UPPE R G R ADE S GUIDE IMPLEMENTATION€¦ · • Skip Counting by 5s 10 • Skip Counting by 6s 10 • Skip Counting by 7s 10 • Skip Counting by 8s 10 • Skip Counting by 9s 10

IMPLEMENTATION

GUIDEU P P E R G R A D E S

Everything you need to know to get the most out of the TouchMath Upper Grades Program

INNOVATIVE LEARNING CONCEPTS INC.

creators of TOUCHMATH®

Innovative Learning Concepts Inc. • 5445 Mark Dabling Blvd., Colorado Springs, CO 80918-3800Toll Free: 1-800-888-9191 • Fax: 1-719-593-2446 • Web: www.touchmath.com • E-mail: [email protected]

Printed in the United States of America

TouchMath materials were first published in 1975. Innovative Learning Concepts Inc.’s publications may not be reproduced or disseminated in any way, or stored in any database or retrieval system, without written permission of the publisher. However, limited permission is granted to reproduce only the blackline activity masters solely for noncommercial educational use with students in a single classroom or a single home, and for no other purpose.

TouchMath®, TouchNumerals®, and The Alphabet of Mathematics® are registered trademarks of Innovative Learning Concepts Inc. Touch2Learn™, TouchPoint™, TouchShapes™, TouchStar™, TouchMath Tunes™, TouchMath Tutor™, StepNumerals™ and Innovative Learning Concepts™ are trademarks of Innovative Learning Concepts Inc. of Colorado Springs, CO.

Copyright 2012 Innovative Learning Concepts Inc. All rights reserved.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–3

• The Philosophy of TouchMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1• Overview of the TouchMath Upper Grades Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2• Activity Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Teaching Aids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Classroom Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

TouchMath Computation Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–18

• Touching/Counting Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8• Beginning Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9• Addition by Counting On . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9• Addition Without Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10• Addition With Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10• Backward Counting Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11• Beginning Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12• Subtraction Without Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12• Subtraction With Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13• Skip Counting Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–15• Skip Counting Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16• Beginning Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17• Beginning Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18• Division With Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Assessment/Progress Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19–20

TouchMath Table of Contents Navigating the Guide

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© 2012 Upper Grades Implementation Guide 1

The Philosophy of TouchMathTh e TouchMath philosophy may be stated in fi ve easy words: REACH AND TEACH ALL LEARNERS. Th e educators who have developed and expanded the TouchMath Program since 1975 have worked constantly to meet this goal. Every TouchMath unit, module, and activity sheet refl ects their dedication.

Th e success TouchMath has experienced is due to its original multisensory approach to math. TouchMath uses the one-of-a-kind TouchPoint system as the base for the TouchMath Program — the ONLY math program that uses the actual numeral as a manipulative. Students use numerals to see, say, hear, touch, and learn math concepts with hands-on manipulatives and paper-and-pencil written activities. As students engage all of their senses, each individual within the group has the opportunity to assimilate information whether he is a visual, auditory, or tactile/kinesthetic learner.

TouchMath activities are meticulously scaff olded and provide all learners with ample opportunities for success. As each skill is mastered, the next simple step is introduced. Th e TouchMath activity sheets are clean and uncluttered with age-appropriate artwork. Th e variety, quantity, and quality of the activities provided make reinforcement immediately available on an as-needed basis. Testing and tracking materials provide instant feedback.

TouchMath materials are straightforward and easy to use. Skills on each page are clearly defi ned and presented using specifi c methodology. Th e materials are eff ective in large group situations, in small groups, or for individual learners. Students master each concept as they see it, say it, hear it, touch it, and learn it.

TouchMath Introduction Philosophy

Janet BullockPresident/CEO

2 © 2012 Upper Grades Implementation Guide

Overview

TouchMath Introduction CONTINUED

Overview of the TouchMath Upper Grades ProgramWelcome to the TouchMath Upper Grades Program from Innovative Learning Concepts Inc. This program will help your student(s) develop a firm foundation in basic addition, subtraction, multiplication, division, time, and money.

