# RIGHTSTART MATHEMATICS

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1 Activities for Learning, Inc. RIGHTSTART MATHEMATICS by Joan A. Cotter, Ph.D. LEVEL B LESSONS FOR HOME EDUCATORS FIRST EDITION Copyright 2001

2 Special thanks to Sharalyn Colvin, who converted RightStart Mathematics: Grade 1 Lessons into RightStart Mathematics: Level B For Home Educators. Note: Rather than use the designation, K-4, to indicate a grade, levels are used. Level A is kindergarten, Level B is first grade, and so forth. Copyright 2001 by Activities for Learning, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission of Activities for Learning, Inc. The publisher hereby grants permission to reproduce the appendix and practice sheets for a single family s use only. Printed in the United States of America For more information: Supplies may be ordered from: Activities for Learning PO Box Hill Street Hazelton ND or fax ISBN August 2014

6 iii 13. The role of the teacher is to encourage thinking by asking questions, not giving answers. Once you give an answer, thinking usually stops. 14. Putting thoughts into words helps the learning process. 15. Help the children realize that it is their responsibility to ask questions when they do not understand. Do not settle for I don t get it. 16. The difference between a novice and an expert is that an expert catches errors much more quickly. A violinist adjusts pitch so quickly that the audience does not hear it. 17. Europeans and Asians believe learning occurs not because of ability, but primarily because of effort. In the ability model of learning, errors are a sign of failure. In the effort model, errors are natural. In Japanese classrooms, the teachers discuss errors with the whole class. 18. For teaching vocabulary, be sure either the word or the concept is known. For example, if a child is familiar with six-sided figures, we can give him the word, hexagon. Or, if he has heard the word, multiply, we can tell him what it means. It is difficult to learn a new concept and the term simultaneously. 19. Introduce new concepts globally before details. This lets the children know where they are headed. 20. Informal mathematics should precede paper and pencil work. Long before a child learns how to add fractions with unlike denominators, she should be able to add one half and one fourth mentally. 21. Some pairs of concepts are easier to remember if one of them is thought of as dominant. Then the non-dominant concept is simply the other one. For example, if even is dominant over odd; an odd number is one that is not even. 22. Worksheets should also make the child think. Therefore, they should not be a large collection of similar exercises, but should present a variety. In RightStart Mathematics, they are designed to be done independently. 23. Keep math time enjoyable. We store our emotional state along with what we have learned. A person who dislikes math will avoid it and a child under stress stops learning. If a lesson is too hard, stop and play a game. Try the lesson again later. 24. In Japan students spend more time on fewer problems. Teachers do not concern themselves with attention spans as is done in the U.S. 25. In Japan the goal of the math lesson is that the student has understood a concept, not necessarily has done something (a worksheet). 26. The calendar must show the entire month, so the children can plan ahead. The days passed can be crossed out or the current day circled. 27. A real mathematical problem is one in which the procedures to find the answer is not obvious. It is like a puzzle, needing trial and error. Emphasize the satisfaction of solving problems and like puzzles, of not giving away the solution to others. Activities for Learning, Inc. 2015

7 iv RightStart Mathematics Ten major characteristics make this research-based program effective: 1. Refers to quantities of up to 5 as a group; discourages counting individually. Uses fingers and tally sticks to show quantities up to 10; teaches quantities 6 to 10 as 5 plus a quantity, for example 6 = Avoids counting procedures for finding sums and remainders. Teaches five- and ten-based strategies for the facts that are both visual and visualizable. 3. Employs games, not flash cards, for practice. 4. Once quantities 1 to 10 are known, proceeds to 10 as a unit. Temporarily uses the math way of naming numbers; for example, 1 ten-1 (or ten-1 ) for eleven, 1-ten 2 for twelve, 2-ten for twenty, and 2-ten 5 for twenty-five. 5. Uses expanded notation (overlapping) place-value cards for recording tens and ones; the ones card is placed on the zero of the tens card. Encourages a child to read numbers starting at the left and not backward by starting at the ones. 6. Proceeds rapidly to hundreds and thousands using manipulatives and placevalue cards. Provides opportunities for trading between ones and tens, tens and hundreds, and hundreds and thousands with manipulatives. 7. Teaches mental computation. Investigates informal solutions, often through story problems, before learning procedures. 8. Teaches four-digit addition on the abacus, letting the child discover the paper and pencil algorithm. 9. Introduces fractions with a linear visual model, including all fractions from 1 2 to Pies are not used initially because they cannot show fractions greater than 1. Later, the tenths will become the basis for decimals. 10. Teaches short division (where only the answer is written down) for single-digit divisors, before long division. Second Edition Many changes have occurred since the first RightStart lessons were begun in First, mathematics is used more widely in many fields, for example, architecture, science, technology, and medicine. Today, many careers require math beyond basic arithmetic. Second, research has given us new insights into how children learn mathematics. Third, kindergarten has become much more academic, and fourth, most children are tested to ensure their preparedness for the next step. This second edition is updated to reflect new research and applications. Topics within a grade level are always taught with the most appropriate method using the best approach with the child and teacher in mind. Activities for Learning, Inc. 2015

