The document discusses learning to solve addition problems at a Level 3+ and Level 4, and includes an extension activity to make your own addition problems.
Enum in C# is used to store a set of named constants such as days of the week or months. Enum constants have default integer values that increment by one, but these can be changed. Enum is declared using the enum keyword and defines a collection of named integer constants that are identified by string constants. For example, an enum could contain days of the week or family members. Enums improve type safety and allow integer constants to be easily maintained.
This document defines and explains key math terms:
1. It explains the order of operations as simplify inside grouping symbols, evaluate powers, multiply/divide left to right, add/subtract left to right.
2. It defines algebraic expressions as containing at least one variable, and formulas as expressing relationships between quantities.
3. It lists types of numbers including rational, irrational, natural, whole, and integers.
This document contains a series of math problems and exercises. It begins with rules for the problem set and an overview of George Polya's problem solving techniques. The bulk of the document consists of 13 math exercises involving topics like patterns, algebra, geometry, trigonometry, and calculus. Exercises are sometimes to be done individually and sometimes in groups.
Learn to solve math problems in 4 easy stepscarolllee
This document provides 4 steps to help students learn to solve math problems:
1. Practice daily by focusing on a small number of problems you understand rather than jumping to complex problems.
2. Use reference books in addition to textbooks to find more examples and practice problems.
3. Clarify any doubts with teachers the next day to avoid forgetting and develop procrastination habits.
4. Use online calculators and solvers as resources that are always available, unlike teachers or textbooks.
This document provides an overview of problem solving using computers. It discusses the 7 stages of problem solving: 1) problem analysis, 2) algorithm development, 3) flowcharting, 4) coding, 5) compilation and execution, 6) debugging and testing, and 7) documentation. It also covers computer programs, programming languages, and the basic structure of a C program, which typically includes documentation, include libraries, definitions, global declarations, the main function, and subprograms.
How To Solve A Math Problem!-new and improvedTaleese
This document outlines a 7-step process for solving math problems:
1) Read the problem carefully multiple times to understand what is being asked.
2) Identify what needs to be found and look for clues about the operation(s) needed like addition, subtraction, multiplication, or division.
3) Select an operation and numbers from the problem to try solving it. Even if incorrect, trying something is better than doing nothing.
4) Solve the problem using the selected operation and numbers.
5) Check that the answer makes logical sense.
6) Ensure any multi-part problems are fully answered.
7) Check the work by working backwards with inverse operations.
Adding Fractions
1. Adding Fractions with Common Denominators
Add the Numerators.
Keep the Denominators the same.
2. Practice time
3. Reduce or simplify if necessary…
4. Adding Fractions with Unlike Denominators
5.Find a common denominator using LCM.
Multiply numerator and denominator by LCM.
Add the converted fractions.
6. Least Common Multiple
7. We need to create fractions with like denominators in order to add these fractions. This is where we need LCM (Least Common Multiples)
8. The first common multiple is the Least Common Multiple
This will become the new denominators in order to create like denominators to add fractions.
9. Adding Fractions with Unlike Denominators
Multiples of 7: 7, 14, 21, 28
Multiples of 4: 4, 8, 12, 16, 20, 24, 28
10. Practice time
Common Multiples for these numbers:
6:
5:
What is the LCM?
11. Review
In order to add fractions, what must you have?
Explain a simplified fraction
What is an LCM?
What are LCMs used for?
Why is it important to be able to find an LCM?
Enum in C# is used to store a set of named constants such as days of the week or months. Enum constants have default integer values that increment by one, but these can be changed. Enum is declared using the enum keyword and defines a collection of named integer constants that are identified by string constants. For example, an enum could contain days of the week or family members. Enums improve type safety and allow integer constants to be easily maintained.
This document defines and explains key math terms:
1. It explains the order of operations as simplify inside grouping symbols, evaluate powers, multiply/divide left to right, add/subtract left to right.
2. It defines algebraic expressions as containing at least one variable, and formulas as expressing relationships between quantities.
