# Number Sense Interventions

by **Nancy C. Jordan, Ed.D.** University of Delaware  
and **Nancy Dyson, Ph.D.** University of Delaware

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# Contents

- About the Photocopiable Activity Sheets and Materials ... vii  
- About the Authors ... viii  
- Acknowledgments ... ix

**1 Introduction.** ... 1  
- What Is Number Sense? ... 1  
- Assessing Number Sense ... 2  
- Number Sense Interventions Research that Supports the Lessons ... 3  
- Guidelines for Implementing the Number Sense Interventions Lessons ... 3  
- Introduction to Lesson Activities by Skill and Common Core State Standards ... 5  
- Incorporating the Lessons into Daily Classroom Life ... 8  
- Number Sense Interventions Activities Organized by Learning Goals with Common Core Framing ... 9  
- Materials List ... 13  
- Materials Made from Black-Line Masters ... 13  
- Teacher-Created Materials ... 14  
- Materials that Can Be Found in the Classroom or Purchased ... 15  
- References ... 15

**2 Number Sense Interventions.** ... 17  
- Lesson 1 ... 17  
- Lesson 2 ... 23  
- Lesson 3 ... 30  
- Lesson 4 ... 36  
- Lesson 5 ... 42  
- Lesson 6 ... 47  
- Lesson 7 ... 52  
- Lesson 8 ... 57  
- Lesson 9 ... 63  
- Lesson 10 ... 68  
- Lesson 11 ... 73  
- Lesson 12 ... 78  
- Lesson 13 ... 83  
- Lesson 14 ... 88  
- Lesson 15 ... 92  
- Lesson 16 ... 96  
- Lesson 17 ... 100  
- Lesson 18 ... 104  
- Lesson 19 ... 109  
- Lesson 20 ... 114  
- Lesson 21 ... 119  
- Lesson 22 ... 124  
- Lesson 23 ... 128  
- Lesson 24 ... 133  
- Extension Partner Activities ... 137

**Photocopiable Activity Sheets.** ... 145  
- Lesson 1 Activity Sheet ... 146  
- Lesson 2 Activity Sheet ... 148  
- Lesson 3 Activity Sheet ... 150  
- Lesson 4 Activity Sheet ... 152  
- Lesson 5 Activity Sheet ... 154  
- Lesson 6 Activity Sheet ... 156  
- Lesson 7 Activity Sheet ... 158  
- Lesson 8 Activity Sheet ... 160  
- Lesson 9 Activity Sheet ... 162  
- Lesson 10 Activity Sheet ... 164  
- Lesson 11 Activity Sheet ... 166  
- Lesson 12 Activity Sheet ... 168  
- Lesson 13 Activity Sheet ... 170  
- Lesson 14 Activity Sheet ... 172  
- Lesson 15 Activity Sheet ... 174  
- Lesson 16 Activity Sheet ... 176  
- Lesson 17 Activity Sheet ... 177  
- Lesson 18 Activity Sheet ... 178  
- Lessons 19–24 Activity Sheet ... 179

## 4 Photocopiable Materials ... 181

- Cardinality Chart ... 182  
- Subitizing Circle Cards ... 183  
- Dot Chart for 2 ... 190  
- Dot Chart for 3 ... 191  
- Dot Chart for 4 ... 192  
- Number Sentence Cards ... 193  
- Partner Dot Cards ... 210  
- Hundreds Chart ... 211  
- Five Frames Master ... 212  
- Ten Frames Master ... 213  
- Decade Cards ... 214  
- Unit Cards ... 220  
- Bigger/Smaller Cards ... 223  
- Teacher Number List ... 224  
- Ten Frame Flash Cards ... 225  
- Student Number List ... 226  
- Activity 18 Hundreds Chart ... 227  
- Activity 19 Hundreds Chart ... 228  
- Activity 20 Hundreds Chart ... 229  
- Activity 21 Hundreds Chart ... 230  
- Activity 22 Hundreds Chart ... 231  
- Activity 23 Hundreds Chart ... 232  
- Activity 24 Hundreds Chart ... 233

## About the Authors

### Nancy C. Jordan, Ed.D., Professor of Education, School of Education, University of Delaware, 206E Willard Hall, Newark, DE 19716

