We Didn't Learn Math This Way! Samples

Peggy Golden & Tricia Salerno

ARE YOU STRUGGLING TO HELP YOUR KID WITH MATH HOMEWORK?

WE CAN HELP! In the past, we were rewarded for correct answers in math class. Today, correct answers are still the goal, but students are also asked to understand the why behind correct answers. This book is a multi-year guide to common yet confounding math topics that will give you the knowledge you need to be helpful on your student’s math journey. You don’t need to be a “math person” to help your kids excel.

No matter how you factor it, this product will help you exponentially. (This is funny! If you don’t get the joke, we’re happy you’re here.)

Our Team Peggy Golden and Tricia Salerno have been writing math curricula since the invention of zero. They are well versed in Singapore math strategies, Common Core State Standards, and everything you wish you knew about math.

Illustrations by Emma Tipping

WE DIDN’T LEARN

MATH THIS WAY!

Emma Tipping spent her early years annoying teachers by doodling on her math lessons. Now, after illustrating this book, she can finally help her kids with their math homework.

A K-5 GUIDE FOR THE CONFUSED ADULT

Published by Singapore Math Inc. 19535 SW 129th Avenue Tualatin, OR 97062 www.singaporemath.com We Didn’t Learn Math This Way! A K–5 Guide for the Confused Adult ISBN 978-1-947226-87-6 First published 2023 Copyright © 2022 by Singapore Math Inc. All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the publisher.

Printed in China

CONTENTS Introduction

2

Number Bonds

7

Manipulatives

15

Basic Facts

31

Mental Math Strategies

39

Addition

41

Subtraction

50

Multiplication

58

Division

63

Unit Form

67

Algorithms

75

Addition

77

Subtraction

83

Multiplication

88

Division

103

Story Problems

117

Addition and Subtraction

119

Multiplication and Division

129

Two Interpretations of Division

139

Fractions

147

Equivalency

153

Addition

162

Subtraction

169

Multiplication

175

Division

187

Glossary

199 1

WELCOME! We’re happy you’ve chosen to use this book. We, the Dream Team, have been working with students, teachers, parents and school administrators for over 20 years, helping them develop their understanding of math.

When the Common Core State Standards were introduced, we noticed that many adults in our country found them confusing. Shortly thereafter we had a dream to write a book that helps adults in their understanding of math so that they could help their children and students.

HOW TO USE THIS BOOK This book contains two sections: math topics and an illustrated glossary. The first section includes nine major topics that we noticed were challenging for many adults. Each topic is color-coded for ease of reference. You can read the topics in any order.

The second section is the Glossary. All words in bold are defined in the Glossary. The Glossary includes a graphic of each term to illustrate its meaning.

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W E DIDN’T LEARN MATH THIS WAY! A K-5 GUIDE FOR THE CONFUSED ADULT

ASIDES Each topic in this book contains at least one aside. is an acronym for “What the Math?!” WTM?! asides contain interesting math ideas with which you may not be familiar. Often, they compare the way many adults were taught math in the U.S. to the way students are learning math today.

Notes from the Dream Team are ideas that we point out when we work with adults.

Notes from a Confused Parent are from our illustrator, Emma Tipping, a math-confused mother of three who has learned all kinds of new skills and perspectives from working on this book.

Quiz Yourself asides suggest ways for you to deepen your own

understanding. We suggest that you pay close attention to the Quiz Yourself sections and take the quizzes without looking at the answers. This will help you when you are working with your young mathematicians.

specific concepts.

asides are included as suggestions for teaching

Progression Badges are included in some of the topics. These are

included to give you an idea of which grade level(s) certain topics and manipulatives are most commonly introduced and taught.

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OUR TEAM The members of the Dream Team are Peggy Golden and Tricia Salerno, who have dreamed of writing this book for many years.

