Lesson 1 alg
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The document introduces students to different types of real numbers including subsets like rational and irrational numbers. It defines sets as collections of objects and discusses finite, infinite, empty, integer, whole, and natural number sets. Examples of rational numbers like fractions and irrational numbers like square roots are provided. Set operations like intersection and union are also introduced.
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Lesson 1
The document provides lesson notes on integers and a number line for students. It defines natural numbers, whole numbers, and integers. It asks questions about these number types and the features of a number line. Examples are given of absolute value and arranging and comparing integers on a number line. Practice problems are included for students to order and compare integers.
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The document provides examples for solving different types of equations. It explains that equalities mean that both sides are equal in value. It then works through examples of solving equations by dividing, adding/subtracting values to both sides, and setting it equal to the solution. These include equations of the form aX = b, X + c = d, and e - fX = g. The document aims to teach students how to solve various equations through worked examples.
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This lesson plan covers several basic math concepts including the Cartesian plane, distance formula, midpoint formula, slope, point-slope formula, functions, and graphs. The goals are for students to demonstrate understanding of quadrants in the Cartesian plane, distance formula, midpoint formula, slope, point-slope formula, functions, and basic graphs. For the classroom activity, the teacher plans to ask students questions about what they've learned and have students come to the board to draw graphs from equations provided.
5. absolute value , sq , sq roots
This document provides information about absolute value, square roots, and quadratic equations. It defines absolute value as the distance from zero on a number line. It explains that the absolute value of a number x is equal to x if x is positive and equal to -x if x is negative. It gives examples of finding the absolute value of different numbers. It also defines the square root as the positive value of a radical. The document provides examples of solving absolute value and quadratic equations and explains the absolute value-square root theorem, which states that the square root of a squared expression is the same as the absolute value of the expression.
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This lesson plan introduces rational numbers. It defines integers as counting numbers, their negatives, and zero. Rational numbers are defined as integers and fractions, both positive and negative. Some key properties of rational numbers are that the sum, difference, product, and quotient of rational numbers are also rational numbers. As an assignment, students are asked to prove these properties.
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Lesson 1
The document provides lesson notes on integers and a number line for students. It defines natural numbers, whole numbers, and integers. It asks questions about these number types and the features of a number line. Examples are given of absolute value and arranging and comparing integers on a number line. Practice problems are included for students to order and compare integers.
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The document provides examples for solving different types of equations. It explains that equalities mean that both sides are equal in value. It then works through examples of solving equations by dividing, adding/subtracting values to both sides, and setting it equal to the solution. These include equations of the form aX = b, X + c = d, and e - fX = g. The document aims to teach students how to solve various equations through worked examples.
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This document provides information about absolute value, square roots, and quadratic equations. It defines absolute value as the distance from zero on a number line. It explains that the absolute value of a number x is equal to x if x is positive and equal to -x if x is negative. It gives examples of finding the absolute value of different numbers. It also defines the square root as the positive value of a radical. The document provides examples of solving absolute value and quadratic equations and explains the absolute value-square root theorem, which states that the square root of a squared expression is the same as the absolute value of the expression.
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Mathematics is the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. Some key types of math discussed include:
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- Geometry - the study of shape, size, relative position of figures, and properties of space.
- Trigonometry - the computational component of geometry concerned with calculating unknown sides and angles of triangles.
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This document discusses simultaneous equations and their elimination. It defines simultaneous equations as independent equations involving the same unknown numbers. These equations can be solved by combining them to obtain a single equation with one unknown number through a process called elimination. As an example, it shows the elimination by addition of the simultaneous equations 5x - 3y = 20 and 2x + 5y = 39 to solve for x and y.
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cheeck this class 8 maths ppt in class 8 students or below can refer this ppt and make their mind map for maths. thank you
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Lesson 2 alg
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- Geometry - the study of shape, size, relative position of figures, and properties of space.
- Trigonometry - the computational component of geometry concerned with calculating unknown sides and angles of triangles.