3. It lists types of numbers including rational, irrational, natural, whole, and integers.
This document contains a series of math problems and exercises. It begins with rules for the problem set and an overview of George Polya's problem solving techniques. The bulk of the document consists of 13 math exercises involving topics like patterns, algebra, geometry, trigonometry, and calculus. Exercises are sometimes to be done individually and sometimes in groups.
Learn to solve math problems in 4 easy stepscarolllee
This document provides 4 steps to help students learn to solve math problems:
1. Practice daily by focusing on a small number of problems you understand rather than jumping to complex problems.
2. Use reference books in addition to textbooks to find more examples and practice problems.
3. Clarify any doubts with teachers the next day to avoid forgetting and develop procrastination habits.
4. Use online calculators and solvers as resources that are always available, unlike teachers or textbooks.
This document provides an overview of problem solving using computers. It discusses the 7 stages of problem solving: 1) problem analysis, 2) algorithm development, 3) flowcharting, 4) coding, 5) compilation and execution, 6) debugging and testing, and 7) documentation. It also covers computer programs, programming languages, and the basic structure of a C program, which typically includes documentation, include libraries, definitions, global declarations, the main function, and subprograms.
How To Solve A Math Problem!-new and improvedTaleese
This document outlines a 7-step process for solving math problems:
1) Read the problem carefully multiple times to understand what is being asked.
2) Identify what needs to be found and look for clues about the operation(s) needed like addition, subtraction, multiplication, or division.
3) Select an operation and numbers from the problem to try solving it. Even if incorrect, trying something is better than doing nothing.
4) Solve the problem using the selected operation and numbers.
5) Check that the answer makes logical sense.
6) Ensure any multi-part problems are fully answered.
7) Check the work by working backwards with inverse operations.
Adding Fractions
1. Adding Fractions with Common Denominators
Add the Numerators.
Keep the Denominators the same.
2. Practice time
3. Reduce or simplify if necessary…
4. Adding Fractions with Unlike Denominators
5.Find a common denominator using LCM.
Multiply numerator and denominator by LCM.
Add the converted fractions.
6. Least Common Multiple
7. We need to create fractions with like denominators in order to add these fractions. This is where we need LCM (Least Common Multiples)
8. The first common multiple is the Least Common Multiple
This will become the new denominators in order to create like denominators to add fractions.
9. Adding Fractions with Unlike Denominators
Multiples of 7: 7, 14, 21, 28
Multiples of 4: 4, 8, 12, 16, 20, 24, 28
10. Practice time
Common Multiples for these numbers:
6:
5:
What is the LCM?
11. Review
In order to add fractions, what must you have?
Explain a simplified fraction
What is an LCM?
What are LCMs used for?
Why is it important to be able to find an LCM?
Fractions - Add, Subtract, Multiply and Dividesondrateer
The document discusses different arithmetic operations that can be performed on fractions, including addition, subtraction, multiplication, and division. It provides examples of how to convert fractions to equivalent fractions with a common denominator to allow for addition and subtraction. For multiplication and division, it notes that fractions can be directly multiplied or divided without requiring a common denominator. Steps are demonstrated through examples for how to perform each operation on fractions.
This presentation teaches how to perform basic fraction operations:
- Adding fractions requires having a common denominator
- Subtracting and multiplying fractions also require a common denominator and use similar processes as addition and multiplication of whole numbers
- Dividing fractions involves flipping the second fraction and turning division into multiplication
- To get a common denominator when adding or subtracting, multiply the denominators and adjust the numerators proportionately
Addition is finding the total or sum of two numbers by combining them, while subtraction is taking one number away from another to find the difference between the numbers. Both addition and subtraction are basic math operations covered along with examples of adding balls and subtracting apples.
This document provides an overview of basic addition concepts including:
1) It defines addition as bringing numbers together to make a new total and provides examples of adding objects and numbers.
2) It discusses counting from 1 to 10 and using a number line to demonstrate addition.
3) It provides multiple models and strategies for teaching addition including set models, measurement models, counting upwards from a number, and using a bunny on a number line.
