041 about the authors
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Adriel G. Roman and Myrichel Alvarez are students at Laguna State Polytechnic University studying Bachelor of Secondary Education with a specialization in Mathematics. Adriel finished elementary school in Caloocan and high school in Balian. Myrichel completed elementary and high school in Siniloan, Laguna, where she is now studying at the university.
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036 lesson 24
The document discusses the rules for dividing integers. It states that if both integers have the same sign, divide the absolute value of the first integer by the absolute value of the second integer. If the integers have different signs, divide the absolute value of the first integer by the absolute value of the second integer and assign the result a negative sign. It provides examples to illustrate these rules and a worksheet for students to practice dividing integers.
040 the whole module
The document provides information about mastering the fundamental operations of addition, subtraction, multiplication and division of whole numbers. It discusses addition in detail, including defining addition, identifying the parts of an addition problem, and the properties of addition like commutativity and associativity. It also introduces addition tables as a method to practice addition facts and provides worksheets with addition exercises for students to work on.
039 references
The document lists 12 image sources from websites like Google, Yahoo, and search engines for pictures and clip art related to mathematics, cartoons, and Looney Tunes characters. Book references are also provided on basic mathematics and algebra textbooks. The sources range from 2009 to 2010.
038 math and technology
The document presents a series of math puzzles that involve using a calculator to reveal letters, words, or answers to questions. The puzzles direct the reader to perform various math operations like division and addition on calculators, then turn the calculators upside down to view letters or numbers that spell out a word or provide an answer. It includes 7 puzzles for the reader to solve that follow this format of using a calculator to reveal a hidden message or response through mathematical calculations.
034 lesson 22
This document discusses subtracting integers and provides examples of how to perform integer subtraction. It explains that to subtract an integer, you convert the subtracted integer to its opposite and add the two numbers. It then gives several practice problems for students to solve by subtracting integers.
037 lesson 25
The document discusses the order of operations in mathematics, noting that operations inside parentheses should be performed first, then multiplication and division from left to right, followed by addition and subtraction from left to right. Several examples demonstrate evaluating expressions using these rules to avoid ambiguity and ensure only one correct solution. Precise use of order of operations is important for correctly solving arithmetic expressions with multiple operations.
035 lesson 23
The document discusses the rules for multiplying integers. It states that if two integers have the same sign, their product is positive, and if they have opposite signs, their product is negative. It also notes that if one or both integers being multiplied is 0, the product is 0. Examples are provided to illustrate multiplying integers with the same sign, opposite signs, and where one factor is 0. The rules are then generalized to multiplying more than two integers. An example problem demonstrates multiplying several integers together and determining the sign of the product based on the number of negative factors.
029 lesson 19
The ski resort sold a total of 111,359 day ski tickets in January. To calculate the average number of tickets sold per day, the total number of tickets was divided by 31, the number of days in January. The average number of tickets sold per day was 3,589.
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036 lesson 24
The document discusses the rules for dividing integers. It states that if both integers have the same sign, divide the absolute value of the first integer by the absolute value of the second integer. If the integers have different signs, divide the absolute value of the first integer by the absolute value of the second integer and assign the result a negative sign. It provides examples to illustrate these rules and a worksheet for students to practice dividing integers.
040 the whole module
The document provides information about mastering the fundamental operations of addition, subtraction, multiplication and division of whole numbers. It discusses addition in detail, including defining addition, identifying the parts of an addition problem, and the properties of addition like commutativity and associativity. It also introduces addition tables as a method to practice addition facts and provides worksheets with addition exercises for students to work on.
039 references
The document lists 12 image sources from websites like Google, Yahoo, and search engines for pictures and clip art related to mathematics, cartoons, and Looney Tunes characters. Book references are also provided on basic mathematics and algebra textbooks. The sources range from 2009 to 2010.
038 math and technology
The document presents a series of math puzzles that involve using a calculator to reveal letters, words, or answers to questions. The puzzles direct the reader to perform various math operations like division and addition on calculators, then turn the calculators upside down to view letters or numbers that spell out a word or provide an answer. It includes 7 puzzles for the reader to solve that follow this format of using a calculator to reveal a hidden message or response through mathematical calculations.
034 lesson 22
This document discusses subtracting integers and provides examples of how to perform integer subtraction. It explains that to subtract an integer, you convert the subtracted integer to its opposite and add the two numbers. It then gives several practice problems for students to solve by subtracting integers.
037 lesson 25
The document discusses the order of operations in mathematics, noting that operations inside parentheses should be performed first, then multiplication and division from left to right, followed by addition and subtraction from left to right. Several examples demonstrate evaluating expressions using these rules to avoid ambiguity and ensure only one correct solution. Precise use of order of operations is important for correctly solving arithmetic expressions with multiple operations.
