The Verbal Math Lesson Book 2: Step-by-Step Math Without Pencil or Paper

204 Pages·2014·0.814 MB·English

by  Michael Levin MD, Charan Langton MS

2
the
verbal
math
lesson
LEVEL 2
FOR CHILDREN AGES 6 TO 9
MICHAEL LEVIN
CHARAN LANGTON
Copyright 2008 Mountcastle Company First Print Edition February 2008
First Electronic Edition June 2011 Second Print Edition April 2014
Edited by Kelsey Negherbon, Ashley Kuhre and Julie Lundy
Design by Tijana Mihajlović
Manufactured in the United States of America
ISBN 978-0-913063-28-6
All Rights Reserved. No part of this book may be reproduced or utilized in any form
or by any means, electronic passages, posting, mechanical including photocopying
and recording on any storage device and retrieval system without the written
permission of the publisher.
www.mathlesson.com
This eBook: July 2020
The Verbal Math Lesson 2 ▶ Page i
When a ball
Bounces off of a wall,
When you cook From a recipe book,
When you know
How much money you owe, That’s mathematics!
When you choose
How much postage to use, When you know
What’s the chance it will snow, When you bet
And you end up in debt, Oh try as you may,
You just can’t get away From mathematics!
- That’s Mathematics!
TOM LEHRER
INTRODUCTION
Verbal math, also called mental math, is
a practical and time-honored method of 2
solving mathematical problems without
the
resorting to pencil and paper. Math with verbal
math
worksheets can be tedious for young
lesson
children and often slows them down.
Bypassing hand writing speeds under-
standing and ability to do math. Short-cuts
and computational tricks learned with mental math also allow
children to advance faster to higher levels.
In this book, we teach addition and subtraction up to one-hundred
and introduce basic multiplication and division. Each lesson starts
with a new concept and exercises. The word problems teach practi-
cal application of the new concept. Some concepts are not obvious
or intuitive at first, and your child might find them confusing. Don't
dwell on them. Instead, move on and watch how working on prob-
lems make concepts easier to understand when you go over them the
second time. The problems use simple language and foster imagina-
tion; they vary within each lesson to keep your child on his or her
"mental toes."
We strongly encourage the child to memorize the multiplication and
corresponding division tables. In our experience, a big hurdle for stu-
dents studying times tables at this point is learning the multiples of 3
and 4. The Verbal Math book devotes extra time to these.
We teach a somewhat different sequence of math operations than
those used in schoolwork. In Verbal Math Book 1, we introduced
addition along with subtraction. In Book 2, we teach multiplica-
tion together with division to demonstrate the reversibility of both
processes. Most of the time, manipulatives and pictures are not neces-
sary. However, from time to time, you may need to illustrate a point
by using objects or images. The decision to use these aides is left to
the parent.
Many word problems in the Verbal Math Lesson books come with
solutions. These solutions are important if your child is having dif-
ficulty solving problems. They help thinking through new or harder
The Verbal Math Lesson 2 ▶ Page iii
problems and serve as a model for similar problems later in the
course.
As in all Verbal Math Lesson books, no paper or pencil is needed. All
problems are to be read to your child and solved mentally (verbally.)
Please, do not hand the book to your child. The Verbal Math is written
for the parents or teachers. It has answers, because, as you know,
adults must keep up with kids at math!
The Verbal Math Lesson is a fun activity, not intended to replace
schoolwork or a more comprehensive math program. Create a sched-
ule of about 10-15 minutes daily and try to solve several problems at
a time, as time permits; do more if your child can handle it.
There are twenty-nine lessons in this book. Some children can do
a lesson quickly, in 3 or 4 days. For others, it might take longer.
Sometimes, repeating the lesson may be necessary before moving
forward. Please make sure that your child understands the concept
and can do all problems correctly and speedily before starting the next
lesson.
We suggest age groups for the books; however, these are just guide-
lines. You know your child better than anyone else. Trust your
parental judgment and go at the speed you feel is right and your
child's skills allow.
Please share your comments and tell us about your experience with
the Verbal Math series. We welcome suggestions for improvement
and corrections.
Michael Levin and Charan Langton
www.mathlesson.com
The Verbal Math Lesson 2 ▶ Page iv
Lessons
1. Operations with 2-Digit Numbers ...............................................................vii
2. Adding Single-Digit Numbers to Double-Digit Numbers ..........................7
3. Subtracting Single-Digit Numbers from Double-Digit Numbers .............15
4. Adding Double-Digit Numbers Ending in 1 or 2 ........................................23
5. Subtracting Double-Digit Numbers Ending in 1 or 2.................................30
6. Adding Numbers Ending in 3 or 4 ...............................................................37
7. Subtracting Numbers Ending in 3 or 4 ........................................................43
8. Adding and Subtracting Numbers Ending in 9 ...........................................48
9. More Adding and Subtracting .......................................................................54
10. Adding Double-Digit Numbers Ending in 5 or 6 ........................................60
11. Subtracting Double-Digit Numbers Ending in 5 or 6.................................67
12. Adding Double-Digit Numbers Ending in 7 or 8 ........................................74
13. Subtracting Double-Digit Numbers Ending in 7 or 8.................................80
14. Adding Two Double-Digit Numbers up to 100 ...........................................87
15. Doubling and Tripling Double-Digit Numbers ...........................................95
16. Subtracting Double-Digit Numbers from Numbers up to 100 .................101
17. Subtracting Double-Digit Numbers .............................................................108
18. Starting Multiplications ................................................................................114
19. Multiplication by 2 and 3 ..............................................................................122
20. Introduction to Division ................................................................................129
21. Division by 2 or 3 ...........................................................................................137
22. Multiplication and Division by 2, 3, or 4 .....................................................145
23. Mixed Operations with 2, 3, or 4 .................................................................153
24. Multiplication and Division by 3 or 4 ..........................................................160
25. Multiplication and Division by 5 or 10 ........................................................166
26. Multiplication and Division by 6 ..................................................................172
27. Multiplication and Division by 7 ..................................................................179
28. Multiplication and Division by 8 ..................................................................185
29. Multiplication and Division by 9 ..................................................................191
The Verbal Math Lesson 2 ▶ Page v