4) It notes other names for addition, how to add numbers with more than one digit by carrying values to the next column, and rules for addition.
Addition is the process of combining sets of items and counting the total. It is demonstrated with examples of having 2 apples and receiving 3 more for a total of 5 apples, and using 4 red apples and 2 yellow apples for a total of 6 apples needed for a pie. Addition finds the full amount when sets are joined together.
This presentation was used by me to help teachers at our community school to learn about Lesson Plans and Classroom managment. Feel free to download and use it
Ashwin Shah
This document provides tips for creating effective PowerPoint presentations. It notes that many presentations are "unbearable" due to a lack of significance, structure, simplicity, and rehearsal. It emphasizes the importance of having a clear purpose for your presentation, using a simple structure like problem-solution, keeping slides concise with minimal text and images over clipart, writing speaker notes instead of long slides for printing, and rehearsing your presentation aloud to work out any issues. The overall message is that presentations should be passionate, memorable and scalable through a focus on simplicity and clarity of message.
Financial literacy within the year 10 STEAM projectAngela Phillips
The WESThink Year 10 End of Year Project aimed to provide students with STEAM enrichment activities over 3 days in December 2017. Students chose between activities like Create Me, Run Me, Puzzle Me, Read Me, Eat Me and Grow Me led by different teachers. Due to changes in timing and regulations, students were unable to sell their products and gain financial literacy skills. Feedback showed students generally enjoyed the hands-on activities but the project did not meet its full potential for enhancing business and math skills. Lessons will be applied to improve the 2018 project.
The document outlines a planning matrix for a week-long enterprise project at a high school. Students will be assigned to groups and each group will create a product to sell at a charity fair. There are seven proposed activities for students to choose from, including developing word games, logic games, outdoor activities, artistic products, food items, and music. The project will be run and showcased at the school's WestTHINK fair. Teachers are assigned to lead each of the proposed activity groups.
Financial literacy for essential mathematics studentsAngela Phillips
The document summarizes a project where Year 10 students were divided into groups and tasked with setting up pop-up catering companies to produce and sell products for a profit. The goals were to provide experience in costing, production, marketing and sales while strengthening math and business skills. Feedback found most students enjoyed the activity but lacked financial literacy, overpaying for supplies and not understanding concepts like break-even points. While students said they learned skills like "making money", they struggled to explain specific lessons. Teachers saw slightly improved financial awareness in these students a year later and attribute this in part to the memorable experiential learning activity.
This document outlines a task for students to use trigonometry to determine the heights of various landmarks at Westminster School. Students will use a clinometer to measure the angle of elevation and distance to landmarks like the chapel, oval trees, and goal posts. Through right-angled triangle trigonometry and these measurements, students can calculate the approximate heights. The purpose is to apply mathematical concepts like trigonometry and communicate the results. Students must introduce the problem, method, apply the method by collecting data, showing work, analyzing results, and stating conclusions.
This document outlines an extended homework task on simple interest that is broken into three sections. Section A requires students to research the simple interest formula and how to use it. Section B consists of answering 10 questions using the simple interest formulas. Section C involves explaining the importance of interest rates for saving and borrowing, presenting recommendations with mathematical examples in a digital format. The document provides references for creating bibliographies and details a marking rubric for the different sections.
Year+8+extension+measurement+homework+task+blooms by kate johnsAngela Phillips
1. Students are assigned a group project to create an image with different shapes that relates mathematically to each other's images. They must decide on a theme.
2. For the individual task, each student must include examples of different shapes like a right triangle, hexagon, and other polygon. They must also include a circle with a specified area and another with a given circumference.
3. Students must show their work and calculations for finding the measurements of the required shapes within their images.
The document analyzed 12 different equations modeling the trajectory of balls hit by 12 different players. By factorizing the equations and graphing them, it was determined that none of the hits were possible as the balls would either continue upward indefinitely or go underground. Two key findings were:
1) When -1 is removed as a common factor when factorizing, the graph flips over the x-axis, changing the trajectory from upward to downward.