035 lesson 23
The document discusses the rules for multiplying integers. It states that if two integers have the same sign, their product is positive, and if they have opposite signs, their product is negative. It also notes that if one or both integers being multiplied is 0, the product is 0. Examples are provided to illustrate multiplying integers with the same sign, opposite signs, and where one factor is 0. The rules are then generalized to multiplying more than two integers. An example problem demonstrates multiplying several integers together and determining the sign of the product based on the number of negative factors.
029 lesson 19
The ski resort sold a total of 111,359 day ski tickets in January. To calculate the average number of tickets sold per day, the total number of tickets was divided by 31, the number of days in January. The average number of tickets sold per day was 3,589.
033 lesson 21
The document provides lesson objectives and rules for adding integers:
1) When adding integers with the same sign, add their absolute values and use the same sign for the result.
2) When adding integers with opposite signs, take the absolute values, subtract the smaller from the larger, and use the sign of the integer with the larger absolute value for the result.
3) The sum of any integer and its opposite integer is always zero.
032 lesson 20
The document defines integers as natural numbers including zero and their negatives. It explains that positive integers are whole numbers greater than zero, while negative integers are the opposites of positive integers. The number line is used to demonstrate that integers increase from left to right and how the absolute value of a number is always positive or zero.
031 chapter v
This document introduces the next chapter on integers in a math workbook. It explains that the chapter will provide an in-depth understanding of integers, including the different types of integers, how they are used in math, and their real-world applications. It notes that integers are a fundamental part of high school math and that the reader has mastered the foundational whole number operations to now move on to applying those same operations with integers.
030 unit ii
This unit overview discusses fundamental integer operations, including the four basic arithmetic operations (addition, subtraction, multiplication, division) and order of operations. The objectives are for students to discuss integers, perform the four operations on integers, appreciate integers, gain knowledge about integers to prepare for algebra, and discuss order of operations. This unit contains lessons to skillfully perform integer operations and critically think through exercises to solve.
028 lesson 18
The document provides instructions on dividing whole numbers using the method of cancelling insignificant zeros. It defines cancelling insignificant zeros as removing the same number of trailing zeros from both the dividend and divisor when performing long division. The document includes examples of cancelling zeros when dividing numbers such as 300/100, 2500/100, and 38175/638175. It then provides a 20 question worksheet for students to practice dividing numbers using this method.
027 lesson 17
The document discusses different methods for dividing whole numbers, including division with remainders where the answer is not a whole number. It provides examples and steps to show how to calculate division problems and expresses the answer as a quotient with a remainder. Mental division strategies are also described, emphasizing knowing multiplication tables and the order of operations.
026 lesson 16
This document defines division and its key components. It discusses division as the inverse of multiplication, with division being described as repeated subtraction and multiplication as repeated addition. Examples are provided to illustrate division with a dividend, divisor, and quotient. Special cases of division by 1 and 0 are also explained. Division by 0 is said to be impossible.
025 chapter iv
Division is one of the fundamental mathematical operations that is explained in this chapter. It will cover the different parts of division and how it can be used to solve word problems. Mastering division is an important part of learning mathematics.
024 lesson 15
The document provides examples of word problems involving multiplication to calculate quantities over time or between groups. It gives step-by-step work for problems such as calculating the number of screws a machine can produce in an hour given its 1-minute rate, or the number of radios a store has if it bought a certain number of crates each containing a set quantity. The document includes practice problems for students to solve using multiplication, such as calculating total seats in a stadium based on the number of sections and rows.
022 lesson 13
This lesson introduces the "99 multiplier" shortcut for multiplying whole numbers mentally. It works by annexing zeros to the multiplicand equal to the number of 9s in the multiplier, then subtracting the original multiplicand. Examples show 999×364 equals 364,000 minus 364, which is 369,636. The lesson aims to help students appreciate exploring multiplication and the multiplication operation.
023 lesson 14
This lesson teaches students about multiplying numbers with factors that are powers of ten. It explains that when multiplying numbers where one factor is a power of ten, such as 10, 100, 1000, students should multiply the non-zero digits and add the appropriate number of zeros to the product based on the power of ten. Some examples are provided. It also notes that when both factors end in zeros, students should multiply the significant digits and use the total number of zeros in both factors for the product. A worksheet with practice problems is included for students.
021 lesson 12
Lesson 12 aims to teach students how to multiply whole numbers quickly and correctly. It introduces multiplication as a shortcut for repeated addition and shows students how to use a multiplication table to solve problems efficiently. Students are given examples and a worksheet to practice their multiplication skills. The objectives are for students to multiply whole numbers easily, develop speed in multiplication, and perform multiplication accurately.