Peggy Golden started her teaching career as an assistant in a Montessori Kindergarten. She went on to teach Kindergarten through eighth grade as a classroom and special education teacher. She later taught math methods at the university level, and she was a New York State Math Mentor. Peggy has contributed to Dimensions Math, EngageNY and Eureka Math as a writer. She continues to work in school settings across the country.

Tricia Salerno has taught math in preschool through eighth grade. In 2006, Tricia was invited to join a cohort of U.S. math teachers that traveled to Singapore to be trained in Singapore math methods. In 2007, Tricia founded SMARTTraining, a math education consulting company. She has contributed to EngageNY, Dimensions Math and Math Sprints as a writer and editor.

All the illustrations and math graphics were created by Emma Tipping. Emma has worked as a professional artist for over 15 years and specializes in creating art for kids and families. As a parent of three who is constantly confused by her kids’ math homework, Emma has loved learning how to help her kids in math while working on this project.

Thanks to our publisher, Singapore Math Inc., with a special nod to Echo Thomas; to our designer, Alison Manning Tasso; our editors, Ken Golden, Cassie Sciortino and Jenny Kempe; our creative consultant, Andy Gouveia; and our friend, Leslie Arceneaux.

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W E DIDN’T LEARN MATH THIS WAY! A K-5 GUIDE FOR THE CONFUSED ADULT

5

We introduce this strategy with single-digit addends, like 9 + 8, in first grade in preparation for using the strategy with multi-digit numbers and fractions in later grades. We call this strategy Make a 10 because the first step is to change one of the addends to 10.

9+8 How We Teach Children This Strategy Step 1

We have 9. How much more do we need to make 10? (1) We’ll take the 1 from 8.

Step 2

What is the other part of 8? (7)

Step 3

Add 10 and 7.

Eventually, the three steps become automatic, and are calculated mentally.

42

|

MENTAL MATH

|

ADDITION

MAKE THE NEXT GREATER UNIT: MAKE THE NEXT 10 As the numbers get larger, we change the name of the strategy. In second grade, students will add problems like 38 + 7 or 57 + 36. In these next two examples, we’re going to make one of the addends into the next 10.

38 + 7 How We Teach Children This Strategy Step 1

Starting with 38, what is the next ten? (40) How much do we need to make 40? (2)

Step 2

What is the other part of 7? (5)

Step 3

Add 40 and 5.

43

DIVIDING WHOLE NUMBERS Here are two ways of thinking about division.

6÷3 = 2 SHARING DIVISION

GROUPING DIVISION

Action

Dealing out

Repeated subtraction

Story

I have 6 marbles. I want to put them equally in 3 bags. How many will go in each bag?

I have 6 marbles. I want to put 3 in each bag. How many bags will I need?

3 groups of what number is 6?

How many groups of 3 in 6?

6÷3=2 2 marbles will go in each bag.

6÷3=2 I need 2 bags.

Problems

Drawings

Models

Clarifying Questions Answers

14 2

|

TWO INTERPRETATIONS OF DIV ISION

We act these problems out using manipulatives. The following describe what we do with the manipulatives. We’ve included a drawing to show the action.

Sharing Division This action looks like dealing cards. We start with 6 marbles.

We put 1 marble in each bag until there are no more marbles to distribute. To find the answer, we count how many marbles end up in 1 bag.

At the start, we know how many groups we have (3). The number of marbles in each group is unknown.

Grouping Division The action here is pulling out groups of 3. This action looks like repeated subtraction. We start out with 6 marbles. We make groups of 3 marbles, until there are no more. To find the answer, we count how many groups we are able to make.

At the start, we know how many marbles will be in each group. The number of groups is unknown.

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20 6

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GLOSSARY

linking cubes

cubes that click together; used for counting, adding and subtracting

manipulatives

items that students can hold in their hands to explore math concepts

mental math

math calculations done internally

minuend

the whole in a subtraction problem

mixed number

a number containing a whole number and a fraction

models

drawings that enhance understanding

multi-digit number

a number with more than one digit

multiple

numbers found when counting by a number