2) The number in front of the factored expression determines the maximum height, with larger numbers producing higher trajectories and smaller or decimal numbers producing lower trajectories closer to the ground.
1. The document investigates the type of hit required to hit a home run based on the distance from home plate to the left field wall at Fenway Park.
2. It analyzes 12 different trajectories modeled by equations to determine if the ball would reach the necessary height and distance to clear the wall.
3. Key factors that determine if a home run is possible are whether the graph of the equation heads up or down, and the maximum height reached by the ball as modeled in the equation.
The document discusses options for wand woods and magical ingredients in Harry Potter. It provides a list of houses and prefects at Hogwarts and asks to represent this information with probability diagrams and calculations. Specifically, it asks to create a two-way table for wand options, draw a tree diagram for houses and prefects with probabilities, and calculate various probabilities related to houses, prefects, wand woods, and magical ingredients.
Year 10 probability the hunger games 10 extensionAngela Phillips
The document discusses using math to analyze statistics and probabilities related to the plot of the book and movie The Hunger Games. It examines the probabilities of being selected as tributes from each district based on age, as well as the probabilities and expected outcomes of randomly selecting food and weapon packages at the start of the Hunger Games. Tables and tree diagrams are suggested to represent the mathematical relationships and calculate the various probabilities.
The document describes how equations and limits were used in FXgraph to plot the Batman logo and the word "Batman". Various types of equations including linear, quadratic, and circle equations were manipulated to create the desired lines and curves. Horizontal and vertical lines were created using y=c and x=c equations. Linear equations with one variable and quadratic equations with two variables were used to form diagonal lines and curves. Circle and arc equations were employed to draw the circular elements. Through combining these different equation types with limits, the full Batman logo and word were accurately replicated on the graph.
North Korea claims it fired a missile that reached a maximum altitude of 2,802 km and traveled 933 km in 39 minutes. An expert said that if fired on a standard trajectory rather than a lofted one, the missile could have a maximum range of 6,700 km, putting locations like Japan and Guam within its reach. The recent missile tests from North Korea have caused international concern, but this document aims to objectively analyze the missile's trajectory through mathematical modeling.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document describes an experiment that recorded the heart rate of a 16-year-old male while running over increasing time intervals. A linear model was fitted to the heart rate data, which showed a steady increase in heart rate as time increased. The linear model was used to determine when the subject's heart rate would enter different exercise zones. While the linear model provided a good initial fit, it was noted that a curved model may better capture how the heart rate increases and then plateaus with prolonged exercise. Graphing the data allowed analysis of fitness levels based on variations in key metrics like heart rate.
Fractions - Add, Subtract, Multiply and Dividesondrateer
The document discusses different arithmetic operations that can be performed on fractions, including addition, subtraction, multiplication, and division. It provides examples of how to convert fractions to equivalent fractions with a common denominator to allow for addition and subtraction. For multiplication and division, it notes that fractions can be directly multiplied or divided without requiring a common denominator. Steps are demonstrated through examples for how to perform each operation on fractions.
This presentation teaches how to perform basic fraction operations:
- Adding fractions requires having a common denominator
- Subtracting and multiplying fractions also require a common denominator and use similar processes as addition and multiplication of whole numbers
- Dividing fractions involves flipping the second fraction and turning division into multiplication
- To get a common denominator when adding or subtracting, multiply the denominators and adjust the numerators proportionately
Addition is finding the total or sum of two numbers by combining them, while subtraction is taking one number away from another to find the difference between the numbers. Both addition and subtraction are basic math operations covered along with examples of adding balls and subtracting apples.
This document provides an overview of basic addition concepts including:
1) It defines addition as bringing numbers together to make a new total and provides examples of adding objects and numbers.
2) It discusses counting from 1 to 10 and using a number line to demonstrate addition.
3) It provides multiple models and strategies for teaching addition including set models, measurement models, counting upwards from a number, and using a bunny on a number line.
4) It notes other names for addition, how to add numbers with more than one digit by carrying values to the next column, and rules for addition.
