Teaching Number : Advancing Children's Skills and Strategies

by Robert J Wright

• ISBN13: 9781412921848
• ISBN10: 1412921848
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-09-14
• Publisher: SAGE Publications Ltd

Summary

The book presents nine guiding principles for advancing children's early number skills and offers clear strategies more advanced instruction in addition, subtraction, multiplication, and division .

Table of Contents

List of Figures	xiii
List of Photographs	xiv
List of Tables	xv
Contributors	xvi
Acknowledgments	xvii
Series Preface	xviii
Preface	xx
Introduction	1	(5)
Advancing Children's Strategies and Knowledge in Early Number	6	(19)
Individualized Teaching in Mathematics Recovery	25	(24)
Whole-Class Teaching	49	(18)
General Introduction to Chapters 5 to 9	67	(6)
Teaching the Emergent Child	73	(26)
Key Topic 5.1 Number Word Sequences from 1 to 20	74	(4)
Copying and Saying Short FNWSs	75	(1)
Copying and Saying Short BNWSs	76	(1)
Saying Alternate Number Words Forwards and Backwards	76	(1)
Saying the Next Number Word Forwards	77	(1)
Saying the Next Number Word Backwards	77	(1)
Saying the Number Word After	77	(1)
Saying the Number Word Before	78	(1)
Key Topic 5.2 Numerals from 1 to 10	78	(3)
Numeral Sequences, Forwards	78	(1)
Numeral Sequences, Forwards and Backwards	79	(1)
Sequencing Numerals	79	(1)
Numeral Recognition	80	(1)
Numeral Identification	80	(1)
Numeral Tracks -- 1 to 5 and 1 to 10	80	(1)
Key Topic 5.3 Counting Visible Items	81	(2)
Counting Items in One Collection	81	(1)
Establishing a Collection of Given Numerosity	82	(1)
Counting Items in a Row, Forwards and Backwards	82	(1)
Counting Items of Two Collections	83	(1)
Counting Items of Two Rows	83	(1)
Key Topic 5.4 Spatial Patterns	83	(2)
Ascribing Numerosity to Patterns and Random Arrays	84	(1)
Making Spatio-Motor Patterns to Match Spatial Patterns	84	(1)
Making Auditory Patterns to Match Spatial Patterns	85	(1)
Key Topic 5.5 Finger Patterns	85	(4)
Sequential Patterns for 1 to 5, Fingers Seen	86	(1)
Sequential Patterns for 1 to 5, Fingers Unseen (Bunny Ears)	87	(1)
Simultaneous Patterns for 1 to 5, Fingers Seen	87	(1)
Simultaneous Patterns for 1 to 5, Fingers Unseen (Bunny Ears)	87	(1)
Double Patterns for 1 to 5	88	(1)
Using Fingers to Keep Track of Temporal Sequences of Movements	88	(1)
Using Fingers to Keep Track of Temporal Sequences of Sounds	89	(1)
Key Topic 5.6 Temporal Patterns and Temporal Sequences	89	(10)
Copying and Counting Temporal Sequences of Movements	90	(1)
Copying and Counting Rhythmic Patterns	90	(1)
Copying and Counting Monotonic Sequences of Sounds	91	(1)
Copying and Counting Arhythmical Sequences	91	(8)
Teaching the Perceptual Child	99	(27)
Key Topic 6.1 Number Word Sequences from 1 to 30	101	(3)
Saying Short FNWSs	101	(1)
Saying Short BNWSs	102	(1)
Saying Alternate Number Words Forwards and Backwards	102	(1)
Saying the Next One, Two or Three Number Words Forwards	102	(1)
Saying the Next One, Two or Three Number Words Backwards	103	(1)
Saying the Number Word After	103	(1)
Saying the Number Word Before	103	(1)
Key Topic 6.2 Numerals from 1 to 20	104	(5)
Numeral Sequences, Forwards and Backwards	104	(1)
Sequencing Numerals	105	(1)
Numeral Recognition	105	(1)
Numeral Identification	106	(1)
Numeral Tracks -- 11 to 15, 16 to 20 and 11 to 20	107	(1)
Numeral Rolls 1 to 20, 1 to 50	108	(1)
Key Topic 6.3 Figurative Counting	109	(2)
Counting Items in Two Collections, with First Collection Screened	109	(1)
Counting Items in Two Collections, with Second Collection Screened	109	(1)
Counting Items in Two Screened Collections	110	(1)