1
Operations with 2-Digit Numbers
PLACE VALUE
Place value is the place of a digit in a number. In number 62, for
example, 6 is in the tens place. This is the second place counting from
the right side of the number. It means we have six 10s in this number.
And 2 is in the ones place, which is the rightmost place of the number.
This means this number has 2 ones. If we write this out, the number 62
is the sum of six 10s and two 1s.
62 = 10 + 10 + 10 + 10 + 10 + 10 + 1 + 1
In a three-digit number, like 108, there is 1 in hundreds place, zero in
tens, and 8 in ones place. So, we can say that 108 is the sum of one
100s, zero tens, and eight ones.

108 = 100 + 0 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
Tell me:
• In the number 29, in what place is 9? Ans: In the ones place.
• In the number 30, in what place is 0? Ans: In the ones place.
• In the number 81, in what place is 8? Ans: In the tens place.
• In the number 50, in what place is 5? Ans: In the tens place.
• In the number 109, in what place is 9? Ans: In the ones place.
• In the number 234, in what place is 3? Ans: In the tens place.
• In the number 234, in what place is 2? Ans: In the hundreds place.
The Verbal Math Lesson 2 ▶ Page vii
• In the number 100, in what place is 1? Ans: In the hundreds place.
• In the number 341, in what place is 1? Ans: In the ones place.
• In the number 341, in what place is 4? Ans: In the tens place.
Complements (not to confuse with compliment, which are words of a
praise or admiration, like "you are so good at math and sing well too):
A complement is a number that makes a mathematical group com-
plete. Here are the pairs of one-digit numbers, which, when added
together, make 10.
1 + 9 = 10 3 + 7 = 10 5 + 5 = 10
2 + 8 = 10 4 + 6 = 10 0 + 10 = 10