Dr. Jordan is Principal Investigator of the Number Sense Intervention Project (funded by the National Institute of Child Health and Human Development) as well as the Center for Improving Learning of Fractions (funded by the Institute of Educational Sciences, U.S. Department of Education). She is author or coauthor of many articles on mathematics learning difficulties and has recently published articles in Child Development, Journal *of Learning Disabilities, Developmental Science, Developmental Psychology, Journal of Experimental Child Psychology,* and Journal of Educational Psychology. Dr. Jordan holds a bachelor’s degree from the University of Iowa, where she was awarded Phi Beta Kappa, and a master’s degree from Northwestern University. She received her doctoral degree in education from Harvard University and completed a postdoctoral fellowship at the University of Chicago. Before beginning her doctoral studies, she taught elementary school children with special needs. Dr. Jordan served on the Committee on Early Childhood Mathematics of the National Research Council of the National Academies.

### Nancy Dyson, Ph.D., School of Education, University of Delaware, 130 Willard Hall, Newark, DE 19716

Dr. Dyson has had an interest in helping children who struggle with mathematics for many years. She received a bachelor’s degree in mathematics from the University of Pennsylvania and a master’s degree in mathematics education from the University of Pennsylvania’s Graduate School of Education. After raising five daughters and serving 30 years as both a teacher and a school director, she returned to school and received a doctoral degree in education with a concentration in mathematics education from the University of Delaware. Since 2009, she has been the project coordinator for the Number Sense Intervention Project (funded by the National Institute of Child Health and Human Development) at the University of Delaware. Dr. Dyson has coauthored articles for the Journal of Learning Disabilities, Journal of Educational Psychology, and Journal of Mathematics *Teacher Education* and has spoken extensively on the topic of kindergarten number sense and the effect of early intervention.

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| Chart 1.1. Number Sense Interventions Activities Organized by Learning Goals with Common Core Framing |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Domain |  | Lesson |  |  |  |  |  |  |  |  |
| Standard | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |  |  |
| Number | Count to 100 by ones and tens. | Count orally to 10 | Count orally to 10 | Count orally to 10 | Count orally to 20 | Count orally to 20 | Count orally to 20 | Count orally to 30 | Count orally to 30 | Count orally to 30 |  |
| Count forward beginning from a given number other than 1. |  |  |  |  |  | Count to 6 beginning from 5 | Count to 7 beginning from 5 | Count to 8 beginning from 5 | Count to 9 beginning from 5 |  |
| Write numbers from 0 to 20. | Write numbers:1,2 | Write numbers:2,3 | Write numbers:3,4 | Write numbers:4,5 | Write numbers:0-5 | Write numbers:5,6 | Write numbers:6,7 | Write numbers:7,8 | Write numbers:8,9 |  |
| Represent a number of objects with a written numeral 0-20. | Connect quantity to numerals0-2 | Connect quantity to numerals0-3 | Connect quantity to numerals0-4 | Connect quantity to numerals0-5 | Connect quantity to numerals0-5 | Connect quantity to numerals0-6 | Connect quantity to numerals0-7 | Connect quantity to numerals0-8 | Connect quantity to numerals0-9 |  |
| When counting objects, say the number names in the standard order, pairing each object with one number (one-to-one correspondence, set enumeration). | Count on fingers to 2 | Count on fingers to 3 | Count on fingers to 4 | Count on fingers to 5 | Count on fingers to 5 | Count on fingers to 6 | Count on fingers to 7 | Count on fingers to 8 | Count on fingers to 9 |  |
| Count 1,2 objects | Count 1-3 objects | Count 1-4 objects | Count 1-5 objects | Count 1-5 objects | Count 1-5 objects | Count 1-6 objects | Count 1-7 objects | Count 1-8 objects | Count 1-9 objects |  |
| Understand that the last number said tells the number of objects counted. Count to answer, How many? (cardinality). | How many?1-2 | How many?1-3 | How many?1-4 | How many?1-5 | How many?1-5 | How many?1-6 | How many?1-7 | How many?1-8 | How many?1-9 |  |
| Recognize small quantities 1-5 without counting (subitize). | 1,2 | 1,2,3 | 1,2,3,4 | 1,2,3,4 | 1,2,3,4,5 | 1,2,3,4,5 | 1,2,3,4,5 | 1,2,3,4,5 |  |  |
| Recognize quantities 6-10 as 5+n. |  |  |  |  |  | 5,6 Using fingers | 5,6,7 Using fingers | 5,6,7,8 Using fingers and Ten Frames | 5,6,7,8,9 Using fingers and Ten Frames |  |
| Number relations | Identify whether the number of objects in one group is more than, less than, or equal to the number of objects in another group. |  |  |  |  |  | Compare quantities 1-5 more than | Compare quantities 1-5 less than | Compare quantities 1-5 more than/less than | Compare quantities 1-5 more than/less than | Compare quantities 1-10 more than/less than |
| Compare two numbers between 1 and 10 presented as written numerals or objects. |  |  |  | Before and after 1-5 | Before and after 1-5 | Before and after 1-6 | Before and after 1-7 | Before and after 1-8 | Before and after 1-9 | Before and after 1-10 |  |
| Understand that each successive number name refers to a quantity that is one larger. | Build 1 and 2 by adding one more block | Build 1-3 by adding one more block | Build 1-4 by adding one more block | Build 1-5 by adding one more block |  | Build 1-6 by adding one more block | Build 1-7 by adding one more block | Build 1-8 by adding one more block | Build 1-9 by adding one more block | Build 1-10 by adding one more block |  |
| Compose and decompose numbers from 11 to 19 into tens and ones. |  |  |  |  |  |  |  |  |  |  |  |

