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

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

/

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?


Modeling: Circles

1.5 ÷ 0.25

How do you model?


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



Math Coach

Essential Question

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





Day 2: Where is the Decimal Fraction? Modeling with Base Ten Blocks


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

http://nlvm.usu.edu/en/nav/frames_asid_264_g_2_t_1.html?from=category_g_2_t_1.html

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




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

http://nlvm.usu.edu/en/nav/search.html

http://nlvm.usu.edu/en/nav/search.html

Essential Question








Day 4: Percent, Common Core, Lessons

20% of 40

20% of 65


[email protected]



Math Coach

Essential Question








Day 4: Percent, Common Core, Lessons

Homework ?#$@?!& ReflectionReflections

Materials

Lessons to share

[email protected]

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

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

Documents

student slide

oe26276ebb66a448486c9

diagram slide

repeated reasoning slide

common core slide

conceptual ideas

student thinking

decimals percents day