This document provides instruction on dividing numbers in mathematics. It defines division, the parts of a division problem (dividend, divisor, quotient), and the steps to solve a division problem. Examples are provided such as 10 lollipops being divided equally between 2 representatives, with the answer being each representative gets 5 lollipops. Word problems are also used as examples, such as Ara having 8 candies and wanting to share them equally with her sibling Sean. The document also notes that division and multiplication are inverse operations.
The document defines key vocabulary terms related to division, including: dividend, divisor, quotient, remainder, inverse operations, and distributive property. It also discusses different methods for solving division problems, such as using visual models, the partial quotients algorithm, and estimating quotients through mental math strategies like the distributive property. The purpose is to introduce foundational division concepts and procedures.
The document provides instructions for teaching students about division. It defines division as sharing objects equally or grouping objects. It gives examples of writing division number sentences and using multiplication to check the answer. It includes word problems and activities to help students practice dividing by 5, 6, and 9. Students are shown divisibility rules to determine if a number is divisible by 5, 6, or 9.
This document provides instructions for using candy and cereal as math manipulatives to teach primary school children basic math concepts. It offers over a dozen lesson plans and examples to teach skills like skip counting, odd/even, greater/less than, addition, subtraction, and more. The lessons use candy and cereal in creative ways to engage children and make math more fun by relating it to treats they enjoy eating.
Division is the process of splitting a quantity into equal parts or groups. The amount being divided is called the dividend, while the number it is being divided by is the divisor. To perform division, the divisor is subtracted from the dividend repeatedly until the remainder is zero. The number of times the divisor is subtracted is the quotient. Common word problems involving division use language like "share", "each", and "equal groups". Strategies for solving division problems include repeated addition, repeated subtraction, writing the division as a symbol, or drawing pictures to represent sharing into groups.
Today's agenda includes a math lesson covering personal strategies for addition, subtraction, multiplication, and division. The schedule also includes a nutrition break, looking at virtual manipulatives and resources, lunch, and an assessment period. The document discusses teaching math concepts conceptually rather than procedurally and the importance of understanding operations rather than just memorizing computations. It provides examples of story problems and strategies adults use to solve math problems informally in everyday life.
The document provides information about preparing for and taking the PSLE Mathematics exam in Singapore. It discusses the structure of the exam, which consists of two papers, and outlines the curriculum focus on problem solving. It also provides examples of different types of math problems students may encounter on the exam. At the end, it discusses a news article where parents complained that this year's PSLE math exam was unusually difficult, possibly because it was the first year calculators were allowed.
The document contains multiple math word problems and questions. It asks the reader to evaluate expressions, find missing values, draw graphs, choose the student with the correct solution, write equations, and determine which variable had the least variation from data. It also provides tables with numbers and asks questions about the data.
This document provides instruction on dividing numbers in mathematics. It defines division, the parts of a division problem (dividend, divisor, quotient), and the steps to solve a division problem. Examples are provided such as 10 lollipops being divided equally between 2 representatives, with the answer being each representative gets 5 lollipops. Word problems are also used as examples, such as Ara having 8 candies and wanting to share them equally with her sibling Sean. The document also notes that division and multiplication are inverse operations.
The document defines key vocabulary terms related to division, including: dividend, divisor, quotient, remainder, inverse operations, and distributive property. It also discusses different methods for solving division problems, such as using visual models, the partial quotients algorithm, and estimating quotients through mental math strategies like the distributive property. The purpose is to introduce foundational division concepts and procedures.
The document provides instructions for teaching students about division. It defines division as sharing objects equally or grouping objects. It gives examples of writing division number sentences and using multiplication to check the answer. It includes word problems and activities to help students practice dividing by 5, 6, and 9. Students are shown divisibility rules to determine if a number is divisible by 5, 6, or 9.
This document provides instructions for using candy and cereal as math manipulatives to teach primary school children basic math concepts. It offers over a dozen lesson plans and examples to teach skills like skip counting, odd/even, greater/less than, addition, subtraction, and more. The lessons use candy and cereal in creative ways to engage children and make math more fun by relating it to treats they enjoy eating.
Division is the process of splitting a quantity into equal parts or groups. The amount being divided is called the dividend, while the number it is being divided by is the divisor. To perform division, the divisor is subtracted from the dividend repeatedly until the remainder is zero. The number of times the divisor is subtracted is the quotient. Common word problems involving division use language like "share", "each", and "equal groups". Strategies for solving division problems include repeated addition, repeated subtraction, writing the division as a symbol, or drawing pictures to represent sharing into groups.
