Fostering Children's Number Sense in Grades K-2 Turning Math Inside Out
, by Nelson, Gregory
- ISBN: 9780132981514 | 0132981513
- Cover: Paperback
- Copyright: 2/6/2013
Fostering Children's Number Sense in Grades K-2is a powerful, hands-on resource that helps in-service teachers, curriculum coaches, and math intervention specialists ensure children's deep understanding of addition and subtraction in ways that enable long-term growth. Packed with child-centered instructional strategies, powerful and engaging learning materials, and revealing assessment tools, the book is clearly laid out and cross-referenced to the Common Core State Standards.
Greg Nelson, Ph.D. has spent the last 35 years involved in early childhood education as a classroom teacher, center owner and director, intern trainer, workshop presenter, author, early childhood consultant, and university instructor. His interests include devising curriculum to support the emergence of early math and science literacy in children, and exploring the interface of developmentally appropriate practice and world-class educational standards. Author of A Teacher’s Bag of Tricks and Math at Their Own Pace, he currently serves as professor of early childhood education at Bridgewater State University in Massachusetts and is president of the Massachusetts Association of Early Childhood Teacher Educators.
SECTION 1: GETTING STARTED
Chapter 1: Rethinking Number Sense
What math is not
Children’s readiness to be mathematicians
How we should teach math
What the experts and the research tell us
Math inside out
Chapter 2: How to Teach Math This Way
Logistics
Space
Preparing the teaching materials
“Math time”
Work, not play
Learner-centered instruction
How we tend to teach…and why
Creating the learning community you want
Teacher-led lessons
The perils of group work
The role of the teacher as the children work
Keeping everyone safe
Authentic assessment
Teaching tips
Helping children talk about what they know
Three levels of vocabulary acquisition
Concrete before abstract
The same thing many ways
Errors are information
Competition
Answer keys, or no answer keys?
Study group discussion starters: Turning math inside out
SECTION 2: EMERGENCE OF SECURE PLACE-VALUE AWARENESS
Chapter 3: Place-Value Awareness Launch Points
What this is, and why it is important
What comes before, and how to get there
Logical quantification (K.NCC.4b)
Accurate counting to ten (K.NCC.1, K.NCC.4, K.NCC.5)
Connecting numerals to quantities (K.NCC.3)
Concepts and skills being reinforced at this developmental stage
The teen counting numbers have 10 as a base (K.NBT.1)
The use of zero as a place holder (1.NBT.2c)
The part-whole concept extended to the place value system (K.NBT.1, 1.NBT.2)
Place value versus face value (1.NBT.2)
The 10:1 relationship between units and tens (1.NBT.2a)
Directionality in reading multi-digit numerals (1.NBT.1)
Counting on using place value categories (K.CC.1, K.CC.2, 1.NBT.1)
Counting backwards through the decades
Estimating larger quantities
Greater than/less than in the place value system (1.NBT.3)
The relationship between hundreds and tens (2.NBT.1)
Launch points
Teen boards
Tens boards
Hands Up #1
“How Old Are We?” books
Hundreds board
Estimation activities (Unifix cubes; Cuisenaire rods; ten frames)
Race to a 100
Chapter 4: Place-Value Awareness Check Points
Assessment probes
Cuisenaire teens
Hundred chain
Page walk
Hundreds board magic windows
Arrow math
Decade transition boards
How Many Now? — Variation #1
How Many Now? — Variation #2
How Many Now? — Variation #3
How Many Now? — Variation #4
Study group discussion starters: Secure place-value awareness
SECTION 3: SECURE PART-WHOLE AWARENESS AND THE EMERGENCE OF ADDITION-SUBTRACTION FLUENCY
Chapter 5: Addition-Subtraction Fluency Launch Points
What this is, and why it is important
What comes before, and how to get there
Basic part-whole awareness (K.OA.3)
Concepts and skills being reinforced in this chapter
Part-whole patterns for numbers up to 20 (K.OA.3, K.OA.4)
Decomposition and composition of numbers (K.OA.3, K.NBT.1, 1.OA.1, 1.OA.6)
The commutative property of addition (1.OA.3, 2.NBT.5, 2.NBT.6)
Addition and subtraction as inverse operations (1.OA.1, 1.OA.4, 1.OA.6, 1.NBT.4, 2.NBT.9)
Launch points
Hands Up #2 — Addition/subtraction
Ten-bar-in-a-cave game
Addition/subtraction using equal-arm balance scale
Addition/subtraction using ten-frames
Double-nines dominoes sorting
Domino trains or squares
Directional rods with addition/subtraction rack
Addition/subtraction using segmented Cuisenaire rods and 1-100 rack
Addition/subtraction using double-fives abacus
Chapter 6: Addition-Subtraction Fluency Check Points
Assessment probes
Pursuit game
Ten-frame flash cards
Fact family triominoes
Parts Of calculator drill
Counting On calculator drill
Addition/subtraction war with playing cards
Addition/subtraction using torque balance scale
More teaching tips
Addition trumps subtraction
The perils of “Mad Minute” drills
Bridging from the concrete to paper-and-pencil
The real scoop on those dreaded word problems
The order in which number-sense based memorization develops
Study group discussion starters: Secure part-whole awareness and the emergence of addition-subtraction fluency
SECTION 4: EXTENDING PLACE-VALUE AWARENESS
AND ADDITION-SUBTRACTION BEYOND THE HUNDREDS
Chapter 7: Place-Value Fluency and Multi-Digit Addition-Subtraction Launch Points
Concepts and skills being reinforced in this chapter
A place value is determined by how many positions it is to the left of the units column (2.NBT.1, 2.NBT.4)
Zero as a place holder (2.NBT.1b, 2.NBT.3)
The maximum face value is 9 in any place-value column
10:1 exchange rates (2.NBT.1a, 2.NBT.7)
Exponential growth in a place-value system
The counting sequence in a place-value system
When combining or removing quantities, only digits in the same place-value location can be combined or decreased (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9)
Composing and decomposing bundles of ten to move them from one place-value category to another can be done at any level of the place-value system as a tool of problem-solving (2.NBT.8, 2.NBT.11)
Standard algorithms can be used to efficiently solve multi-digit addition and subtraction problems, but alternative algorithms and strategies are sometimes preferable (2.NBT.10, 2.NBT.12, 2.NBT.13)
Launch points
200 board
Make-your-own place-value materials
Bank game with place-value blocks and place-value cards
Place-value materials sorter tray
Hundred and thousand extensions of ten-frames and Hand Game cards
Expanded notation strip
Modeling multi-digit addition-subtraction with exchanging
Mental math problem sets
Decimeter rods, meter rods, centimeter rods, metric measuring tape, and metric trundle wheel
Reading and writing really big numerals
Chapter 8: Place-Value Fluency and Multi-Digit Addition-Subtraction Check Points
Assessment probes
Hundred-square in a cave game
Wacky numbers
I have, who has? game
Parts-of calculator drill
Skip-counting calculator drill
Target game
What’s wrong with this picture? sets
Final teaching tips
Words matter
Keeping children fluid
Teaching as improv
Collaboration and transformation
Keeping your eye on the prize
Study group discussion starters: Extended place-value awareness and addition-subtraction beyond the hundreds
Appendices
Appendix A: Research-based teaching-learning paths
Appendix B: Assessment templates — Use for individual child, tracking progress over time
Appendix C: Assessment templates — Use for whole class, tracking outcomes of a particular lesson or activity
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