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Fostering Children's Number Sense in Grades K-2: Turning Math Inside Out, CourseSmart eTextbook

By Gregory Nelson

Published by Pearson

Published Date: Jul 15, 2013

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Ensure children’s deep understanding of addition and subtraction in ways that enable long-term growth—with child-centered instructional strategies, powerful and engaging learning materials, and revealing assessment tools. Common Core aligned.


Based on his belief that children are mathematically curious by nature, author Greg Nelson presents a variety of tools classroom teachers can use to give students access to the deep structure of numbers, carefully scaffold their inquiry, and help them excel in math. The goal of this resource is to guide teachers as they feed children’s innate mathematical curiosity and scaffold their insights without taking ownership of the process away from them. To that end the author provides effective tools of instruction and assessment, with clear guidelines for teaching a different way.


In order to help ensure that mathematics learning is a learner-centered process, rather than one forced by adult-sequenced series of rules and facts, the book focuses on seeding the environment with mathematically intriguing tasks just beyond children’s current level of mastery and then giving them the freedom to use that environment in personally meaningful ways. In doing so the book provides a host of suitable materials and activities that encourage self-educating, and suggests how adults can maximize their impact on the child’s learning through careful observation and strategic intervention.

Table of Contents



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



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


Answer keys, or no answer keys?

Study group discussion starters: Turning math inside out




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




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




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



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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Fostering Children's Number Sense in Grades K-2: Turning Math Inside Out, CourseSmart eTextbook
Format: Safari Book

$20.99 | ISBN-13: 978-0-13-299631-0