Addition is the process of combining sets of items and counting the total. It is demonstrated with examples of having 2 apples and receiving 3 more for a total of 5 apples, and using 4 red apples and 2 yellow apples for a total of 6 apples needed for a pie. Addition finds the full amount when sets are joined together.
This presentation was used by me to help teachers at our community school to learn about Lesson Plans and Classroom managment. Feel free to download and use it
Ashwin Shah
This document provides tips for creating effective PowerPoint presentations. It notes that many presentations are "unbearable" due to a lack of significance, structure, simplicity, and rehearsal. It emphasizes the importance of having a clear purpose for your presentation, using a simple structure like problem-solution, keeping slides concise with minimal text and images over clipart, writing speaker notes instead of long slides for printing, and rehearsing your presentation aloud to work out any issues. The overall message is that presentations should be passionate, memorable and scalable through a focus on simplicity and clarity of message.
Financial literacy within the year 10 STEAM projectAngela Phillips
The WESThink Year 10 End of Year Project aimed to provide students with STEAM enrichment activities over 3 days in December 2017. Students chose between activities like Create Me, Run Me, Puzzle Me, Read Me, Eat Me and Grow Me led by different teachers. Due to changes in timing and regulations, students were unable to sell their products and gain financial literacy skills. Feedback showed students generally enjoyed the hands-on activities but the project did not meet its full potential for enhancing business and math skills. Lessons will be applied to improve the 2018 project.
The document outlines a planning matrix for a week-long enterprise project at a high school. Students will be assigned to groups and each group will create a product to sell at a charity fair. There are seven proposed activities for students to choose from, including developing word games, logic games, outdoor activities, artistic products, food items, and music. The project will be run and showcased at the school's WestTHINK fair. Teachers are assigned to lead each of the proposed activity groups.
Financial literacy for essential mathematics studentsAngela Phillips
The document summarizes a project where Year 10 students were divided into groups and tasked with setting up pop-up catering companies to produce and sell products for a profit. The goals were to provide experience in costing, production, marketing and sales while strengthening math and business skills. Feedback found most students enjoyed the activity but lacked financial literacy, overpaying for supplies and not understanding concepts like break-even points. While students said they learned skills like "making money", they struggled to explain specific lessons. Teachers saw slightly improved financial awareness in these students a year later and attribute this in part to the memorable experiential learning activity.
This document outlines a task for students to use trigonometry to determine the heights of various landmarks at Westminster School. Students will use a clinometer to measure the angle of elevation and distance to landmarks like the chapel, oval trees, and goal posts. Through right-angled triangle trigonometry and these measurements, students can calculate the approximate heights. The purpose is to apply mathematical concepts like trigonometry and communicate the results. Students must introduce the problem, method, apply the method by collecting data, showing work, analyzing results, and stating conclusions.
This document outlines an extended homework task on simple interest that is broken into three sections. Section A requires students to research the simple interest formula and how to use it. Section B consists of answering 10 questions using the simple interest formulas. Section C involves explaining the importance of interest rates for saving and borrowing, presenting recommendations with mathematical examples in a digital format. The document provides references for creating bibliographies and details a marking rubric for the different sections.
Year+8+extension+measurement+homework+task+blooms by kate johnsAngela Phillips
1. Students are assigned a group project to create an image with different shapes that relates mathematically to each other's images. They must decide on a theme.
2. For the individual task, each student must include examples of different shapes like a right triangle, hexagon, and other polygon. They must also include a circle with a specified area and another with a given circumference.
3. Students must show their work and calculations for finding the measurements of the required shapes within their images.
The document analyzed 12 different equations modeling the trajectory of balls hit by 12 different players. By factorizing the equations and graphing them, it was determined that none of the hits were possible as the balls would either continue upward indefinitely or go underground. Two key findings were:
1) When -1 is removed as a common factor when factorizing, the graph flips over the x-axis, changing the trajectory from upward to downward.
2) The number in front of the factored expression determines the maximum height, with larger numbers producing higher trajectories and smaller or decimal numbers producing lower trajectories closer to the ground.
1. The document investigates the type of hit required to hit a home run based on the distance from home plate to the left field wall at Fenway Park.