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| Domain | Number operations | Represent and solve addition and subtraction problems with objects, fingers, and equations. | Story problems 2 family | Story problems 3 family | Story problems 4 family (1+3,etc.) | Story problems 4 family (2+2,etc.) |  | Story problems 5 family (plus) on Five Frames | Story problems 5 family (minus) on Five Frames | Story problems 5+(1,2,3) | Story problems 5+(1,2,3,4) | Story problems 5-(1,2,3,4,5) |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Number sentences 2 family | Number sentences 3 family | Number sentences 4 family (1+3,etc.) | Number sentences 4 family (2+2,etc.) | Number sentences 5 family (plus) | Number sentences 5 family (plus) | Number sentences 5 family (minus) | Number sentences 5+(1,2,3) | Number sentences 5+(1,2,3,4) | Number sentences 5-(1,2,3,4,5) |  |  |  |
| Decompose numbers less than or equal to 10 into pairs. | Finding partners: 2 | Finding partners: 3 | Finding partners: 4 (1/3) | Finding partners: 4 (2/2) | Finding partners: 5 on Five Frames |  |  | Finding partners: 6,7,8 as 5+n on Ten Frames | Finding partners: 6,7,8 as 5+n on Ten Frames | Finding partners: 6-10 as 5+n on Ten Frames |  |  |
| Fluently add and subtract within 5. | Number sentences 1 and 2 families | Number sentences 2 and 3 families | Number sentences 2,3,4 (1/3) families | Number sentences 4 family (2+2,etc.) | Number sentences 5 family (plus) | Number sentences 5 family (plus) | Number sentences 5 family (minus) | Review | Review | Review |  |  |
|  |  |  | Lesson |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| Standard | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |  |  |
| Domain Number | Count to 100 by ones and tens. | Count orally to 40 | Count orally to 40 | Count orally to 50 | Count orally to 80, by tens to 100 | Count orally to 90, by tens to 100 | Count orally to 100, by tens to 100 | Count orally to 100, by tens to 100 | Count orally to 100, by tens to 100 | Count orally to 100, by tens to 100 | Count orally to 100, by tens to 100 | Count orally to 100 |
| Count forward beginning from a given number. | From 11 | From 11 | From 21 | From 45,55,65 | From 65,75,85 | From 76,86 | From 25,47,54,66,78 | From 57,64,76,88 | From 25,67,74,86,95 | From 25,36,47,55,66,77,85,96 |  |  |
| Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 | Count to 6-10 beginning from 5 |  |  |  |
|  |  |  | Count on to solve sums of 6 | Count on to solve sums of 7 | Count on to solve sums of 8 | Count on to solve sums of 9 | Count on using fingers | Count on using fingers |  |  |  |
| Write numbers from 0 to 20. | Write number sentences | Write number sentences | Write number sentences | Write number sentences | Write number sentences | Write number sentences | Write number sentences | Write number sentences | Two-digit numbers Write number sentences | Two-digit numbers Write number sentences |  |  |
| Represent a number of objects with a written numeral 0-20. |  |  |  |  |  |  |  |  | Write number sentence for story problem | Write number sentence for story problem |  |  |
| When counting objects, say the number names in the standard order, pairing each object with one number (one-to-one correspondence, set enumeration). |  | Count on fingers to 12 | Count on fingers to 13 | Count on fingers to 14 | Count on fingers to 15 | Count on fingers to 16 | Count on fingers to 17 | Count on fingers to 18 | Count on fingers to 19 | Count on fingers to 20 |  |  |
| Count 1-11 objects | Count 1-12 objects | Count 1-13 objects | Count 1-14 objects | Count 1-15 objects | Count 1-16 objects | Count 1-17 objects | Count 1-18 objects | Count 1-19 objects | Count 1-20 objects |  |  |  |

