## Description

*Fostering Children's Number Sense in Grades K-2* is 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.

## Table of Contents

**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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