grade 1 math volume 2 en

Brain-Inspired Math

Grade 1, Volume 2

A new technique for teaching mathematics

and boosting a child's math skills.

Margery J. Doyle Cognitive Systems Scientist and Engineer

Cognitive Architects and Engineers

Dr. Ahmed A. Moustafa

Senior Lecturer in Cognitive and Behavioral Neuroscience,

University of Western Sydney

Dr. Mustafa Fouad Ebaid

Math Curriculum Development Adviser

Mohamed Ibrahim Khadr

Math Curriculum Developer

distributed, or transmitted in any form or by any means, including

photocopying, recording, or other electronic or mechanical methods,

without the prior written permission from Alpha Smart Brain.

978-0-9963035-7-6

Introduction

There are two different systems for learning and solving

mathematical problems, the visual-spatial and the formal

language systems. Precisely because, the visual-spatial

system responds so well to moving stimuli, it helps us

recognize large animals moving across open areas so this

system evolved earlier than did our formal language

system. This is also why, to this day, it is thought that the

visual-spatial system matures faster during the child’s

development than does the formal language system.

In addition, the spatial method of learning, which relies on

forming mental models and images to understand

mathematics, is similar to the type we use in our everyday

interactions with the world; rendering this method a more

intuitive way to learn math. However, our formal language

system is slower, and more difficult to use, but as it

matures, it enables the learning of more complex math

problems.

We argue that, for children, learning mathematics is more

efficient when it relies, more on the visual-spatial system

rather than on an immature formal language system in

the brain. In fact, relying heavily on the formal language

system can cause mathematics anxiety when learning

mathematics, which in turn, decrease a student's ability to

learn mathematics effectively.

Mathematics anxiety has been defined as feelings of tension

that interfere with the manipulation of numbers and the

solving of mathematical problems in a wide variety of

ordinary life and academic situations. In addition,

dyscalculia is but one disorder thought to impede on a

child's ability to learn mathematics and to manipulate

symbols when working on math problems. Math anxiety can

increase the effects of these disorders and can cause

children to forget what they learn, often leading to a loss in

self-confidence. However, anxiety is but one factor

underlying inefficient learning of mathematics in schools

around the world the other is the way in which mathematics

is taught to young children.

The problem is most mathematics curricula teach the

subject matter using mostly formal language, making the

process inversely beneficial for children training to learn

mathematics at such a young age, when their formal

language systems have yet to mature.

The Authors

Margery J. Doyle Margery is a founder or at Cognitive

System Architects and Engineer Research Consultant and

serves at AFRL WPAFB, OH as a Cognitive Systems

Research Scientist and Engineer with L3 Communications

Link Simulation and Training supporting the Air Force

Research Lab 711 HPW/RHA Warfighter Readiness Research

Division at Wright-Patterson Air Force Base, OH. Margery

leads the Not-So-Grand-Challenge to support integration,

validation, and use of cognitive, behavior, and

computationally based models/agents within a modular

architecture for use in Live Virtual Constructive Distributed

Mission Operations training environments.

She earned her M.A. in Experimental Psychology with a

certificate in Cognitive Psychology from the University of

West Florida in 2007.

In addition, Margery completed the research and study

toward completion of a PhD in Cognitive Science at the

University of Louisiana-Lafayette Recently she co-edited a

special edition of Cognitive Systems Research focusing on

the properties of distributed agency, stigmergy, and

emergence in complex adaptive systems.

Dr. Ahmed A. Moustafa, PhD.

Ahmed is currently a Senior Lecturer (Associate Professor)

in Cognitive and Behavioural Neuroscience at Marcs

Institute for Brain and Behavior and the School of Social

Sciences and Psychology, University of Western Sydney.

Ahmed graduated from Cairo University in Egypt with an

undergraduate degree in mathematics and computer

science. After that, Ahmed received his PhD from the

Institute of Cognitive Science, University of Louisiana-

Lafayette. His PhD work consisted of building computational

models of brain functions and disorders. Ahmed then took a

postdoctoral research position at University of Arizona.