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| Domain | Number | Understand that the last number said tells the number of objects counted (cardinality). | How many? 11 | How many? 11-12 | How many? 11-13 | How many? 11-14 | How many? 11-15 | How many? 11-16 | How many? 11-17 | How many? 11-18 | How many? 11-19 | How many? 11-20 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Recognize small quantities 1-5 without counting (solitize). |  |  |  |  |  |  |  |  |  |  |  |
| Recognize quantities 6-10 as 5+n. |  | 5-10 using fingers and Ten Frames |  | 5-10 using fingers and Ten Frames | 5-10 using fingers and Ten Frames | 5-10 using fingers and Ten Frames | 5-10 using fingers and Ten Frames | 5-10 using fingers and Ten Frames | 5-10 using fingers and Penny Ten Frames | 5-10 using fingers and Nickel and Penny Ten Frames |  |  |
| Identify whether the number of objects in one group is more than, less than, or equal to the number of objects in another group. |  | Compare quantities 1-10 |  |  |  |  |  |  |  |  |  |  |
| Number relations | Compare two numbers between 1 and 10 presented as written numerals. | Bigger/smaller (1-10) |  | Bigger/smaller (1-10) | Bigger/smaller (1-10) | Bigger/smaller (1-10) |  | Bigger/smaller (1-10) |  | Bigger/smaller (1-10) |  |  |
| Before and after 1-10 | Before and after 1-10 | Before and after 1-10 | Before and after 1-10 |  | Before and after 1-10 | Before and after 1-10 | Before and after 1-10 | Before and after 1-10 | Before and after 1-10 | Before and after 1-10 |  |  |
| After on Number list |  | Before on Number list |  |  |  |  |  |  |  |  |  |  |
| Understand that each successive number name refers to a quantity that is one larger. | Build 11 as 10 and 1 more | Build 11 and 12 by adding 1 | Build 11-13 by adding 1 | Build 11-14 by adding 1 | Build 11-15 by adding 1 | Build 11-16 by adding 1 | Build 11-17 by adding 1 | Build 11-18 by adding 1 | Build 11-19 by adding 1 | Build 11-20 by adding 1 | Build 11-20 by adding 1 |  |
|  | Plus 1 on number list |  | Minus 1 on number list | Plus 1, minus 1 on number list | Review game n + 1/-1 |  | Review game n + 1/-1 |  | Review game n + 1/-1 | Review game n + 1/-1 |  |  |
| Compose and decompose numbers from 11 to 19 into tens and ones. | Build 11 as a stick of 10 plus 1 | Build 12 as a stick of 10 plus 2 | Build 13 as a stick of 10 plus 3 | Build 14 as a stick of 10 plus 4 | Build 15 as a stick of 10 plus 5 | Build 16 as a stick of 10 plus 6 | Build 17 as a stick of 10 plus 7 | Build 18 as a stick of 10 plus 8 | Build 19 as a stick of 10 plus 9 | Build 20 as sticks of 10 |  |  |
| Number operations | Represent and solve addition and subtraction problems. | Story problems 5+/-n | Story problems 5+/-n | Story problems 5+/-n |  |  | Story problems Drawing models | Story problems Drawing models | Story problems Drawing models | Story problems | Story problems | Story problems |
| Number sentences 5+/-n; 2-5 families | Number sentences 5+/-n; 2-5 families | Number sentences 5+/-n; 2-5 families | Vertical problems; mixed | Vertical problems; mixed |  |  |  |  | Write number sentences for story problems | Write number sentences for story problems |  |  |
| Decompose numbers less than or equal to 10 into pairs. |  |  |  |  |  |  |  |  |  |  |  |  |
| Fluently add and subtract within 5. | Review | Review | Review | Review | Review | Review | Review | Review | Review | Review | Review |  |

