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Components of Number Sense OverviewUnit 4
What’s the “Big Idea”? Multiple authors recommend that teachers utilize the
“Big Ideas” in their instruction. Generally authors present the “Big Ideas” as lesson
specific. Often lessons are disconnected from each other and / or
focus on one “Big Idea” for that lesson.
Big Ideas Revisited We use the “Components of Number Sense” to connect
every part of the curriculum in almost every lesson, thus, making our lessons more powerful and more efficient.
Outcome equals stronger teachers and stronger math students.
How does this fit with the NCTM?
The NCTM utilizes a strands curriculum The Components of Number Sense are
not in conflict with the NCTM strands. The Components enable teachers to
build true understanding of the mathematical strands.
This helps maintain and build connections for the way students think about mathematics.
NCTM Strands Without Number Sense
Number &
Operatio
n
s
Measurem
ent
Geometry
Data Analysis and Probability
Algebra
NCTM Strands With Number Sense
Number &
Operatio
n
s
Measurem
ent
Geometry
Data Analysis and Probability
Algebra
What are the Components of Number Sense?
Language Connections
Classroom Implementation of the Components of Number Sense
Components of Number Sense
Quantity and Magnitude
Numeration
Equality
Reflection
Write down individually: Reinforced Learned Want to Know
Share with a partner or a small group
Complete this task in five minutes.
Base Ten
Hundreds Tens Units One tenth
One hundredth
Weights 102 101 100 10-1 10-2
Digits 6 5 4 5 2
Weighted Value
600 50 4 0.5 0.02 Total654.52
* Table taken from Binary Number Systems, 2007Total654.52
Form of a Number
“Arithmetic in American Mathematics Education”
1. What are the steps for solving a mathematical problem in China?
2. What is the American equivalent to Lie Shi?
3. Using 10 sticks model a figure and then talk about the mathematical expressions that exist within the visual.
4. What are the key points that Ma makes in this article?
Proportional Reasoning
Geometric and Algebraic Thinking
Reflection
Write down individually: Reinforced Learned Want to Know
Share with a partner or a small group
Complete this task in five minutes.
NumerationNumeration
Quantity/Quantity/
MagnitudeMagnitude
Base TenBase Ten
EqualityEqualityForm of a Form of a NumberNumber
Proportional Proportional
ReasoningReasoning
Algebraic and Geometric Thinking
Components of Number Sense
Analyze the Lesson!
How is that each component of the Components of Number Sense gets expressed in the teaching of the lesson as we connect the language and build true mathematical understanding?
Story One
You have a dime (1/10 of a dollar) and seven nickels (7/20 of a dollar).
In fractional form show how much money you have all together.
Story Two
A team has two team members 3-point shots 1/10 and 7/20.
How did the two of them perform as a team ?
Just Do It!
Language and Math Language
Is math-language language?
How can we use some of what we do in reading instruction to improve our mathematics instruction?
NumerationNumeration
Quantity/Quantity/
MagnitudeMagnitude
Base TenBase Ten
EqualityEqualityForm of a Form of a NumberNumber
Proportional Proportional
ReasoningReasoning
Algebraic and Geometric Thinking
Components of Number Sense © 2007 Cain/Doggett/Faulkner/Hale/NCDPI
Language
We have to teach math like we teach reading!
How is math exactly like a mystery novel?
Do we really try to see the BIG picture?
How does our chapter in the novel fit the whole story?
Two stories
You have a dime (1/10 of a dollar) and seven nickels (7/20 of a dollar). In fractional form show how much
money you have all together. Two team members record their 3-
point shots as 1/10 and 7/20. How did they do as a team?
Set 2 WCPSS Middle School Remedial Warm-upsWake County Public School System/Valerie Faulkner [email protected]
© 2006 Valerie N. Faulkner/Wake County Public School System
Trashketball
The Power to Understanding Percents, Fractions and
Decimals
Let’s Try It!
Agreements How far will the foul line be from the
basket? Are backboards allowable? What else?
Demo with two players How hot is their shot as a team? Representing their stats
Trashketball Procedures
Team members rotate shots. After you shoot, you record your result. Return to end of line for your next shot Team Members stay positive with team
members: “Nice shot!” “Nice try.” “You’re getting better.” “We’re doing great.”
Stay humble with other teams: “Great percentage!”, “Thanks”.
In teams of four, play Trashketball.
Trashketball StatsGroup Name _____________Group Members: 1._________,(2)________,(3) _________(4) __________
Shots taken: Make or Miss:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Total made/Total taken _______/20 Decimal _____ Percentage_____
What was our percent?
How do we determine this ratio?
___ / ___
How Do We Represent the Money Problem Story One?
How do we determine this ratio?
___ / ___
1 Dime
7 Nickels
Trashketball Stats for Story TwoGroup Name _____________
Group Members: 1._________,(2)________,(3) _________(4) __________
1. Shots taken: Make or Miss:
1 2 3 4 5 6 7 8 9 10 Total made/Total taken 1/10 Decimal ___.10__ Percentage__10%_
2. Shots taken: Make or Miss:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Total made/Total taken 7/20 Decimal __.35___ Percentage_35%___
100s Grids for Story Two
How can our ratios be represented?
___ / 10 ___ / 20
How Did the Team Do AltogetherStory Two?
How do we determine this ratio?
___ / ___
How can the Quantity
and its connections to the Math Structure
provide understanding for the Symbolic?
What Do We Ask?
Quantity/Magnitude Numeration Equality Base Ten Form of a Number Proportional Reasoning Algebraic and Geometric Thinking
Trashketball StatsGroup Name _____________
Team Members: 1._______,(2)_______,(3)________,(4)________
1. Shots taken: Make or Miss:
1 2 3 4 5 6 7 8Total made/Total taken _______5/8 Decimal _____ Percentage_____
2. Shots taken: Make or Miss:
1 2 3 4 5 6 7 8 9 10 11 12 13 14Total made/Total taken _______7/14 Decimal _____ Percentage_____
3. Shots taken: Make or Miss:
1 2 3 4 5 6 7 8 9 10 11 Total made/Total taken _______7/11 Decimal _____ Percentage_____
4. Shots taken: Make or Miss:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total made/Total taken ______7/16 Decimal _____ Percentage_____
___5/ 8 ___7/ 14
___7/ 11 ____7/ 16
PICTURE IT!
Bobcats Stats!
A coach can choose any one player to shoot “technical fouls.”
If you were the assistant coach of the Bobcats and your team had to shoot technical fouls, who would you suggest to the head coach to shoot the foul shots and why?
Bobcats Stats
NumerationNumeration
Quantity/Quantity/
MagnitudeMagnitude
Base TenBase Ten
EqualityEqualityForm of a Form of a NumberNumber
Proportional Proportional
ReasoningReasoning
Algebraic and Geometric Thinking
Components of Number Sense © 2007 Cain/Doggett/Faulkner/Hale/NCDPI
Language
It is all about the language---
“I have heard many People say, ‘Give me the Ideas. It is no matter what Words you put them into.’”
To this he replies, “Ideas cannot be Given but in their minutely Appropriate Words.”
William Blake(quoted by J. Newman, The World of Mathematics, 1956)
Assignments for Units 3 and 4
Due Day 3 Learning Task 4
(Components of Number Sense Questions)