Counting Items in a Row with Some Items Screened	110	(1)
Key Topic 6.4 Spatial Patterns	111	(2)
Partitioning Visible Patterns to 6	111	(1)
Partitioning Flashed Patterns to 6	112	(1)
Partitioning Visible Patterns to 10	112	(1)
Partitioning Flashed Patterns to 10	112	(1)
Combining Patterns Using 4-grids, 6-grids, 8-grids, 10-grids	113	(1)
Key Topic 6.5 Finger Patterns	113	(3)
Five Plus Patterns for 6 to 10	114	(1)
Partitioning Numbers 3 to 10	115	(1)
Doubles Plus One	115	(1)
Partitioning 10 Fingers	115	(1)
Key Topic 6.6 Equal Groups and Sharing	116	(10)
Describing Equal Groups	116	(1)
Organizing Equal Groups	117	(1)
Making Equal Groups	117	(1)
Describing Equal Shares	117	(1)
Organizing Equal Shares	118	(1)
Partitioning into Equal Shares	118	(8)
Teaching the Figurative Child	126	(41)
Key Topic 7.1 Number Word Sequences from 1 to 100	127	(4)
Saying Short FNWSs	128	(1)
Saying Short BNWSs	128	(1)
Saying One, Two or Three Numbers After a Given Number	129	(1)
Saying One, Two or Three Numbers Before a Given Number	129	(1)
Counting the Number of Jumps Forwards from a to b	129	(1)
Counting the Number of Jumps Backwards from b to a	130	(1)
Forwards and Backwards Using the Sequence of Decade Numbers from 10 to 100	130	(1)
Key Topic 7.2 Numerals from 1 to 100	131	(6)
Sequencing Numerals	131	(1)
Sequencing Decade Numerals	132	(1)
Sequencing Off-Decade Numerals	132	(1)
Ordering 2-Digit Numerals	132	(1)
Numeral Recognition	133	(1)
Numeral Identification	133	(1)
Numeral Tracks in Range 20 to 100	134	(1)
Numeral Roll 1 to 100	134	(1)
Hundred Square	135	(1)
Blank Hundred Square	136	(1)
Key Topic 7.3 Counting-On and Counting-Back	137	(4)
Counting Items in Two Screened Collections	137	(1)
Counting Items in a Row with Some Items Screened	138	(1)
Missing Addend Tasks	138	(1)
Removed Items Tasks	139	(1)
Missing Subtrahend Tasks	139	(1)
Subtractive Tasks Using a Row	140	(1)
Comparison Tasks	140	(1)
Key Topic 7.4 Combining and Partitioning Involving Five and Ten	141	(4)
Combining Numbers to 5	142	(1)
Partitioning 5	143	(1)
Combining 5 and a Number in the Range 1 to 5	143	(1)
Using 5 to Partition Numbers in the Range 6 to 10	143	(1)
Combining Numbers to 10	144	(1)
Partitioning 10	144	(1)
Key Topic 7.5 Partitioning and Combining Numbers in the Range 1 to 10	145	(3)
Describing and Recording Partitions of a Number	145	(1)
Partitioning Using Flashed Ten Frames	146	(1)
Partitioning and Recording Using Flashed Ten Frames	146	(1)
Combining Two Numbers Using Visible, Pair-Wise Frames	146	(1)
Combining Two Numbers Using Visible, Five-Wise Frames	147	(1)
Combining Two Numbers Using Flashed Frames	147	(1)
Combining Two Numbers Using Flashed Frames and Recording	147	(1)
Key Topic 7.6 Early Multiplication and Division	148	(19)
Combining and Counting Equal Groups	148	(2)
Determining the Number of Equal Groups	150	(1)
Determining the Number in an Equal Share	150	(1)
Describing Visible Arrays	151	(1)
Building Visible Arrays	152	(1)
Determining the Number of Dots on Visible Arrays	152	(15)
Teaching the Counting-On Child	167	(37)
Key Topic 8.1 Number Word Sequences by 2s, 10s, 5s, 3s and 4s	169	(4)
FNWSs by 2s, from 2	170	(1)
FNWSs and BNWSs by 2s	170	(1)
FNWSs by 10s, from 10	170	(1)
FNWSs and BNWSs by 10s	171	(1)
FNWSs by 5s, from 5	171	(1)
FNWSs and BNWSs by 5s	171	(1)
FNWSs by 3s, from 3, and by 4s from 4	172	(1)
FNWSs by 3s and by 4s	172	(1)
Key Topic 8.2 Numerals from 1 to 1,000	173	(4)
Sequencing and Naming 100s Cards	173	(1)
Naming 3-Digit Numerals Using Arrow Cards	174	(1)
Naming 3-Digit Numerals Using Digit Cards	175	(1)