Today's agenda includes a math lesson covering personal strategies for addition, subtraction, multiplication, and division. The schedule also includes a nutrition break, looking at virtual manipulatives and resources, lunch, and an assessment period. The document discusses teaching math concepts conceptually rather than procedurally and the importance of understanding operations rather than just memorizing computations. It provides examples of story problems and strategies adults use to solve math problems informally in everyday life.
The document provides information about preparing for and taking the PSLE Mathematics exam in Singapore. It discusses the structure of the exam, which consists of two papers, and outlines the curriculum focus on problem solving. It also provides examples of different types of math problems students may encounter on the exam. At the end, it discusses a news article where parents complained that this year's PSLE math exam was unusually difficult, possibly because it was the first year calculators were allowed.
The document contains multiple math word problems and questions. It asks the reader to evaluate expressions, find missing values, draw graphs, choose the student with the correct solution, write equations, and determine which variable had the least variation from data. It also provides tables with numbers and asks questions about the data.
The document explains how multiplication and division are related. Multiplication is a shortcut for addition of equal groups, while division is the opposite of multiplication and involves splitting things into equal groups. Examples are provided to illustrate how to use multiplication to solve division problems by thinking of the division sign as asking "what number multiplied by the given number equals the total?"
This document outlines lessons on dividing by one-digit numbers. Lesson 9-1 covers division with and without remainders. Lesson 9-2 discusses dividing multiples of 10, 100, and 1,000. Lesson 9-3 introduces the problem-solving strategy of guess and check. Lesson 9-4 is about estimating quotients. Each lesson provides examples and relates the content to California math standards.
This document contains a mathematics practice test for 4th grade students with multiple choice, true/false, word problems, and challenge questions. It covers topics like arithmetic operations, order of operations, word problems involving money, factors, and properties of numbers. The document tests students on their ability to perform calculations, translate between word sentences and mathematical expressions, solve multi-step word problems, and reason about number patterns.
This document discusses key facts about division:
1) If the dividend is zero, the quotient will be zero regardless of the divisor.
2) If the divisor is 1, the quotient will equal the dividend.
3) The product of the divisor and quotient plus the remainder will always equal the original dividend. This relationship can be used to check the accuracy of a division problem.
First New Teachers' Conference, Manila, 10 September 2011Jimmy Keng
This document contains summaries from presentations given at various schools around the world on teaching mathematics. It discusses lessons from Chile, Japan, and the Philippines on public lessons, as well as a LEAP program in Manila. Participants at Keys Grade School in Manila provided methods for finding the difference between two numbers. At De Tweemaster in the Netherlands, participants demonstrated methods for finding the area of polygons by counting dots. The document outlines three main points about teaching mathematics through visualization, generalization, and communication. It provides further examples and solutions for percentage and angle problems.
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This document provides an overview of a presentation on helping children with primary mathematics. It discusses how mathematics can develop intellectual competence and reflects on shifts in test questions to require more conceptual understanding and real-world problem solving over rote algorithms. Examples of math questions and lessons from various primary grades in Singapore, the US, UK, Netherlands and Japan are presented, covering topics like number sense, patterns, problem solving and visual models. Key competencies and strategies for problem solving are discussed.
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This document provides an introduction to algebra and ratio and proportion concepts. It begins with defining algebra as the study of mathematical symbols and the rules for manipulating them. The document then covers order of operations, including the PEMDAS method, and provides examples of simplifying expressions and solving equations. It also defines ratios as a comparison of quantities and proportions as equal ratios. Examples are given for setting up and solving ratio and proportion word problems.
The document provides activities and lessons for students in Year 1 for the week commencing March 30th. It includes English, maths, and other subjects. The maths lessons focus on addition and subtraction using number lines and by counting forwards and backwards. Other activities include independent writing, spelling practice, handwriting practice, and a shared reading text about caring for dogs.
1) The document discusses 4 levels of mathematics language used in teaching: students' language using familiar objects, materials language using concrete objects, mathematics language using proper terms, and symbolic language using symbols.
2) It provides strategies and concepts for addition, subtraction, multiplication, and division, including counting on, doubles, decomposition, cover-ups, repeated addition, arrays, measurements, combinations, partitioning and quoting.
3) Visual and verbal models are recommended for introducing new concepts along with using familiar objects and materials to help students make connections.
1) The document discusses 4 levels of mathematics language used in teaching: students' language using familiar objects, materials language using concrete objects, mathematics language using proper terms, and symbolic language using symbols.
2) It provides strategies and concepts for addition, subtraction, multiplication, and division, including counting on, doubles, decomposition, cover-ups, repeated addition, arrays, measurements, combinations, partitioning and quoting.