Included in the Program: • Implementation Guide• Pre- and Posttests (downloadable from www.touchmath.com/homeschool)

Recommended Classroom Aids: • TouchMath TouchPoint Posters• TouchMath TouchNumeral• TouchMath Skip Counting Poster and CD Set• TouchMath Connect interactive whiteboard program (compatible with IWBs and computers)

Guide ComponentsSince TouchMath concepts, particularly the TouchPoint® counting system, are basic elements of the student activity sheets, information on the TouchMath Touching/Counting Patterns and the steps of TouchMath addition, subtraction, multiplication, and division are included in this guide. As you read this subject matter, it will give you all of the information you require to understand and teach TouchMath fundamentals. If you have not been trained in the TouchMath Program, we encourage you to take advantage of our free Teacher Training DVD loan program. You can learn more about the free training by going to www.touchmath.com/training.

An Assessment/Progress Monitoring Record form is also available. See page 21 of this guide for more information.

DownloadablesAll students should be given the pretest for placement purposes. These tests can be downloaded from www.touchmath.com/homeschool. See page 4 of this guide for more information.

The TouchMath Homeschool Upper Grades Activity Sheet topics are presented in specific sequence and uses a defined series of steps within each of those sections. See page 3 of this guide for a complete list of available sets.

Recommended Classroom Aids and SoftwareThe TouchMath TouchPoint Poster Set may be purchased separately to help students learn or review the correct TouchMath Touching/Counting Patterns.

The TouchMath TouchNumerals may be purchased separately, and are designed as a manipulative teaching aid to instruct students in numeral shapes, quantity/numeral associations, Touching/Counting Patterns, skip counting, place value, addition, subtraction, multiplication, and division.

The TouchMath Skip Counting Poster and CD Set may be purchased separately to aid students in mastering the counting sequences to be applied in multiplication and division.

The TouchMath Connect software may be purchased separately, and is an excellent way to demonstrate TouchMath number concepts, addition, and subtraction to the class or small groups. It also provides hands-on student interaction with the processes before they do the paper-and-pencil activities. See page 5 of this guide for more information.


Activity Sheets

TouchMath Introduction CONTINUED

Number Concepts Page Count• Touching/Counting Patterns 15• Counting to 10 10• Counting to 100 20• Backward Counting from 10 and Below 20• Backward Counting from 18 and Below 15• Skip Counting by 2s 10• Skip Counting by 3s 10• Skip Counting by 4s 10• Skip Counting by 5s 10• Skip Counting by 6s 10• Skip Counting by 7s 10• Skip Counting by 8s 10• Skip Counting by 9s 10

Addition• Beginning Addition Adding 1 to 5 20• Beginning Addition Adding 1 to 9 25• Addition with Counting On 25• Double-Digit Addition Without Regrouping 10• Double-Digit Addition With Regrouping 10• Double-Digit Addition With and Without Regrouping 10• Addition Word Problems 10

Subtraction• Beginning Subtraction Subtracting 1 to 5 20• Beginning Subtraction Subtracting 1 to 9 25• Double-Digit Subtraction Without Regrouping 10• Double-Digit Subtraction With Regrouping 05• Double-Digit Subtraction With and Without Regrouping 10• Subtraction Word Problems 10

Mixed Addition and Subtraction• Mixed Beginning Addition and Subtraction 10• Mixed Double-Digit Addition and Subtraction wo Regrouping 10• Mixed Double-Digit Addition and Subtraction With Regrouping 10• Mixed Double-Digit Addition and Subtraction w/wo Regrouping 10

Multiplication• Beginning Multiplication Multiplying by 0 to 5 20• Beginning Multiplication Multiplying by 0 to 9 30• Multiplication of Two Digits by One Digit w/wo Regrouping 15

Division• Beginning Division Dividing by 1 to 5 20• Beginning Division Dividing by 1 to 9 20• Beginning Division Dividing by 1 to 9 With Remainders 10

Money• Coins: Pennies through Half-Dollars 25• Bills: Ones through Twenties 20• Making Change 10

Time• Hours and Minutes 10

Downloadable Activity Sheet SetsThis list of Activity Sheet Sets is provided for an easy reference to all of the activity sheets available in the Upper Grades Homeschool Program. Included skills are scaffolded from simple to more complex, ensuring the learners’ understanding. Used in conjunction with the pre- and posttests and Progress Monitoring Record, this can be useful for differentiated instruction.