8 v Daily Lessons Objectives. The objectives outline the purpose and goal of the lesson. Some possibilities are to introduce, to build, to learn a term, to practice, or to review. Materials. The Math Set of manipulatives includes the specially crafted items needed to teach RightStart Mathematics. Occasionally, common objects such as scissors will be needed. These items are indicated by boldface type. Warm-up. The warm-up time is the time for quick review, memory work, and sometimes an introduction to the day s topics. The dry erase board makes an ideal slate for quick responses. Activities. The Activities for Teaching section is the heart of the lesson; it starts on the left page and continues to the right page. These are the instructions for teaching the lesson. The expected answers from the child are given in square brackets. Establish with the children some indication when you want a quick response and when you want a more thoughtful response. Research shows that the quiet time for thoughtful response should be about three seconds. Avoid talking during this quiet time; resist the temptation to rephrase the question. This quiet time gives the slower child time to think and the quicker child time to think more deeply. Encourage the child to develop persistence and perseverance. Avoid giving hints or explanations too quickly. Children tend to stop thinking once they hear the answer. Explanations. Special background notes for the teacher are given in Explanations. Worksheets. The worksheets are designed to give the children a chance to think about and to practice the day s lesson. The children are to do them independently. Some lessons, especially in the early levels, have no worksheet. Games. Games, not worksheets or flash cards, provide practice. The games, found in the Math Card Games book, can be played as many times as necessary until proficiency or memorization takes place. They are as important to learning math as books are to reading. The Math Card Games book also includes extra games for the child needing more help, and some more challenging games for the advanced child. In conclusion. Each lesson ends with a short summary called, In conclusion, where the child answers a few short questions based on the day s learning. Number of lessons. Generally, each lesson is be done in one day and each manual, in one school year. Complete each manual before going on to the next level. Other than Level A, the first lesson in each level is an introductory test with references to review lessons if needed. Comments. We really want to hear how this program is working. Please let us know any improvements and suggestions that you may have. Joan A. Cotter, Ph.D. Activities for Learning, Inc. 2015

11 Level B page 3 Lesson 90 (5 days) Adding Four-Digit Numbers on the Abacus Lesson 91 (several days) Adding Four-Digit Numbers on Paper Lesson 92 The > and < Symbols Lesson 93 Introducing Subtraction Lesson 94 Subtraction as the Missing Addend Lesson 95 Making Change Lesson 96 More Making Change Activities Lesson 97 Introduction to Measuring Lesson 98 (2 days) Finding Perimeter Lesson 99 (2 days) Finding Rectangles with a Given Perimeter & Diagonals Lesson 100 Measuring Long Distances & Estimating Lesson 101 Constructing Triangles & Finding Perimeters Lesson 102 (2 days) Subtracting by Going Back Lesson 103 Reading Scales Lesson 104 Time to the Minute Lesson 105 Halves and Fourths Lesson 106 (1 or 2 days) Graphing Lesson 107 Final Test Practice Record & Practice Sheets Tests Appendix B: Joan A. Cotter 2001

15 151 EXTRA HELP Using a hundred square may help the child. For example, to add , first locate the 35. Next to add 20, move down two columns to 55; lastly, to add 3, move to the right three spaces. If the hundred chart is used, be certain that the child understands why it works Adding on a hundred chart by using the tens and the ones. Worksheet. Worksheet 29 gives the child practice in adding mentally, that is, without the abacus, although, you might want to ask him to check his work with it. The examples and problems are shown below = = = = = = = = = = = = = = = = 65 Practice sheets. The child should continue using the practice sheets until the facts are mastered. B: Joan A. Cotter 2001

16 To see the pattern, find your answers and mark the squares when your answer is less than B: Joan A. Cotter 2001 Name Worksheet 29, Mentally Adding 2-Digit Numbers

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