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Workbook 1, Seventh grade mathematics of Basic Education, It is owned by the Secretary
of State in the Office of Education, it was prepared by teachers from the Departmental
Departments of Education, in the framework of the national emergency COVID-19, in
response to the needs of monitoring the teaching-learning process in government
educational centers of Honduras, CA
Presidency of the Republic
Secretary of State in the Office of Education
Secretariat for Administrative and Financial Affairs
Undersecretary for Technical Pedagogical Affairs
General Directorate of Curriculo and Evaluation
General Sub-Directorate for Basic Education
Departmental Directorate of Education of Cortés
General Directorate of Educational Modalities
Dirección General de Educación para Pueblos Indígenas y Afrohondureños
Adaptation
Valle de Sula Regional Permanent Training Center
Jorge Alberto Árias Moreno
Technical-graphic and pedagogical review
General Directorate for Technological and Educational Innovation
Curriculo Review
General Sub-Directorate for Basic Education
Lilian Elizabeth Gradiz
Juan José Muñoz
Desing and Diagramming
Arlen Adalixi Llanos Hernández
Eleazar Tomé Escobar
© Secretary of Education
1st street, between 2nd and 4th avenue of Comayagüela, MDC,
Honduras, CA
www.se.gob.hn
Workbook 1, Math, Seventh grade
2020 single edition
FREE DISTRIBUTION - SALE PROHIBITED
Presentation
Boys, girls, young people, parents, faced with the national emergency
generated by Covid-19, the Ministry of Education, makes this study and
work tool available to you for the I, II and III cycle of basic education ( 1st to
9th grade) that will allow you to continue your studies on a regular basis,
guaranteeing that you can stay at home and at the same time can obtain
the relevant knowledge and develop skills in the area of Mathematics.
Dad, mom and teacher will help you review each lesson and clarify any
doubts you may have. Your job is to develop the activities, exercises and
problems that arise in the Work notebook, in an orderly, creative and clean
way, to later present it to their teachers when we return to the Educational
Center.
Secretary of State in the Office of Education
1
Mathematics/ Seventh Grade
Zymology to Use
It is used to indicate and point out properties and
critera.
It is used to indicate the use of the
Calculator to make or verify calculations.
It is used to make clarifications, suggestions or
extensions of the knowledge of the class.
The solutions in the examples are marked with the
sign
The GD carries the solution of the exercises proposed
in the LE. Teachers have to take in account that in
the case of exercises and problems with open
answers there may be other answers.
To highlight the important points of a topic, use
And for some relevant explanations.
2
Mathematics/ Seventh Grade
The point that corresponds to zero is called the origin and is represented
by the letter O.
The graphical representation of a number on the number line is a point.
Lesson 1 Negative Positive Numbers
Order relationship
We answer one.- In which direction are the positive numbers located?
_____________________________________________
2.- In which direction are the negative numbers located?
_____________________________________________
3.- What is the point that corresponds to zero called?
_____________________________________________
let's remember
Direction to the
left (negative)
Negative direction Positive direction
Direction to the
right (positive)
3
Mathematics/ Seventh Grade
Example 1 On the number line which number is furthest to the right of +3 or +5?
Which of them is the largest?
Solution
Answer: The +5 is further to the right. +5 is the greater the ratio of +5 greater
than +3 is written + 5˃ + 3
The relationship can also be written as +3 less than + 5 + 3 <+5
We answer
one.- How are the numbers that are located to the right of another?
_____________________________________________
Let's draw
Draw the symbols of the order relationship in the rectangles
What do they ask you?
To draw Greater than Smaller than
On the number line the
number to the right is
higher.
Smaller than Greater than
4
Mathematics/ Seventh Grade
Example 2
On the number line write the order relationship of the following pair
Of numbers.
a) -4, +3
Solution
b) -4 is to the left of +3 -4 is said to be less than + 3y
-4 <+3 is written
We answer
one. - How are the numbers that are located to the left of another?
_____________________________________________
Exercise 1
a) Mark on the number line with a point, using colors the
Numbers presented to you in each pair of numbers.
b) Write on the line in the middle of each pair of numbers
Sign <or ˃
a) +3 _____ +8
b) -8 ____ -10
c) +11 _____ +8
d) +5 _____ -6
If the number is located to
the left of another is less.
You can also write
+3>- 4.
5
Mathematics/ Seventh Grade
e) 0_____ -2
f) 0_____ 3
Exercise 2 Write the sign <or ˃ in each of the pairs.
a) -21 ________- 36
b) -5 ________ -4
c) +2.3 _______ 0
d) -6.1 _______ +2.2
e) +3.4 _______ -2.6
f) +6.5 _______ -4.3
WE ANSWER
• When placing a positive number on the number line, the one that
is located furthest from zero will be greater.
• Placing a negative number on the number line will be greater if it is
closer to zero.
• Zero is greater than any negative number but less than any positive
number.
Answers: Exercise 1 a) <b) ˃ c) ˃ d) ˃ e) ˃ f) <
Answers: Exercise 2 a) ˃ b) <c) ˃ d) <e) ˃ f) ˃
6
Mathematics/ Seventh Grade
Absolute value
We answer
Mark the correct answer to the questions
one.- How many integer spaces are there between 0 and -3?
to. Three spaces
b. Two spaces
c. A space
2.- How many integer spaces are there between 0 and +3?
to. Three spaces
b. Two spaces
c. A space
3.- Which number is furthest from zero on the number line +3 or -3?
to. -3
b. +3
c. They are at the same distance
0
n
e
s
p
a
c
e
s
2
s
p
a
c
e
s
3
s
p
a
c
e
s
Spaces Equal
distance
7
Mathematics/ Seventh Grade
Exercise 3
Write the absolute value of the numbers
Exercise 4
Write the sign <or ˃ in each of the pairs
• Among the positive numbers, the one with the highest absolute
value is greater.