Overview

TouchMath Assessments

Assessment Overview for All Grade LevelsThe TouchMath pre- and posttests are available for download at www.touchmath.com/homeschool. The directions measure computational abilities expected for four levels. Pre-assessment determines a student’s current level of number concepts and computational competence. Posttesting with the same instrument demonstrates a student’s progress.

Educators may administer any one of the four TouchMath Assessments to their students at any grade level. Select an assessment based on the current level of individual student performance. For instance, a first-grade student may take the Level A test if the student is beginning to count and identify numerals. If a student answers most of the problems correctly on an assessment, advance to the next level test. The following guidelines will help determine which level of testing is best administered to an individual student.

Level A: This assessment is designed for the student beginning to understand numbers. It includes counting tasks, recognition of numerals, oral identification of numerals, and beginning addition and subtraction. The test involves no writing and should be administered individually.

Level B: This assessment is designed for the student learning to identify and write numerals one through ten and attempting basic one-digit addition and subtraction. The test may be administered individually or in a small group setting.

Level C: This assessment is designed for the student learning to add and subtract two-digit numbers with regrouping (44 + 27, 76 – 58). It may be administered individually or in a small group setting.

Level D: This assessment is designed for the student further developing the ability to add and subtract with regrouping and also learning basic multiplication and division. The test may be administered individually or in a small group setting.

Pre- and Posttest DirectionsAdminister the TouchMath pretest before beginning the use of TouchMath materials. The assessments may be administered individually or in a small group setting. Read the test descriptions above, and choose the assessment according to the student’s ability level.

Pretest:

1. Fill in the name, date, and grade level at the top of each page of the assessment.

2. Say, “Answer as many problems as you can. There are no grades on this assessment. Do not worry if you don’t know how to figure out these problems. Watch the signs! The dark line on each page will remind you to change operations. Just do your best.” Never cue or correct a student’s answer.

3. Record the total number of correct and incorrect responses at the top of the assessment page.

Posttest:

1. Administer the TouchMath posttest following a comprehensive use of the TouchMath materials.

2. Administer the posttest following the same instructions used for the pretest.

Adaptation Note: The pre- and posttests may be adapted by enlarging the problems for those with physical limitations. Students may say the answer orally, place a marker on the bubble, point to the answer, or use meaningful communication gestures to indicate they are able to complete each task. Visual distraction may be kept to a minimum by working one problem at a time while the other problems are covered.


Overview

TouchMath Technology

TouchMath Connect Interactive Whiteboard ProgramTouchMath’s new interactive whiteboard program, TouchMath Connect, revolutionizes the way you teach and the way your students learn math. Th e program can be used with an interactive whiteboard (IWB) or on stand-alone computers for individual student practice. All senses are activated when students engage, and TouchMath comes to life as students move, see, say, hear, touch, and learn math like never before!

In line with all TouchMath programs and products, TouchMath Connect epitomizes the concrete-symbolic-abstract approach to teaching and learning mathematics. Th e concrete, hands-on manipulatives are abundantly and thoroughly symbolized and represented through this IWB program, which eventually leads to a fi rm grasp on the abstract paper-pencil elements so essential to success. Designed for use with all age levels, TouchMath Connect allows for teacher-customized playlists and problem choices as well as a fun competition mode for students.

TouchMath Connect is an excellent way to demonstrate math concepts to the class or small groups. Th e program also provides hands-on student interaction with the processes before doing the individual paper-and-pencil activities.

Th e following activities are included in the TouchMath Connect program.

Number Concepts• Learning Touching/Counting Patterns• Placing TouchPoints• Counting to 20• One-to-One Correspondence to 9• One-to-One Correspondence 10–20• Greater/Less Th an to 9• Greater/Less Th an 10–20• Greater/Less Th an 1–20• Counting to 100• Backward Counting Number Line from 18• Backward Counting Sequencing from 18 and Below• Place Value to 99• Place Value to 999

Addition• Addition with Objects• Addition with Object TouchPoints• Addition with TouchPoints• Addition with Counting On• Double-Digit Addition• Th ree-Digit Addition• Double-Digit Addition with Regrouping

Subtraction• Subtraction Crossing Out Objects• Subtraction with TouchPoints & Objects• Subtraction with TouchPoints• Fact Families• Double-Digit Subtraction• Th ree-Digit Subtraction• Double-Digit Subtraction with Regrouping

Touching/Counting Patterns

Number Concepts

Addition

Subtraction


Overview

TouchMath Teaching Aids

TouchPoint Posters TouchNumerals

Additional Tools for the ClassroomWhen using TouchMath, it is critical that students master the TouchMath Touching/Counting Patterns correctly and are able to touch and count consistently in the proper order. TouchMath recommends the following materials and activities to ensure student success.