Following that, Ahmed served as a Research Scientist for

the Center for Molecular and Behavioral Neuroscience at

Rutgers University where he worked on computational and

neuropsychological studies of schizophrenia, Parkinson’s

disease, PTSD, and Depression.

To his credit, Ahmed has published over 50 papers in high-

ranking journals including Science, Proceedings of the

National Academy of Science, Brain, Journal of

Neuroscience, among others. Currently, Ahmed works on

Computational and Experimental Neuroscience research,

focusing on modeling brain disorders.

Dr. Mustafa Fouad Ebaid

Math Curriculum Development Adviser

Mohamed Ibrahim Khadr

Math curriculum Developer

What we think is wrong with the current mathematics

education system in elementary schools in the United

States?

1- The current mathematics education system in elementary

schools in the United States is relying heavily on the use of

formal language.

2- The current mathematics curricula teach the subject

matter using mostly formal language, making the process

inversely beneficial for children training to learn

mathematics at such a young age, when their formal

language systems have yet to mature.

3- Relying heavily on the formal language system can cause

mathematics anxiety when learning mathematics, which in

turn, decrease a student's ability to learn mathematics

effectively.

How to easily teach math to first graders using brain-

inspired math curriculum?

1- Because visual-spatial capabilities are well-developed

and mature at a young age, a math curriculum in the form

of tables conveying the concepts allows the students an

opportunity to easily learn mathematical concepts.

2- Using the visual-spatial x y z system with first grade

students will help students to form abstract concepts and

master math so easily.

3- Using Brain Training software ( Alpha Smart Math

Booster ), to build strong mathematics processing

networks and processes in the student's brain.

4- Using Brain Training software should be done after the

student finishes studying Volume 1. The student should use

this software twice every week, every time about 15

minutes.

5- Explaining tables and mathematical concepts to the

students should be conducted by using informal language

and visual-spatial methods students more readily

understand.

6- Any formal language vocabulary used should be kept to

a minimum, and should be easy to understand.

7- Using concrete materials is very important for visualizing

the concepts to the students, so the students can visualize

the concept easily in their heads.

8- The teacher should avoid asking students difficult

questions, especially the questions that contain heavy

language. The difficult questions in that young age can

cause mathematics anxiety.

9- When the teacher explains a new mathematical concept

to the students, the teacher should explain the concept

using as few words as possible. After the students

understand the concept deeply, they should complete the

tables by themselves, this will help in storing information in

the brain effectively.

10- After building the mathematics area in the student's

brain, we introduce word problems in Volume 2.

11- Because formal language systems of first grade

students have yet to mature, so teachers should explain

word problems to students using informal language and

visual-spatial methods students more readily understand.

Table of Contents

Unit 1 .............................................. 1

Unit 2 .............................................. 21

Unit 3 .............................................. 33

Unit 4 .............................................. 38

Unit 5 .............................................. 46

Unit 6 .............................................. 51

Teacher's

Guide .............................................. 81

Volume 3

Contents .............................................. 83

Suggested Timeline

Volume 1 Volume 2 Volume 3

20 weeks 8 weeks 8 weeks

Note: Students should use Brain Training software

(Alpha Smart Math Booster) after finishing studying

Volume 1. The student should use this software twice every

week, every time about 15 minutes.