2. It analyzes 12 different trajectories modeled by equations to determine if the ball would reach the necessary height and distance to clear the wall.
3. Key factors that determine if a home run is possible are whether the graph of the equation heads up or down, and the maximum height reached by the ball as modeled in the equation.
The document discusses options for wand woods and magical ingredients in Harry Potter. It provides a list of houses and prefects at Hogwarts and asks to represent this information with probability diagrams and calculations. Specifically, it asks to create a two-way table for wand options, draw a tree diagram for houses and prefects with probabilities, and calculate various probabilities related to houses, prefects, wand woods, and magical ingredients.
Year 10 probability the hunger games 10 extensionAngela Phillips
The document discusses using math to analyze statistics and probabilities related to the plot of the book and movie The Hunger Games. It examines the probabilities of being selected as tributes from each district based on age, as well as the probabilities and expected outcomes of randomly selecting food and weapon packages at the start of the Hunger Games. Tables and tree diagrams are suggested to represent the mathematical relationships and calculate the various probabilities.
The document describes how equations and limits were used in FXgraph to plot the Batman logo and the word "Batman". Various types of equations including linear, quadratic, and circle equations were manipulated to create the desired lines and curves. Horizontal and vertical lines were created using y=c and x=c equations. Linear equations with one variable and quadratic equations with two variables were used to form diagonal lines and curves. Circle and arc equations were employed to draw the circular elements. Through combining these different equation types with limits, the full Batman logo and word were accurately replicated on the graph.
North Korea claims it fired a missile that reached a maximum altitude of 2,802 km and traveled 933 km in 39 minutes. An expert said that if fired on a standard trajectory rather than a lofted one, the missile could have a maximum range of 6,700 km, putting locations like Japan and Guam within its reach. The recent missile tests from North Korea have caused international concern, but this document aims to objectively analyze the missile's trajectory through mathematical modeling.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document describes an experiment that recorded the heart rate of a 16-year-old male while running over increasing time intervals. A linear model was fitted to the heart rate data, which showed a steady increase in heart rate as time increased. The linear model was used to determine when the subject's heart rate would enter different exercise zones. While the linear model provided a good initial fit, it was noted that a curved model may better capture how the heart rate increases and then plateaus with prolonged exercise. Graphing the data allowed analysis of fitness levels based on variations in key metrics like heart rate.
Using units of measurements extended homework taskAngela Phillips
This document outlines 5 tasks for a homework assignment on units of measurement, surface area, volume, and time. The tasks involve: 1) calculating dimensions and surface area of a 1m3 prism; 2) dimensions and surface area of a 1L cylinder; 3) sketching a tank that fits a unusual 2.5m by 2m space and has an 8m2 base; 4) calculating fill times for a 40m3 tank using pumps of 10ml/s and 25ml/s; and 5) determining which tank is a better value - one that costs $10,000 and lasts 15 years or one that costs $25,000 and lasts 1900 weeks. Students are instructed to show working and assumptions
This document provides information and questions about calculating calorie and kilojoule amounts in foods and estimating the amount of exercise needed to burn off those calories/kilojoules. It includes sample word problems about two teachers eating breakfast and their different exercise routines, estimating how long it would take Lebron James to burn off the calories from a Big Mac meal by playing basketball, comparing calorie burn rates of different activities, and designing a poster advertising nutritional information in terms of exercise.
28 plenary ideas_for_mathematics by Jean KnappAngela Phillips
This document provides 27 different plenary ideas for mathematics lessons. The plenaries involve students working in pairs or small groups to discuss and summarize the key ideas from the lesson, check understanding of concepts, and reflect on their learning. Some examples include having students list things they learned and comparing with a partner, describing calculations without saying the answer for their partner to guess, and asking self-assessment questions to gauge understanding. The plenaries aim to actively involve students in reviewing and consolidating what was covered in the lesson.
1. Today I will learn to solve number problems using addition Level 3+
Today I will learn to solve number problems using addition Level 4
Extension Activity:
Make some of your own number problems like these above.