1. The reversible TouchMath TouchPoint Posters may be laminated and used by students to place objects on the TouchPoints. Use objects that are stackable for numerals with double TouchPoints. The front of each poster has the Touching/Counting Patterns printed and may be used as a first step to learning the Touching/Counting Patterns. The backs of the posters do not have the Touching/Counting Patterns printed and are easy to use as a mini-test to see if students know the patterns.

2. The TouchPoint Posters also provides excellent wall posters for visual reinforcement as students progress in the program.

3. Paper-and-pencil activities for learning the TouchPoint placement will be found in the student activity sheets. These pages may also be used with objects such as small plastic toys, candies, washers, etc. as long as the objects are stackable.

4. The TouchMath TouchNumerals set contains three sets of 6” foam numerals (0–9), 205 TouchPoints, operation signs, and ten Base 10 trays. The TouchNumerals may be used to teach numeral shapes, quantity/numeral association, Touching/Counting Patterns, place value, addition, subtraction, skip counting, multiplication, and division.

5. As students practice the Touching/Counting Patterns, explore basic computation with the numerals 1–9 with TouchPoints, and learn the more advanced place value and regrouping using the Base 10 trays in the TouchMath TouchNumerals set, they begin to make the connection between concrete objects and numerical values. A complete teacher’s manual is included with the set.


Overview

TouchMath Classroom Guide

Setting up the ClassroomHaving the TouchMath Program in the classroom is one part of a successful overall strategy to implement quality math instruction. To ensure user fidelity and augment the effectiveness of the program, suggestions are included for classroom use.

Using this Classroom Guide will help maximize instruction time and individual learning time for each specific task.

TouchMath Classroom Setup

• Display all TouchMath classroom aids during math instruction, and use them with the students.• Establish small group areas to differentiate instruction and provide individualized guidance.

TouchMath Program Implementation

• Include in your lessons visual, auditory, and tactile/kinesthetic components.• Model using TouchMath materials, manipulatives, and counters during whole group instruction.• Use the vocabulary words included for each objective in your instruction with the children. • Assess students at the end of each activity sheet set to monitor progress.• Incorporate the skills in the TouchMath Program throughout the day.

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Touching/Counting Patterns

TouchMath Computation Steps

When working with the TouchPoints, students are to count aloud and consistently follow the correct Touching/Counting Patterns. Single TouchPoints are touched and counted one time, and double TouchPoints are touched and counted twice.

Zero has no TouchPoints, so you never touch a zero.

The one is touched at the top while counting: “One.”

The two is touched at the beginning and the end of the numeral while counting: “One, two.”

The three is touched at the beginning, middle, and end of the numeral while counting: “One, two, three.”

The four is touched from top to bottom on the down strokes while counting: “One, two, three, four.” For the triangle-shaped 4, use the same square counting pattern. To help students not forget the first TouchPoint, it may be referred to as in “outer space.”

The five is touched and counted in the sequential order pictured: “One, two, three, four, five.” To help in remembering the fourth TouchPoint, it may be referred to as the “belly button.”

The six begins the use of double TouchPoints (dots with circles). These double TouchPoints should be touched and counted twice whenever they appear. Six is touched and counted from top to bottom: “One-two, three-four, five-six.”

The seven is touched and counted from top to bottom, counting the double TouchPoints first: “One-two, three-four, five-six,” followed by the single TouchPoint: “seven.” The single TouchPoint can be thought of as the nose. Teachers sometimes tell young or remedial students to “touch him on the nose” to help them remember the final TouchPoint.

The eight is touched and counted from left to right: “One-two, three-four, five-six, seven-eight.” Tell the young or remedial students that the eight looks like a robot. Count his head first and then his body. You may also tell students the eight is touched in the same pattern as you write the letter Z.