Lesson 1 Worksheet 1 Unit 1

x = 2 3 0 1 2 0 1 4 0 1

x = 3 5 0 1 4 0 1 3 0 1

x = 4 4 0 1 5 0 1 6 0 1

x = 5 7 0 1 6 0 1 5 0 1

x = 6 7 0 1 6 0 1 8 0 1

x = 7 7 0 1 8 0 1 9 0 1

x = 8 9 0 1 8 0 1 10 0 1

z = 7 + 1 1 0 7 1 0 8 1 0 9

z = 8 + 1 1 0 10 1 0 8 1 0 9

z = 9 + 1 1 0 10 1 0 9 1 0 11

z = 10 + 1 1 0 12 1 0 10 1 0 11

z = 11 + 1 1 0 11 1 0 12 1 0 13

z = 12 + 1 1 0 14 1 0 12 1 0 13

z = 13 + 1 1 0 14 1 0 13 1 0 15

x + y = z 7 1 9 7 1 8 7 1 10

x + y = z 8 1 11 8 1 10 8 1 9

x + y = z 9 1 11 9 1 10 9 1 12

x + y = z 10 1 11 10 1 12 10 1 13

x + y = z 11 1 14 11 1 13 11 1 12

x + y = z 12 1 14 12 1 13 12 1 15

x + y = z 13 1 14 13 1 15 13 1 16

y = 2 1 4 0 1 3 0 1 2 0

y = 3 1 3 0 1 4 0 1 5 0

y = 4 1 6 0 1 5 0 1 4 0

y = 5 1 6 0 1 5 0 1 7 0

y = 6 1 6 0 1 7 0 1 8 0

y = 7 1 9 0 1 8 0 1 7 0

y = 8 1 9 0 1 8 0 1 10 0

x - y = z 6 1 3 6 1 4 6 1 5

x - y = z 7 1 5 7 1 6 7 1 4

x - y = z 8 1 5 8 1 6 8 1 7

x - y = z 9 1 8 9 1 7 9 1 6

x - y = z 10 1 7 10 1 8 10 1 9

x - y = z 11 1 9 11 1 10 11 1 8

x - y = z 12 1 9 12 1 10 12 1 11

x = 3 + 2 4 0 1 5 0 1 3 0 1

x = 4 + 2 4 0 1 5 0 1 6 0 1

x = 5 + 2 7 0 1 6 0 1 5 0 1

x = 6 + 2 6 0 1 7 0 1 8 0 1

x = 7 + 2 8 0 1 9 0 1 7 0 1

x = 8 + 2 10 0 1 9 0 1 8 0 1

x = 9 + 2 10 0 1 11 0 1 9 0 1

z = 10 + 2 1 0 10 1 0 11 1 0 12

z = 11 + 2 1 0 12 1 0 13 1 0 11

z = 12 + 2 1 0 12 1 0 13 1 0 14

z = 13 + 2 1 0 15 1 0 14 1 0 13

z = 14 + 2 1 0 14 1 0 15 1 0 16

z = 15 + 2 1 0 16 1 0 17 1 0 15

z = 16 + 2 1 0 16 1 0 17 1 0 18

x + y = z 6 2 9 6 2 8 6 2 10

x + y = z 7 2 11 7 2 10 7 2 9

x + y = z 8 2 11 8 2 10 8 2 12

x + y = z 9 2 11 9 2 12 9 2 13

x + y = z 10 2 14 10 2 13 10 2 12

x + y = z 11 2 14 11 2 13 11 2 15

x + y = z 12 2 16 12 2 15 12 2 14

x - y = z 8 2 4 8 2 5 8 2 6

x - y = z 9 2 6 9 2 7 9 2 5

x - y = z 10 2 6 10 2 7 10 2 8

x - y = z 11 2 9 11 2 8 11 2 7

x - y = z 12 2 8 12 2 9 12 2 10

x - y = z 13 2 10 13 2 11 13 2 9

x - y = z 14 2 10 14 2 11 14 2 12

z = 11 + 10 1 0 22 1 0 21 1 0 23

z = 12 + 10 1 0 24 1 0 23 1 0 22

z = 13 + 10 1 0 23 1 0 24 1 0 25

z = 14 + 10 1 0 26 1 0 25 1 0 24

z = 15 + 10 1 0 25 1 0 26 1 0 27

z = 16 + 10 1 0 27 1 0 26 1 0 28

z = 17 + 10 1 0 29 1 0 28 1 0 27

x < 50 53 0 1 2 0 1 54 0 1

x < 50 55 0 1 56 0 1 3 0 1

x < 50 4 0 1 57 0 1 58 0 1

x < 50 60 0 1 59 0 1 5 0 1

x < 50 6 0 1 62 0 1 61 0 1

x < 50 64 0 1 63 0 1 7 0 1

x < 50 8 0 1 66 0 1 65 0 1

x > 50 12 0 1 11 0 1 60 0 1

x > 50 61 0 1 14 0 1 13 0 1

x > 50 15 0 1 16 0 1 62 0 1

x > 50 17 0 1 63 0 1 18 0 1