021 lesson 11
The document discusses various properties of multiplication, including:
1) The identity property where multiplying any number by 1 leaves the number unchanged.
2) The zero property where multiplying any number by 0 equals 0.
3) The commutative property where changing the order of factors does not change the product.
It provides examples to illustrate each property and a worksheet for students to practice applying the properties.
020 lesson 10
The document defines multiplication as repeated addition. It provides an example of 3 x 5 being solved by adding 5 three times to get 15. The document identifies the terms in a multiplication problem, with the number on top called the multiplicand and on bottom called the multiplier, and the answer called the product. It includes a worksheet for students to identify terms in multiplication problems and calculate products.
019 chapter iii
This chapter teaches students about multiplication, including its parts, methods for solving multiplication problems, and how to apply multiplication to word problems. Lessons and exercises are provided to help students master multiplying whole numbers.
018 lesson 9
The document provides examples of word problems involving subtraction to demonstrate the problem solving process. It gives two examples of subtraction word problems, showing the steps of identifying what is asked, what is given, and which operation to use. It then provides a worksheet with additional subtraction word problems for students to solve.
016 lesson 7
This document defines subtraction and identifies its key parts and how it differs from addition. Subtraction is defined as the process of taking away or removing something. It identifies the minuend, subtrahend, and difference as the key parts of a subtraction expression. It provides examples of subtraction expressions and how regrouping or "borrowing" is used when the subtrahend digit is larger than the corresponding minuend digit. Worksheets are also included for students to practice identifying subtraction terms and solving subtraction problems.
015 chapter ii
Subtraction is a fundamental mathematical operation that is used to find the difference between two numbers. It involves identifying the minuend, subtrahend, and difference. Word problems can also be solved using subtraction to determine unknown values.
014 lesson 6
The document provides examples and instructions for solving word problems involving addition of whole numbers. It gives two examples of adding whole numbers: 875 + 648 = 1,523 and 5,986 + 3,759 = 9,745. It then provides a worksheet with 5 word problems for students to solve involving addition of whole numbers.
013 lesson 5
1. The document discusses a 4 step process for solving word problems: understand the problem, devise a plan, carry out the plan, and check the answer.
2. An example problem is provided about the number of sacks harvested by a farmer in two different seasons.
3. Students are expected to use the 4 step process to solve sample word problems provided in a worksheet.
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033 lesson 21
The document provides lesson objectives and rules for adding integers:
1) When adding integers with the same sign, add their absolute values and use the same sign for the result.
2) When adding integers with opposite signs, take the absolute values, subtract the smaller from the larger, and use the sign of the integer with the larger absolute value for the result.
3) The sum of any integer and its opposite integer is always zero.
032 lesson 20
The document defines integers as natural numbers including zero and their negatives. It explains that positive integers are whole numbers greater than zero, while negative integers are the opposites of positive integers. The number line is used to demonstrate that integers increase from left to right and how the absolute value of a number is always positive or zero.
031 chapter v
This document introduces the next chapter on integers in a math workbook. It explains that the chapter will provide an in-depth understanding of integers, including the different types of integers, how they are used in math, and their real-world applications. It notes that integers are a fundamental part of high school math and that the reader has mastered the foundational whole number operations to now move on to applying those same operations with integers.
030 unit ii
This unit overview discusses fundamental integer operations, including the four basic arithmetic operations (addition, subtraction, multiplication, division) and order of operations. The objectives are for students to discuss integers, perform the four operations on integers, appreciate integers, gain knowledge about integers to prepare for algebra, and discuss order of operations. This unit contains lessons to skillfully perform integer operations and critically think through exercises to solve.
028 lesson 18
The document provides instructions on dividing whole numbers using the method of cancelling insignificant zeros. It defines cancelling insignificant zeros as removing the same number of trailing zeros from both the dividend and divisor when performing long division. The document includes examples of cancelling zeros when dividing numbers such as 300/100, 2500/100, and 38175/638175. It then provides a 20 question worksheet for students to practice dividing numbers using this method.
027 lesson 17
The document discusses different methods for dividing whole numbers, including division with remainders where the answer is not a whole number. It provides examples and steps to show how to calculate division problems and expresses the answer as a quotient with a remainder. Mental division strategies are also described, emphasizing knowing multiplication tables and the order of operations.
026 lesson 16
This document defines division and its key components. It discusses division as the inverse of multiplication, with division being described as repeated subtraction and multiplication as repeated addition. Examples are provided to illustrate division with a dividend, divisor, and quotient. Special cases of division by 1 and 0 are also explained. Division by 0 is said to be impossible.
025 chapter iv
Division is one of the fundamental mathematical operations that is explained in this chapter. It will cover the different parts of division and how it can be used to solve word problems. Mastering division is an important part of learning mathematics.