The nine is touched and counted from top to bottom, counting the double TouchPoints first: “One-two, three-four, five-six, seven-eight,” followed by the single TouchPoint: “nine.” To the tune of “Head, Shoulders, Knees, and Toes,” have the students touch these body parts with both hands while singing, “Head, shoulders, knees, and toes, touch the nose” (with one finger). This will physically show the nine TouchPoint counting pattern on the numeral.

1

2

12

3

1

2

3

4

123

45

1,23,45,6

7 1,23,4

5,6

1,2 3,45,6 7,8

91,23,45,67,8

1


Addition

TouchMath Computation Steps CONTINUED

Beginning AdditionThe TouchMath Beginning Addition section teaches the steps used in adding single columns of numbers. Any student who misses an addition problem on a worksheet is touching or counting incorrectly. To identify the problem, simply observe the student touching and counting aloud.

1. Teach the Beginning Addition Statement: “I touch and count all the TouchPoints on the numerals.”

2. Begin at the top of the column.

3. Touch with a pencil point and count aloud using the correct Touching/Counting Pattern on the five: “One, two, three, four, five.”

4. Work straight down the column, touching and counting on the four: “Six, seven, eight, nine.”

5. Record the answer: 9.

6. Reinforce facts by repeating the problem and the answer aloud: “Five plus four equals nine.” This step is critical for many students and should be emphasized at every opportunity.

Example

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Addition by Counting OnThis section teaches the steps in TouchMath Addition by Counting On. Students who miss a problem are counting or touching incorrectly or may be attempting to count a number twice. To identify the problem, have the student work a problem aloud while you watch the process.

1. Say the Addition Counting On Statement: “I touch the greater number, say its name, and continue counting on the TouchPoints of the other numeral.”

2. Say the name of the greater number: “Six.”

3. Continue by counting on the TouchPoints of the three: “Seven, eight, nine.”


5. Reinforce facts by repeating the problem and the answer aloud: “Six plus three equals nine.”

Example

6 q# yy 9


Addition


Addition Without RegroupingTouchMath Addition Without Regrouping incorporates the prior steps of addition and requires a new visual cue, the arrow above the ones column.

1. Teach the Arrow Statement. “I start on the side with the arrow. The arrow is in the ones column on the right side.”

2. Say the greater number in the ones column: “5,” and continue counting on the TouchPoints of the 3: “6, 7, 8.”


4. Repeat step 2 in the tens column: “4”, and continue counting on the TouchPoints of the 3: “5, 6, 7.”


6. Repeat the problem and answer aloud.*

* This step reinforces the ability to read and recognize large numbers.

Example

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Addition With RegroupingTouchMath Addition With Regrouping incorporates all prior addition steps and introduces the visual cue of the box above the tens column. The box is used to hold the regrouped number.

1. Teach the Addition Regrouping Statement: “I must regroup if my answer is more than 9.”

2. Locate the greater number in the ones column and say its name: “Nine.”

3. Continue counting on the other number: “Ten, eleven, twelve.”

4. To reduce reversals, record the number of tens in the box first: 1.

5. Record the number of ones in the ones column: 2.

6. Add the tens column. Begin with the number in the box and count straight down the column. You may also start with the greater number, cross it out and continue counting from the top.

7. Record the number of tens in the tens column: 6.

Example

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1


Backward Counting


Backward Counting ActivitiesThe first step of TouchMath Subtraction is backward counting. Students should be able to count backward from 18 or from any number below 18. They must also be able to stop at numbers other than zero. For example, they will need to count backward from 17–5, 14–3, 16–9, etc. Backward counting activity sheet sets are available in the TouchMath Homschool Upper Grades products.

The following activities will also help students learn backward counting: 1. Take several minutes daily to practice counting backward orally from 18 and from every number below

18. Activities might include counting backward while walking backward around the room, passing a ball around a circle while counting backward, or counting backward while standing in line for lunch.

2. Distribute 18 beans or other small objects to students, putting them in one pile. Direct students to count 10 of the objects into a second pile. Then have them count backward from 10 until all objects are returned to the original pile. Repeat the process and change the number of objects to be counted.