3) Visual and verbal models are recommended for introducing new concepts along with using familiar objects and materials to help students make connections.
This document contains materials for teaching students about multiplication using repeated addition, fractions including halves and quarters, and division using equal grouping. It includes learning intentions, success criteria, examples of dividing shapes into halves and quarters, and names of iPad games to reinforce these concepts. Word problems are provided as practice for multiplication using repeated addition with topics like bananas, marbles, tulips and money.
The document contains a collection of math word problems and exercises for students. It includes problems involving geometry, algebra, time, money, fractions, probability and other topics. After each problem section, it provides the answers and an explanation of the problem solving strategies and concepts involved. The purpose is to challenge students with complex multi-step problems and help them improve their problem solving skills.
This document provides learning activities and materials for home learning during week 6. It includes:
- A spelling test with 10 words and information on phonics work involving suffixes
- Sentence unscrambling and reading comprehension exercises
- Daily maths activities involving topics like doubling, sequences, fractions
- Suggestions for writing sentences and fact files about local animals
- A multiplication game using snakes and ladders
- A science challenge to make a junk model insect
- Materials for a Covid-19 time capsule project
The document discusses subtracting whole numbers. It defines whole numbers as positive numbers without fractions or decimals. Examples are provided of subtracting numbers using the column method, including "borrowing" from the next column when the digit being subtracted is greater. Students are divided into groups to answer subtraction questions and complete subtraction activities to reinforce the concepts covered.
This document contains materials for a mathematics lesson on ratios and proportions. It includes examples of writing ratios using fractions and colons, forming proportions, and finding missing terms in proportions. Activities guide students to form ratios, write proportions, solve word problems involving ratios, and evaluate their understanding through questions and applications using visual representations. Cooperative learning strategies and using various tools like charts and presentations are suggested for instruction.
The document discusses various problem-solving heuristics or methods that can be used in mathematics, including:
1) The bar model method which involves visualizing a problem using bars or diagrams to represent quantities.
2) Using guess and check or making a table to systematically try values in a problem.
3) Breaking problems into number sentences to write mathematical expressions that can then be solved.
4) Looking for patterns or structures in numbers that can provide clues for solving problems.
The document provides instructions for viewing an animated PowerPoint presentation correctly in slide show mode. It explains that some text and images may overlap or be difficult to read if viewed outside of slide show mode. It recommends selecting "from beginning" or "from current slide" in the slide show menu to enter slide show mode. It concludes by stating that it hopes users find the website and resources useful.
The document provides strategies and examples for teaching multiplication facts to students. It discusses equal groups, comparison, and combination word problems. It also outlines strategies like using doubles, fives facts, zeros and ones, nifty nines, and helping facts to help students relate new multiplication facts to ones they already know. The document emphasizes using models and real-world examples to build students' conceptual understanding of multiplication.
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This document contains summaries from presentations given at various schools around the world on teaching mathematics. It discusses lessons from Chile, Japan, and the Philippines on public lessons, as well as a LEAP program in Manila. Participants at Keys Grade School in Manila provided methods for finding the difference between two numbers. At De Tweemaster in the Netherlands, participants demonstrated methods for finding the area of polygons by counting dots. The document outlines three main points about teaching mathematics through visualization, generalization, and communication. It provides further examples and solutions for percentage and angle problems.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
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Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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DIVISION
- Means splitting the
numbers or objects into
equal parts.
7. - is the number to be divided.
DIVIDEND
DIVISOR
QOUTIENT
- is the number that divides the
dividend.
- is the answer in division.
10 ÷ 2 = 5
DIVIDEND DIVISOR QOUTIENT
We say, “10 divided by 2 equals 5.”
EXAMPL
E:
10. 1. How many pens does T. Jasmine have?
Let’s have another example:
2. How many students does T. Jasmine have?
8 4
3. How many pens for each of them?
÷ = 2
We say, “10 divided by 2 equals 5.”
14. Let’s have an example:
Sarah have 12 crayons and
she put 3 crayons in each
paper bag.
How many paper bags did she
use?
12 ÷ 3 =
? Remember: We have
to subtract the
dividend and divisor
until the remainder is
0.
15. 12 crayons
- 3 crayons in 1st bag.
How many paper bags did she use?
9 crayons left.
- 3 crayons in 2nd
bag.
6 crayons left.
- 3 crayons in 3rd bag.
3 crayons left.
- 3 crayons in 4th bag.
0 no more crayons left.
12 ÷ 3 = 4
16. 27 ÷ 9 =
27
- 9
18
- 9
9
- 9
0
We got the answer 27 ÷ 9
by subtracting 9 form 27
until the remainder is 0.