• Among the negative numbers it is less than the one with the highest
absolute value
• Between a positive and a negative number the positive will be greater.
Answers: Exercise 3 a) 8 b) 5 c) 0 d) 11 e) 12 f) 15 g) 19 h) 7
Distance is
never
negative.
The absolute value of +3 is 3 and is represented
/+3/=3
The absolute value of -3 is 3 and is represented as /-
3/=3
The absolute value of 0 is 0 and is represented as
/0] = 0
8
Mathematics/ Seventh Grade
Adding numbers with the same sign
Example 3
let's remembe
r
Answers: Exercise 4 a) ˃ b) <c) ˃ d) <e) ˃ f) ˃ g) <h) ˃
The point 0
is the origin
Observe the direction of movements and the final
position.
West East
The highway extends from West to East. An eastward movement is
expressed with a positive sign and a westward movement with a
negative sign followed by the number representing the distance of the
movement
If the following movement occurs, how much can be considered to
have moved eastward from point 0?
Case (1): first it moves 3km to the East starting from point 0 and it
moves 2km to the East.
Solution
West East
We use to express the positive
(East) direction with blue arrow Answer
9
Mathematics/ Seventh Grade
Exercise 5
Example 4
Exercise 6
Exercise 7
Calculate without using number line.
Answers: Exercise 7. +5 Exercise 6. -5 Exercise 7. a) +8 b) +7 c) -5 d) -7
We use to express the negative
(west) direction with a red arrow Answer: 5 km to the west (-5 km)
Calculate without using number line.
Using the graph
West East
If the following movement occurs. How much can be considered to have moved west starting
from point 0?
Case (2): first it travels 3 km to the west (-3 km) starting from point 0 and then it moves 2 km to
the west (-2 km)
Solution
West East
Calculate (-2)+(-3) using the grph
West East
10
Mathematics/ Seventh Grade
Adding different numbers sign
Example 5
Calculate
Exercise 8
Example 6
What is the final position after the two movements? Case: first it travels 3
km to the East starting from point 0 and then it move 5 km to the West.
What is the final position after the two movements? Case: first it travels 3 km
to the west starting from point 0 and then it displaces 5 km to the East
2 km to the East,
represents for + 2
km. Solution
West East
Answer
Solution
West East
2 km to the East,
represents for + 2
Answer:
11
Mathematics/ Seventh Grade
Example 7
Exercise 9
Answers: Exercise 9. a) +4 b) -4
Exercise 9. a) +4 b) -1 c) -2 d) +2 e) -4 f) -7
Analyze
It stay ble
Answer: +2 (positive)
It stay red
Answer: -2 (Negative)
When two numbers with different signs are
added together, the sign of the answer
equals the longest arrow (“longer arrow
means it has a geater absolute value)
The length of the response date is
the difference between the length
of the long arrow and the lenght
of the short date.
calculate
12
Mathematics/ Seventh Grade
Commutative and Associative Property
Example 8
Example 9
Exercise 10 Calculate using the commutative and associative property
Let's look Solution
Answer: they are the same
With positive and negative numbers the following property is valid: commutative
property + = +
They are
equal
Compare the result of
Compare the result of
It Works out first what is
inside of the bracket (1.
Solution
Answer: they are the same They are equal
With positive and negative numbers the following property is valid: associative
property ( + )+ = + ( + )
13
Mathematics/ Seventh Grade
Subtraction
Example 10
Exercise 11 Convert the following subtractions into addition and calculate
Analyze
Convert the following subtraction into additions and calculate
Solution:
14
Mathematics/ Seventh Grade
Example 11
Exercise 12
Approach only with Addition
Example 12 Convert to PO only with addition
Answers: Exercise 12. a) +4 b) -4 c) +9 d) -1
Exercise 11. a) +3 b) -5 c) +4 d) +4 e) -5
Exercise 12 a) +4 b) -1 c) -1 d) +2 e) -4 f) -7
Calculate
Solution
To subtract one number (positive or negative) from another,
add to the opposite number.
As seen in the previous section, you can turn a subtraction into an addition. By
applying this conversion multiple times, you can convert a PO with addition and
subtraction to a PO with addition.
15
Mathematics/ Seventh Grade
Combined Addition and Subtraction
Example 13
Let's calculate
If lama i end each number of a PO that is represented only by addition.
In the previous exercise the terms are +3,-5,-8 and +9
Calculate
Solution
To remove parentheses in combined addition and subtraction if the
parentheses are preceded by the “+” sign, it is removed leaving the
addends inside with their signs.
If the parentheses are preceded by the sign “, deleting it transforms the
signs of the addends inside, each one is changed by the opposite.
Only the numbers are
placed as they are
inside the
parentheses
Remember that
+5=5,
Then
16
Mathematics/ Seventh Grade
Multiplication
Example 14
Exercise 13 Let's calculate
From the PO and the answers in the previous examples, the following can be concluded:
Multiplication of two positive and negative numbers according to the sign
if the two numbers have the same sign, the product has the positive sign if
the two number have a different sign, the product has a negative sigh
according to the absolute value the absolute value is the product of the
absolute values of the numbers
17
Mathematics/ Seventh Grade
Exercise 14 Let's calculate
Answers: Exercise 14
a) +8 b) +15 c) +12 d) +12 e) +10 f) +18 g) +21 h) +32
Exercise 15 a) -8 b) -15 c) -12 d) -8 e) -10 f) -18 g) -21 h) -32
Workbook 1- Mathematics
Seventh grade of Basic Education
Printed and published by the Secretary of Education
In the framework of the national emergency COVID-19
Tegucigalpa, MDC, Honduras, CA
2020