024 lesson 15
The document provides examples of word problems involving multiplication to calculate quantities over time or between groups. It gives step-by-step work for problems such as calculating the number of screws a machine can produce in an hour given its 1-minute rate, or the number of radios a store has if it bought a certain number of crates each containing a set quantity. The document includes practice problems for students to solve using multiplication, such as calculating total seats in a stadium based on the number of sections and rows.
022 lesson 13
This lesson introduces the "99 multiplier" shortcut for multiplying whole numbers mentally. It works by annexing zeros to the multiplicand equal to the number of 9s in the multiplier, then subtracting the original multiplicand. Examples show 999×364 equals 364,000 minus 364, which is 369,636. The lesson aims to help students appreciate exploring multiplication and the multiplication operation.
023 lesson 14
This lesson teaches students about multiplying numbers with factors that are powers of ten. It explains that when multiplying numbers where one factor is a power of ten, such as 10, 100, 1000, students should multiply the non-zero digits and add the appropriate number of zeros to the product based on the power of ten. Some examples are provided. It also notes that when both factors end in zeros, students should multiply the significant digits and use the total number of zeros in both factors for the product. A worksheet with practice problems is included for students.
021 lesson 12
Lesson 12 aims to teach students how to multiply whole numbers quickly and correctly. It introduces multiplication as a shortcut for repeated addition and shows students how to use a multiplication table to solve problems efficiently. Students are given examples and a worksheet to practice their multiplication skills. The objectives are for students to multiply whole numbers easily, develop speed in multiplication, and perform multiplication accurately.
021 lesson 11
The document discusses various properties of multiplication, including:
1) The identity property where multiplying any number by 1 leaves the number unchanged.
2) The zero property where multiplying any number by 0 equals 0.
3) The commutative property where changing the order of factors does not change the product.
It provides examples to illustrate each property and a worksheet for students to practice applying the properties.
020 lesson 10
The document defines multiplication as repeated addition. It provides an example of 3 x 5 being solved by adding 5 three times to get 15. The document identifies the terms in a multiplication problem, with the number on top called the multiplicand and on bottom called the multiplier, and the answer called the product. It includes a worksheet for students to identify terms in multiplication problems and calculate products.
019 chapter iii
This chapter teaches students about multiplication, including its parts, methods for solving multiplication problems, and how to apply multiplication to word problems. Lessons and exercises are provided to help students master multiplying whole numbers.
018 lesson 9
The document provides examples of word problems involving subtraction to demonstrate the problem solving process. It gives two examples of subtraction word problems, showing the steps of identifying what is asked, what is given, and which operation to use. It then provides a worksheet with additional subtraction word problems for students to solve.
016 lesson 7
This document defines subtraction and identifies its key parts and how it differs from addition. Subtraction is defined as the process of taking away or removing something. It identifies the minuend, subtrahend, and difference as the key parts of a subtraction expression. It provides examples of subtraction expressions and how regrouping or "borrowing" is used when the subtrahend digit is larger than the corresponding minuend digit. Worksheets are also included for students to practice identifying subtraction terms and solving subtraction problems.
015 chapter ii
Subtraction is a fundamental mathematical operation that is used to find the difference between two numbers. It involves identifying the minuend, subtrahend, and difference. Word problems can also be solved using subtraction to determine unknown values.
014 lesson 6
The document provides examples and instructions for solving word problems involving addition of whole numbers. It gives two examples of adding whole numbers: 875 + 648 = 1,523 and 5,986 + 3,759 = 9,745. It then provides a worksheet with 5 word problems for students to solve involving addition of whole numbers.
013 lesson 5
1. The document discusses a 4 step process for solving word problems: understand the problem, devise a plan, carry out the plan, and check the answer.
2. An example problem is provided about the number of sacks harvested by a farmer in two different seasons.
3. Students are expected to use the 4 step process to solve sample word problems provided in a worksheet.
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041 about the authors
- 1. -1242191-1166648ABOUT THE AUTHORS<br />5969027305Adriel G. Roman is a student of Laguna State Polytechnic University. In Siniloan, Laguna. He is taking Bachelor of Secondary Education (Mathematics as a field of specialization. He had finished his Elementary level at Andres Bonifacio Elementary School (located at Sangandaan, Caloocan) he had finished his High School level in Balian National High School. <br />5969048260Myrichel Alvarez is a student of Laguna State Polytechnic University Siniloan Campus, located at Siniloan Laguna. She had finished her Elementary level at Siniloan Elementary School, located at Siniloan, Laguna. She also finished her High School level at Siniloan National High School. Now she is taking Bachelor of Secondary Education Mathematics as a field of specialization.<br />