3. Provide a beanbag or a lightweight ball. Line students up with 18 in each line. Leave two to three feet between students. The first student says, “18” while tossing the ball across to the student opposite him who says, “17” as he catches it. Continue until the last student has the ball. Rotate positions and start again.

4. As students line up to exit the classroom for recess, lunch, etc., have them count backward. Use every possible opportunity for verbal practice.

5. Have students walk forward in a circle or a line while they count forward, then count backward as they walk backward. For instance, “Let’s count forward from 3 to 15 and then backward from 15 to 3.” Start and end with different numbers each time the activity is repeated.

6. Students are paired, and each pair is given a beanbag or ball. Call out the starting number and have the paired students pass the beanbag back and forth as they count backward. Vary this by changing the starting and the ending number. For instance, “Count backward from 15 to 4.”

7. Line students up in one or more parallel lines, with 18 children in each line. Have them progressively count forward, each student calling out his or her number and squatting as they do so (all 1s squat together, then 2s, and so on). After the number 18 is reached, all students will be squatting. Then, have them stand back up as they count backward from 18 to 1. Vary this by starting the lines with 17 students, 16 students, etc. and by changing the ending number to 1, 3, 6, etc.


Subtraction


Beginning SubtractionThe TouchMath Beginning Subtraction section teaches the steps used in subtracting single columns of numbers. Any student who misses a subtraction problem on a worksheet is touching or counting incorrectly. To identify the problem, simply observe the student touching and counting aloud.

1. Teach the Beginning Subtraction Statement: “I touch the first number, say its name, and count backward on the TouchPoints of the other number.”

2. Touch the top number and say its name: “7.”

3. Count backward on the TouchPoints of the 4: “6, 5, 4, 3.”

4. The answer is the last number spoken: “3”


6. Reinforce the subtraction facts by repeating the problem and the answer aloud.*

* This step engages auditory learning and is key in helping students begin to memorize number facts.

Example

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Subtraction Without RegroupingTouchMath Subtraction Without Regrouping incorporates the prior steps of subtraction and requires a new visual cue, the arrow above the ones column.

1. Say the Arrow Statement: “I start on the side with the arrow. The arrow is on the right side.”

2. Begin in the ones column below the arrow.

3. Locate the top number and say its name: “Seven.”

4. Count backward on the TouchPoints of the bottom numeral: “Six, five, four, three.”

5. Record the answer in the ones column: 3.

6. Repeat steps 3–5 for the tens column, and record the answer in the tens column: 4.

7. Reinforce the ability to read and recognize large numbers by repeating the problem and answer aloud.

Example

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Subtraction


Subtraction With RegroupingTouchMath Subtraction With Regrouping incorporates all prior subtraction steps and introduces the visual cue of the line segment. The line segment is used to hold the reduced number in the tens column.

1. Teach subtraction with regrouping using the regrouping bar. Write the new number of tens on the bar after regrouping.

2. Teach the Subtraction Regrouping Statement: “If I cannot count all of the TouchPoints, I must regroup.”

3. Count backward in the ones column from 3: “2, 1, 0.” Students will discover they cannot count all the TouchPoints on the 6.

4. Regroup, or borrow, one ten from the tens column. Cross out the top number in the tens column, 8, and write the regrouped number, 7, on the bar.

5. Write the regrouped ten in front of the 3 in the ones column, making it as large as the 3. Then count backward from the regrouped number, 13: “12, 11, 10, 9, 8, 7.”


7. Subtract the tens column: “7, 6, 5, 4.”


9. Repeat the problem and answer aloud.*

* This step reinforces the ability to read and recognize large numbers.