x > 50 19 0 1 20 0 1 64 0 1

x > 50 65 0 1 21 0 1 22 0 1

x > 50 24 0 1 66 0 1 23 0 1

x = y 2 3 0 2 2 0 2 4 0

x = y 3 5 0 3 4 0 3 3 0

x = y 4 5 0 4 4 0 4 6 0

x = y 5 7 0 5 6 0 5 5 0

x = y 6 6 0 6 7 0 6 8 0

x = y 7 8 0 7 7 0 7 9 0

x = y 8 10 0 8 9 0 8 8 0

x = z 5 0 7 5 0 6 5 0 5

x = z 6 0 7 6 0 6 6 0 8

x = z 7 0 9 7 0 8 7 0 7

x = z 8 0 8 8 0 9 8 0 10

x = z 9 0 11 9 0 10 9 0 9

x = z 10 0 11 10 0 10 10 0 12

x = z 11 0 11 11 0 12 11 0 13

x = 2 and y = 3 2 4 6 2 3 5 2 5 7

x = 3 and y = 4 3 6 8 3 5 7 3 4 6

x = 4 and y = 5 4 5 7 4 6 8 4 7 9

x = 5 and y = 6 5 8 10 5 7 9 5 6 8

x = 6 and y = 7 6 8 10 6 7 9 6 9 11

x = 7 and y = 8 7 8 10 7 9 11 7 10 12

x = 8 and y = 9 8 10 12 8 9 11 8 11 13

x = 6 and z = 8 6 0 10 6 0 9 6 0 8

x = 7 and z = 9 7 0 9 7 0 10 7 0 11

x = 8 and z = 10 8 0 11 8 0 10 8 0 12

x = 9 and z = 11 9 0 13 9 0 12 9 0 11

x = 10 and z = 12 10 0 12 10 0 13 10 0 14

x = 11 and z = 13 11 0 15 11 0 14 11 0 13

x = 12 and z = 14 12 0 15 12 0 14 12 0 16

x is an even number. 11 0 1 12 0 1 13 0 1

x is an odd number. 34 0 1 32 0 1 31 0 1

x is an odd number. 34 0 1 33 0 1 36 0 1

x is an odd number. 38 0 1 36 0 1 35 0 1

x is an odd number. 38 0 1 37 0 1 40 0 1

x is an odd number. 39 0 1 40 0 1 42 0 1

x is an odd number. 44 0 1 42 0 1 41 0 1

x is an odd number. 44 0 1 43 0 1 46 0 1

x, y, and z are even numbers. 11 13 15 12 14 16

x, y, and z are odd numbers. 32 34 36 31 33 35

The Next Number to 7 9 6 8

The Previous Number to 14 16 15 13

Number greater than 50 11 10 60

Number less than 50 52 51 11

12 ....... 22 > < =

23 ....... 13 = < >

14 ....... 14 = < >

15 ....... 25 > < =

16 ....... 26 = > <

27 ....... 17 > < =

18 ....... 28 = > <

The Largest Number 27 47 28

The Smallest Number 69 68 48

Number close to 10 23 13 33

The number has 3 ones. 25 24 23

Even Number 13 14 15

Odd Number 34 32 31

Odd Number 33 34 36

Odd Number 36 35 38

Odd Number 40 38 37

Odd Number 40 39 42

Odd Number 41 42 44

Odd Number 44 43 46

11 14 13 16

12 14 15 17

13 18 16 15

14 17 16 19

15 17 18 20

16 19 18 21

17 22 20 19

3 5 7 9 .... 13 12 11

4 6 8 10 .... 11 12 14

5 7 9 11 .... 13 14 15

6 8 10 12 .... 13 14 16

7 9 11 13 .... 17 16 15

8 10 12 14 .... 15 16 18

9 11 13 15 .... 17 18 19

6 9 12 15 .... 20 19 18

7 10 13 16 .... 19 18 21

8 11 14 17 .... 22 21 20

9 12 15 18 .... 20 21 23

10 13 16 19 .... 22 23 24

11 14 17 20 .... 25 22 23

12 15 18 21 .... 25 24 26

5 9 13 17 .... 22 21 23

6 10 14 18 .... 24 21 22

7 11 15 19 .... 23 24 25