Sequencing and Naming Decade Numerals beyond 100	176	(1)
Sequencing 3-Digit Numerals	176	(1)
Ordering 3-Digit Numerals	176	(1)
Sequences of Multiples with Numerals	176	(1)
Key Topic 8.3 Incrementing by Tens and Ones	177	(4)
Incrementing and Decrementing on the Decade, by Tens	177	(1)
Incrementing and Decrementing off the Decade, by Tens	178	(1)
Incrementing by Tens and Ones	179	(1)
Decrementing by Tens and Ones	180	(1)
Key Topic 8.4 Adding and Subtracting to and from Decade Number	181	(3)
Adding from a Decade	181	(1)
Subtracting to a Decade	182	(1)
Adding to a Decade: 1--5	182	(1)
Subtracting from a Decade: 1-5	182	(1)
Adding to a Decade: 6--9	183	(1)
Subtracting from a Decade - 6--9	183	(1)
Key Topic 8.5 Addition and Subtraction to 20, Using 5 and 10	184	(4)
Building Numbers 6--10	185	(1)
Doubles: 3 + 3, 4 + 4, 5 + 5	185	(1)
Building Numbers 11--20	185	(1)
Doubles -- 6 + 6 to 10 + 10	186	(1)
Doubles Plus or Minus 1	186	(1)
Addition by Going through Ten	186	(1)
Commutativity of Addition	187	(1)
Addition by Compensation	187	(1)
Subtraction by Going through Ten	187	(1)
Key Topic 8.6 Developing Multiplication and Division	188	(16)
Determining the Number in Partially Screened Equal Groups	188	(1)
Determining the Number in Screened Equal Groups	188	(1)
Determining the Number of Groups	189	(1)
Determining the Number in Each Group	189	(1)
Determining the Number in a Screened Array	189	(1)
Determining the Number of Rows	189	(1)
Determining the Number in Each Row	190	(14)
Teaching the Facile Child	204	(32)
Key Topic 9.1 Counting by 10s and 100s	206	(3)
Counting by 10s off the Decade	206	(1)
Counting by 100s to 1000	207	(1)
Counting by 10s beyond 100	207	(1)
Counting by 100s off the 100	207	(1)
Counting by 100s off the Hundred and off the Decade	208	(1)
Counting by 10s beyond 100 off the Decade	208	(1)
Key Topic 9.2 2-Digit Addition and Subtraction through Counting	209	(6)
Adding Tens to a 2-Digit Number	209	(2)
Adding Two 2-Digit Numbers Without Regrouping	211	(2)
Adding Two 2-Digit Numbers With Regrouping	213	(1)
Subtracting Tens from a 2-Digit Number	214	(1)
Subtraction Involving Two 2-Digit Numbers Without Regrouping	214	(1)
Subtraction Involving Two 2-Digit Numbers With Regrouping	215	(1)
Missing Addend Tasks Involving Two 2-Digit Numbers	215	(1)
Key Topic 9.3 Non-Canonical Forms of 2-Digit and 3-Digit Numbers	215	(3)
2-Digit Numbers in Canonical Form	216	(1)
2-Digit Numbers in Non-Canonical Forms	216	(1)
3-Digit Numbers in Canonical Form	217	(1)
3-Digit Numbers in Non-Canonical Forms: Hundreds and Tens	217	(1)
3-Digit Numbers in Non-Canonical Forms: Hundreds, Tens and Ones	217	(1)
Key Topic 9.4 2-Digit Addition and Subtraction through Collections	218	(2)
Adding Two 2-Digit Numbers Using Visible Collections	218	(1)
Adding Two 2-Digit Numbers Using Screened Collections	219	(1)
Missing Addend Tasks Using Visible Collections	219	(1)
Missing Addend Tasks Using Screened Collections	219	(1)
Subtraction Using Visible Collections	220	(1)
Subtraction Using Screened Collections	220	(1)
Key Topic 9.5 Higher Decade Addition and Subtraction	220	(3)
Using Addition Facts Within the Decade	221	(1)
Using Subtraction Facts Within the Decade	221	(1)
Using Addition Facts Across the Decade	222	(1)
Using Subtraction Facts Across the Decade	222	(1)
Key Topic 9.6 Advanced Multiplication and Division	223	(13)
Word Problems -- Multiplication	223	(1)
Word Problems -- Quotition Division	223	(1)
Word Problems -- Partition Division	224	(1)
Commutativity with Arrays	224	(1)
Combining Two Sets of Equal Groups	225	(1)
Partitioning Arrays	225	(11)
Bibliography	236	(3)
Index	239