Example

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71

2


Skip Counting Skip Counting Patterns


2s Sequence

3s Sequence

4s Sequence

5s Sequence

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510

15

5

10

15

20

510

1520

25

5,10

15,20

25,30

5,10

15,20

25,30

355,10 15,20

25,30 35,40

5,1015,20

25,30

35,40

45

44

8

48

12

4

8

12

16

48

1216

20

4,8

12,16

20,24

4,8

12,16

20,24

284,8 12,16

20,24 28,32

4,812,16

20,24

28,32

36

33

6

36

9

3

6

9

12

36

912

15

3,6

9,12

15,18

3,6

9,12

15,18

213,6 9,12

15,18 21,24

3,69,12

15,18

21,24

27

22

4

24

6

2

4

6

8

4

68

10

2,4

6,8

10,12

2,4

6,8

10,12

142,4 6,8

10,12 14,16

2,46,8

10,12

14,16

18


Skip Counting Skip Counting Patterns


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66

12

612

18

6

12

18

24

612

1824

30

6,12

18,24

30,36

6,12

18,24

30,36

426,12 18,24

42,48

6,1218,24

30,36

42,48

54

6s Sequence

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77

14

714

21

7

14

21

28

714

2128

35

7,14

21,28

35,42

7,14

21,28

35,42

497,14 21,28

35,42

30,36

49,56

7,1421,28

35,42

49,56

63

7s Sequence

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88

16

816

24

8

16

24

32

816

2432

40

8,16

24,32

40,48

8,16

24,32

40,48

568,16 24,32

40,48 56,64

8,1624,32

40,48

56,64

72

! @ # $ % ̂ & * (

99

18

918

27

9

18

27

36

918

2736

45

9,18

27,36

45,54

9,18

27,36

45,54

639,18 27,36

45,54 63,72

9,1827,36

45,54

63,72

81

9s Sequence

8s Sequence


Skip Counting


Skip Counting ActivitiesThe paper-and-pencil activities sheets for skip counting in the TouchMath Upper Grades Program will teach the skip counting patterns for each number sequence 2 through 9.

Total body movement and oral practice (saying the number sequences aloud) are powerful reinforcements for students mastering any new skill, and this definitely applies to skip counting. This kind of practice is frequently necessary in helping tactile/kinesthetic learners succeed. Numerous multisensory activities are discussed in this guide to help all students master each counting pattern.

There are two important ideas to keep in mind and share with your students before you teach the number sequences: There are only ten numbers in each sequence (for example, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20). It is important for students to understand this in order to keep them from feeling overwhelmed.

When counting by twos, students are saying every second number; by threes, they are saying every third number; by fours, they are saying every fourth number, etc. This helps them when working with a hundred chart or a number line. When introducing a sequence, provide students with a copy of a hundred chart (available in the skip counting activity sheet sets) and have them highlight the number sequence. If you have students highlight each sequence to 100, they can easily see the number patterns.

If the TouchMath Skip Counting Poster and CD Set is available, it will help students master skip counting through visual cues and music. Since pictures and sound are two of the most efficient ways to help students recall information, these should be used as frequently as possible. Have students master each sequence before moving to the next sequence.

The group games that follow can involve groups of any size and may be adapted to available time periods. These games are only a sample. Many other classroom games may be adapted to skip counting.

Beanbag TossStudents stand in a circle. The student holding the beanbag calls out the series to be counted, for instance, “3s”. The bean bag is then randomly tossed from student to student while each student says the next number in the sequence. If a student misses, the sequence begins again. Play continues until the sequence is correctly completed 2–3 times.

Sequence RaceDivide the class into two or three lines at the board. Call out the sequence. The first person in each line goes to the board, writes the first number in the sequence, passes the chalk to the next person and walks to the end of the line. This continues through the sequence. The first group to write the sequence correctly three times wins the race.

Sequence CircleOn large cards, write each number in the desired sequence using one number per card (4, 8, 12, 16 ...). Include in the set some numbers that are NOT in the sequence so that each student has a card. Students stand in a circle holding their cards face out. In turn, each student with a correct card steps forward one step, saying the number aloud. After the sequence is completed, students exchange cards and repeat the activity.

Classroom RoutinesStudents can be asked to skip count on their way in/out of the door to lunch or a bathroom break. Ask the students to count an entire sequence by themselves or in pairs, or have them give just one number of the sequence in order to exit the classroom. An error results in the student going to the end of the line and trying again.

KaraokeIf the TouchMath Skip Counting Poster and CD Set is available, ask for a volunteer who thinks she might be able to sing the targeted song without looking at the TouchMath Skip Counting Poster. Have the student choose a friend to sing with, or sing the sequences as a small group.


Multiplication


Beginning MultiplicationBe certain that students are very adept at skip counting because it is the foundational skill in multiplication. Memorizing basic facts will be facilitated by emphasizing the auditory channel, so ask students to repeat the problems aloud that deal with the facts. Provide additional fact mastery practice using TouchMath flashcards.