EXERCISE I
25 + 25 = 50 30 + 45 = 75 22 + 30 = 52 33 + 11 = 44
40 + 17 = 57 19 + 11 = 30 40 + 50 = 90 30 + 29 = 59
45 + 15 = 60 11 + 32 = 43 33 + 66 = 99 30 + 50 = 80
46 + 24 = 70 22 + 33 = 55 32 + 23 = 55 34 + 26 = 60
25 + 35 = 60 12 + 27 = 39 34 + 36 = 70 53 + 36 = 89
EXERCISE II
25 - 11 = 14 67 - 27 = 40 65 - 45 = 20 55 - 34 = 21
20 - 7 = 13 40 - 11 = 29 45 - 13 = 32 47 - 30 = 17
20 - 8 = 12 50 - 30 = 20 35 - 25 = 10 57 - 15 = 42
30 - 14 = 16 70 - 40 = 30 75 - 24 = 51 66 - 15 = 51
40 - 20 = 20 45 - 25 = 20 45 - 25 = 20 57 - 16 = 41
50 - 20 = 30 55 - 35 = 20 48 - 35 = 13 45 - 21 = 24
The Verbal Math Lesson 2 ▶ Page 1
WORD PROBLEMS
1. A redwood tree is 80 feet tall, and a fir tree is 60 feet. How much
taller is the redwood than the fir tree? Ans: 20 feet.
2. A redwood tree is 80 feet tall, and a birch is 30 feet. How much
taller is the redwood than the birch tree? Ans: 50 feet.
3. If a birch is 40 feet tall and a fir tree is 30 feet, what will be their
height together? Ans: 70 feet.
4. A redwood is 90 years old, and a fir tree is 60. By how much the
redwood is older than the fir tree? Ans: 30 years.
5. Nancy paid $40 for groceries and has $60 left. How much did she
have before buying the groceries? Ans: $100.
6. Mina paid $40 for the new coat with a $50 bill. How much did
she get in change? Ans: $10.
7. A carpenter's box had 100 nails. He used 20 nails on the first
day and 30 the next day. How many nails are left in the box?
Ans: 50 nails (100 - 20 = 80; then, 80 - 30 = 50).
8. A plumber connected three 20-foot pipes, then cut 10 feet from
the newly made pipe. How long is the pipe now? Ans: 50 feet
(20 + 20 + 20 = 60; then, 60 - 10 = 50).
9. An electrician spliced (joined together) a 30-foot wire and a
50-foot wire. How long is the new wire? Ans: 80 feet.
10. A roofer used 40 shingles on one side of the roof and 60 on the
other. How many shingles did he use? Ans: 100 shingles.
11. A cable installer used 70 feet of cable from the street to the house
and another 30 feet inside the house. How much cable did he use?
Ans: 100 feet.
12. A butcher wrapped 20 ounces of beef and 70 ounces of lamb.
How much meat did he wrap? Ans: 90 ounces.
13. A baker baked 50 cakes and 50 pies. How many cakes and pies
did she bake? Ans: 100 cakes and pies.
The Verbal Math Lesson 2 ▶ Page 2
14. A cook pickled 40 cucumbers and 40 tomatoes. How many
veggies did he pickle? Ans: 80 veggies.
15. Robert brought two checks to the bank, one for $30 and the
other for $50. How much were both checks? Ans: $80.
16. A famous writer received 90 letters and wrote back 40. How
many letters are waiting for his reply? Ans: 50 letters.
17. An absent-minded professor bought 40 pairs of glasses. He lost
20 pairs and broke 10. How many pairs of glasses are left for him
to break or lose? Ans: 10 pairs of glasses.
Solution: 40 (pairs he bought) - 20 (he lost) = 20 (pairs not lost);
then, 20 - 10 (broken) = 10 (pairs left). Another way to solve this
problem: 20 (lost) + 10 (broken) = 30 (lost and broken), then
40 (total) - 30 = 10 (pairs left).
18. There are 30 students on the tennis team and 40 on the wrestling
team. How many students are on both teams? Ans: 70 students.
a) How many more students are on the wrestling team than on
the tennis team? Ans: 10 more students.
19. The city hall building is 70 years old; the concert hall is 30 years
old, and the school is 20 years old.
a) By how much the city hall is older than the concert hall?
Ans: by 40 years.
b) By how much the city hall is older than the school? Ans: by
50 years.
c) By how much the concert hall is older than the school?
Ans: by 10 years.
20. Mr. Handel can handle 30 candles. Mrs. Handel can handle
40 candles. How many candles the two Handels can handle?
Ans: 70 candles.
21. There are 60 students, 20 teachers, and 10 custodians in a village
school. How many people are in the school? Ans: 90 people
(60 + 20 = 80 and 80 + 10 = 90).
a) How many students and teachers are in the school?
Ans: 80 students and teachers.
b) How many more students than teachers are in the school?
Ans: 40 more students.
The Verbal Math Lesson 2 ▶ Page 3