$@?!Journal (?) of where we see/use percent & decimals everyday
Did you try anything new?
Reflections
Ordering DecimalsWhich 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?
http://www.youtube.com/watch?v=1qPBzKctgMk
Mini Price Is Right:You Just Won…maybe
$20,000
What will you buy?
You cannot go over!!
Who’s Closest?Contestant 1:$16,789.50
Contestant 2:$20,005.99
Homework ?#$@?!& ReflectionFind a lesson to share
Create some math talk ideas & try one this week
Reflection
Decimals & PercentsMore Than Just Procedures
Jennifer M North Morris
Professional Development Specialist
Math Coach
3.6 x 2.4On Grid Paper
Warm Up
Base Ten Blocks
Why?
When?
Multiplying Decimals?
Why?
When?
Represent 0.45What 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 rulesStart by CountingImportant source of information
Key IdeaBy 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 ?#$@?!& ReflectionFind a lesson to share
Create some math talk ideas & try one this week
Reflection
Finding Your Place
Virtual Manipulativeshttp://nlvm.usu.edu/en/nav/search.html
Essential Question
What types of lessons and learning experiences can increase the conceptual understanding of percents and decimals for students?
ObjectivesExplore 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 & PercentsMore 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?
ObjectivesExplore 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
100 gridsNCTM 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 bearsUse grid to represent 20%
How many students like gummy bears?
Venn DiagramsMath 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