1. Teach the Multiplication Statement: “I skip count by one number while touching the TouchPoints on the other numeral.”

2. Skip count by 4 while touching the TouchPoints on the numeral 6: “Four, eight, twelve, sixteen, twenty, twenty-four.”


4. Reinforce facts by repeating the problem and answer aloud: “Four times six equals twenty-four.”

5. Multiplication problems without TouchPoints allow students to respond to a multiplication problem in different ways. Students may remember the fact and not use the TouchMath strategy; or, they may count by the number of their choice on the other numeral. Often students will learn to “touch” the points visually in order to figure out a product.

Example

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12,164,8

20,24


Division


Beginning DivisionThis section reviews the steps in beginning TouchMath division. Students should be able to skip count before beginning division.

1. Teach the Division Statement: “I skip count by the divisor and get as close to the dividend as possible without going over the dividend.”

2. In Example A, skip count by 2, and get as close to the 8 as possible without going over 8.

3. Count: “Two, four, six, eight.” As each number in the sequence is counted, make a tally mark in the box: //// . The number of tally marks equals the answer (quotient).

4. Count the tally marks, and record the answer (quotient): 4.

5. Repeat the problem and answer aloud: “Eight divided by two equals four.”

6. When double-digit dividends for the facts are introduced, demonstrate the division process with a placeholder. In Example B, record the 0 as a placeholder since 1 can’t be divided by 3.

7. Skip count by the divisor and get as close to the dividend as you can without going over the dividend: “Three, six, nine, twelve, fifteen, eighteen.”

8. As each number in the sequence is counted, make a tally mark in the box: //// / . The number of tally marks equals the quotient.

9. Count the tally marks and record the quotient: 6.

10. Repeat the problem and the answer aloud: “Eighteen divided by three equals six.”

Example A Example B

Division With Remainders1. Teach the Division with Remainders Statement: “I skip count by the divisor and get as close to the dividend

as possible without going over the dividend. Then I continue counting by one up to the dividend.”

2. Skip count by 3.

3. As each number is counted, make a tally mark in the box. Come as close to 23 as you can without going over: “Three, 6, 9, 12, 15, 18, 21.”

4. To find the remainder, continue counting forward by ones. Put dots outside of the box for each number counted: “22, 23.”

5. Count the tally marks, and record the answer (quotient): 7. Count the dots. Record the remainder: 2.

Example

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hk hk

2ty 3ty \\8 \\\18 4 06

//// /////

hk

hk

3ty \\ 23 7r2

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Pret

est

Skills

Post

test

Activity Sheets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Student Name Comments

TouchMath Progress Monitoring RecordSecondary Summer School Program


Overview

TouchMath Assessment/Progress Monitoring

Review. Assess. Record.Regular assessment of specifi c skills is essential to ensure student success. Th ese assessments should occur upon completion of work on a particular skill, and the results should be used for reteaching and remediation.

Each level includes a pretest and a posttest, which are to be used for student placement and as an indication of skill profi ciency. Th ey may also be used as a tool to direct future planning by enhancing data-driven decision making and identifying needs for diff erentiated instruction.

A Progress Monitoring Record is also included in the TouchMath Upper Grades Program. Th e top of the sheet can be used to identify each skill and the activity sheet on which it is taught, and space is provided for teacher notations. Teachers may use any appropriate record keeping method they wish (e.g., check marks, diff erent colors for completed or needs help, letter grades, etc.). When used eff ectively, these monitoring records provide an ongoing snapshot of each student’s progress and are very helpful for conferences with the parent/guardian.

Write in topics for each activity sheet for easy reference and progress monitoring.

There is room to record individual student name, track lesson completion, and make notes on progress.

Skills can be clearly defi ned.

Pretest

Skill

s

Posttest

Act

ivity

She

ets

12

34

56

78

910

1112

1314

1516

1718

1920

2122

2324

25

Stud

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Reco

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UPPE R G R ADE S GUIDE IMPLEMENTATION€¦ · • Skip Counting by 5s 10 • Skip Counting by 6s 10 • Skip Counting by 7s 10 • Skip Counting by 8s 10 • Skip Counting by 9s 10

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