8 12 16 20 .... 23 24 26

9 13 17 21 .... 27 26 25

10 14 18 22 .... 26 25 28

11 15 19 23 .... 29 28 27

7 12 17 22 .... 29 26 27

8 13 18 23 .... 28 29 30

9 14 19 24 .... 28 29 31

10 15 20 25 .... 32 31 30

11 16 21 26 .... 31 30 33

12 17 22 27 .... 34 33 32

13 18 23 28 .... 32 33 35

12 22 32 42 .... 54 51 52

13 23 33 43 .... 53 54 55

14 24 34 44 .... 53 54 56

15 25 35 45 .... 57 56 55

16 26 36 46 .... 56 55 58

17 27 37 47 .... 58 57 59

18 28 38 48 .... 60 57 58

11 = ? + 1 2 1 10

12 = ? + 2 1 10 2

13 = ? + 3 10 1 2

25 = ? + 5 3 2 20

26 = ? + 6 20 2 3

35 = ? + 5 3 30 4

36 = ? + 6 4 3 30

35 + 16 = ? 52 51 53

36 + 17 = ? 53 54 55

37 + 18 = ? 57 56 55

38 + 19 = ? 58 57 59

39 + 20 = ? 61 60 59

40 + 21 = ? 61 62 63

41 + 22 = ? 65 64 63

10 + ? = 12 3 2 4

11 + ? = 14 5 4 3

12 + ? = 16 4 5 6

13 + ? = 18 7 6 5

14 + ? = 20 7 6 8

15 + ? = 22 7 8 3

16 + ? = 24 6 7 8

? + 12 = 15 5 4 3

? + 13 = 17 5 4 6

? + 14 = 19 5 6 7

? + 15 = 21 7 6 8

? + 16 = 23 9 8 7

? + 17 = 25 8 9 10

? + 18 = 27 10 9 8

x + 12 = 15 x = 5 x = 4 x = 3

x + 13 = 17 x = 5 x = 4 x = 6

x + 14 = 19 x = 5 x = 6 x = 7

x + 15 = 21 x = 7 x = 6 x = 8

x + 16 = 23 x = 8 x = 7 x = 9

x + 17 = 25 x = 8 x = 9 x = 10

x + 18 = 27 x = 11 x = 10 x = 9

9 - 2 = ? 5 6 7

10 - 2 = ? 8 7 6

11 - 2 = ? 7 9 8

15 - 12 = ? 5 4 3

16 - 12 = ? 2 4 3

17 - 12 = ? 3 5 4

18 - 12 = ? 4 5 6

99 - 12 = ? 86 87 85

99 - 13 = ? 84 85 86

99 - 14 = ? 85 84 83

99 - 15 = ? 82 83 84

99 - 16 = ? 82 83 81

99 - 17 = ? 82 81 80

99 - 18 = ? 79 80 81

10 - ? = 8 3 2 4

11 - ? = 8 2 4 3

12 - ? = 8 4 3 2

13 - ? = 9 2 3 4

14 - ? = 9 3 5 4

15 - ? = 9 6 5 4

16 - ? = 9 5 6 7

x + y = z

7 ? 10

8 ? 11

9 ? 12

x + y = z

? 6 10

? 7 11

? 8 12

? 9 13

? 10 14

x - y = z

10 6 ?

11 7 ?

12 8 ?

13 9 ?

14 10 ?

x - y = z

10 ? 5

11 ? 6

12 ? 7

13 ? 8

14 ? 9

15 ? 10

9 red marbles and 5 green marbles are in the basket.

How many marbles are in the basket?

x + y = z

8 small marbles and 5 big marbles are in the basket.

How many marbles are in the basket?

x + y = z

John has 12 red marbles and 4 green marbles. How

many marbles does John have in all?

x + y = z

12 4 ?

There are 12 girls and 10 boys in a class. How many

students are in the class in all?

x + y = z

12 10 ?

Mary has 9 marbles and Sophia has 5 marbles. How

many marbles do they have altogether?

x + y = z

There are 10 children sitting on the rug and 7

children standing. How many children are there in

x + y = z

10 7 ?