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|  |  | Lesson |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| Standard | 21 | 22 | 23 | 24 |  |  |
| Domain | Number | Count to 100 by ones and tens. | Count orally to 100 | Count orally to 100 | Count orally to 100 | Count orally to 100 |
| Count forward beginning from a given number. | From 25,36,47,55,66,77,85,96 | From 25,36,47,55,66,77,85,96 | From 25,36,47,55,66,77,85,96 | From 25,36,47,55,66,77,85,96 |  |  |
| Count on to solve sums 7-9 | Count on to solve sums 8-10 | Count on to solve sums 6-10 | Count on to solve sums 6-10 |  |  |  |
| Write numbers from 0 to 20. | Two-digit numbers Write number sentences | Two-digit numbers Write number sentences | Two-digit numbers Write number sentences | Two-digit numbers Write number sentences |  |  |
| Represent a number of objects with a written numeral 0-20. | Write number sentence for story problem | Write number sentence for story problem | Write number sentence for story problem | Write number sentence for story problem |  |  |
| When counting objects, say the number names in the standard order, pairing each object with one number (one-to-one correspondence, set enumeration). | Count 21 objects |  |  |  |  |  |
| Understand that the last number said tells the number of objects counted (cardinality). | Solve story problems by finger counting | Solve story problems by finger counting | Solve story problems by finger counting | Solve story problems by finger counting |  |  |
| Recognize small quantities 1-5 without counting (subitize). | Make 1-10 on fingers without counting | Make 1-10 on fingers without counting | Make 1-10 on fingers without counting | Make 1-10 on fingers without counting |  |  |
| Recognize quantities 6-10 as 5+n. | 5-10 using fingers and Nickel and Penny Ten Frames | 5-10 using fingers and Nickel and Penny Ten Frames | 5-10 using fingers and Nickel and Penny Ten Frames | 5-10 using fingers and Nickel and Penny Ten Frames |  |  |
| Number relations | Identify whether the number of objects in one group is more than, less than, or equal to the number of objects in another group. |  |  |  |  |  |
| Compare two numbers between 1 and 10 presented as written numerals. | Bigger/smaller(1-10) |  | Bigger/smaller(1-10) |  |  |  |
|  | Before and after 1-10 |  | Before and after 1-10 |  |  |  |
| Understand that each successive number name refers to a quantity that is one larger. | Review game n + 1/-1n=1-19 | Review game n + 1/-1n=1-20 | Review game n + 1/-1n=1-30 | Review game n + 1/-1n=1-30 |  |  |
| Compose and decompose numbers from 11 to 19 into tens and ones. | Build 21 as 2 sticks of 10 plus 1 | Build numbers to 100 as a decade plus a unit | Build numbers to 100 as a decade plus a unit | Build numbers to 100 as a decade plus a unit |  |  |
| Number operations | Represent and solve addition and subtraction problems. | Solve combinations with sums 7-9 | Solve combinations with sums 8-10 | Solve combinations with sums 6-10 | Solve combinations with sums 6-10 |  |
| Write number sentences for story problems | Write number sentences for story problems | Write number sentences for story problems | Write number sentences for story problems |  |  |
| Decompose numbers less than or equal to 10 into pairs. |  |  |  |  |  |  |
|  | Fluently add and subtract within 5. | Review | Review | Review | Review |  |