9 oranges are in the basket. 5 more oranges are put in

the basket. How many oranges are in the basket

x + y = z

John has a dog and a bird. How many legs in all?

x + y = z

Sophia has a dog and a cat. How many legs in all?

x + y = z

Olivia has 2 cats. How many legs in all?

x + y = z

15 marbles are in the basket. 10 are red and the rest

are green. How many marbles are green?

x + y = z

10 ? 15

12 oranges were in the basket. More oranges were

added to the basket. Now there are 17 oranges in the

basket. How many oranges were added to the

basket?

x + y = z

12 ? 17

Olivia and Lucy pick 15 flowers. Olivia picks 9

flowers. How many flowers does Lucy pick?

x + y = z

9 ? 15

Some oranges were in the basket. 14 more oranges

were added to the basket. Now there are 19 oranges

in the basket. How many oranges were in the basket

to start with?

x + y = z

? 14 19

Mary had some eggs in the fridge. She bought 10

more eggs. Now, she has 15 eggs in all. How many

eggs did Mary have in the fridge at first?

x + y = z

? 10 15

John has some books. Toni has 11 books. John and

Toni have 15 books in all. How many books does

John have?

x + y = z

? 11 15

15 apples are in the basket. 10 apples are taken from

the basket. How many apples are in the basket now?

x - y = z

15 10 ?

Sophia has $12. She spends $8. How much money

does she have now?

x - y = z

12 8 ?

Jim has 19 books. He sold 14 books. How many

books does he have left?

x - y = z

19 14 ?

John had 14 balloons at his birthday party. He gave 9

balloons to his friends. How many balloons did he

have left?

x - y = z

14 9 ?

Sophia sees 9 birds in the tree. 5 birds fly away. How

many birds are still in the tree?

x - y = z

John has 15 marbles. William has 10 marbles. How

many more marbles does John have than William?

x - y = z

15 10 ?

Sophia has 15 books. Mary has 12 books. How many

fewer books does Mary have than Sophia?

x - y = z

15 12 ?

12 apples were in the basket. Some apples were

taken from the basket. Now there are 8 apples in the

basket. How many apples were taken from the

basket?

x - y = z

12 ? 8

Jordan has 15 marbles. He gave some to William.

Now, he has 10 marbles left. How many marbles did

he give to William?

x - y = z

15 ? 10

Jim has 15 books. He sold some books. Now, he has

11 books. How many books did he sell?

x - y = z

15 ? 11

Jim has 7 more marbles than Jordan. Jim has 10

marbles. How many marbles does Jordan have?

x - y = z

10 ? 7

William has 8 fewer marbles than Michael. Michael

has 12 marbles. How many marbles does William

x - y = z

12 ? 8

Jordan has 6 red marbles, 4 blue marbles, and 7

green marbles. How many marbles does Jordan

x + y + z

x y z x + y + z

6 4 7 ?

Sophia went to the store. She bought 8 bananas, 2

apples, and 5 oranges. How many pieces of fruit did

she buy in all?

x + y + z

x y z x + y + z

8 2 5 ?

A guide for teachers and parents.

...................................................

Unit 1 objectives:

After completing the unit, the student will be expected to:

1- Use the visual-spatial x y z system.

2- Solve Worksheets 1 - 20 ( homework ).

......................................................................................

Unit 2 objectives:

1- Use verbal condition.

......................................................................................

Unit 3 objectives:

1- Find the missing number in increasing sequences.

Unit 4 objectives:

1- Find the unknown part in addition equations.

2- Find the unknown part in subtraction equations.

......................................................................................

Unit 5 objectives:

1- Use the visual-spatial x y z system.

......................................................................................

Unit 6 objectives:

1- Solve word problems by using the visual-spatial x y z

system.

Volume 3 Contents

Unit 1: Geometry

Unit 2: Fractions

Unit 3: Measurement

Unit 4: Money

Unit 5: Time

grade 1 math volume 2 en

mathematics anxiety

formal language systems

teaching mathematics

mathematics curricula

visualspatial system

math anxiety

cognitive system architects

complex math problems

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