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Prepared by:
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what is sets, rational, irrational, real and complex numbers
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Chae un simultaneous equation
The document discusses the history and methods of solving simultaneous equations, which are sets of equations that contain multiple unknown values that must be solved for at the same time. It explains that the Babylonians were using simultaneous equations as early as 1800 BC and describes the elimination and substitution methods for solving such equations, involving adding/subtracting equations or substituting a value of one unknown into the other equation. Real-life examples of simultaneous equations include air traffic control, economics, and choosing menus.
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This document discusses simultaneous equations and their elimination. It defines simultaneous equations as independent equations involving the same unknown numbers. These equations can be solved by combining them to obtain a single equation with one unknown number through a process called elimination. As an example, it shows the elimination by addition of the simultaneous equations 5x - 3y = 20 and 2x + 5y = 39 to solve for x and y.
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cheeck this class 8 maths ppt in class 8 students or below can refer this ppt and make their mind map for maths. thank you
and understant the table given in power point presentation
give me like please
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This document provides an overview of solving absolute value equations through examples of basic, intermediate, and advanced problems. It begins with definitions of absolute value and examples of basic absolute value equations. Intermediate examples show how to isolate the absolute value term and then solve the resulting simple equations. More complex advanced examples involve fractions, which are solved by clearing fractions to get a common denominator before isolating and solving the absolute value term. The goal is to build skill in solving various types of absolute value equations.
Mental computation
Mental computation focuses on students explaining their own strategies for solving problems and listening to others' explanations. This helps students learn mathematical argumentation and reasoning. It is important to record different student approaches so all can see various methods and potentially improve their own thinking. Models like empty number lines and partitioning numbers support place value understanding and mental computation. While written algorithms manipulate digits, mental computation preserves the relative value of number parts.
U5 l1 simultaneous equations
The document discusses systems of linear equations and using them to solve word problems. It introduces the concept of simultaneous equations and using variables like x and y to represent quantities in a real world scenario. As an example, it shows how to set up a system of equations to model a situation where Derek scored a total of 30 points through some combination of 2-point and 3-point shots. The solution is the ordered pair (x, y) that satisfies both equations.
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This document introduces different types of numbers including natural numbers, whole numbers, integers, and square numbers. It provides examples of each. Square numbers are defined as integers that are the square of another integer. Properties of square numbers are described, such as how the last digit is determined based on the last digit of the number being squared. Patterns with square numbers are shown, such as the sum of two consecutive triangular numbers being a square number, and the sum of the first n odd natural numbers being n squared.
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Algebra was developed as a separate section of mathematics to solve problems involving unknown numbers. In algebra, unknown numbers are represented by variables like x, allowing problems to be solved using the same addition, subtraction, etc. operations as regular arithmetic. For example, if the number of boys in a class is unknown and represented by x, we can write an equation relating x to the total number of students and known number of girls to solve for x. Algebra introduces variables like x to represent unknowns, but applies the same basic math operations as used with numbers.
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The document provides a study plan and review for a test on systems of equations and inequalities. It lists that the student spent 1428 minutes each on Khan Academy on Saturday for review. It includes a quick 6 question review on various math topics. It asks if the student has any other questions before taking the test. It provides 2 sample word problems to solve systems of equations and notifies the student that a pencil and scratch paper will be provided for the test.
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The document describes two word problems and their solutions. The first problem involves balls moving around a circle and meeting after 7 moves. The second problem involves 5 positive numbers where the sums of some numbers are known, and asks to find the largest number which is 20.
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This document provides an overview of 7 lessons in pre-algebra covering topics such as:
1) Converting between improper fractions and mixed numbers, and solving problems involving fractions.
2) Graphing lines using slope-intercept form, finding the midpoint of a line, and graphing linear equations and inequalities.
3) Calculating the mean, median, range, and mode of data sets.
4) Additional topics covered in later lessons include proportions, percentages, systems of equations, geometry, transformations, statistics, and an introduction to quadratic equations.
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This document discusses how to solve equations and inequalities. It covers topics such as: balancing equations, combining like terms, expanding brackets, rearranging formulas to change the subject, representing inequalities on number lines, and solving one-step and two-step inequalities. Examples are provided to demonstrate each concept and practice problems are included for readers to try.
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1) The document discusses two methods for solving systems of equations: setting the two equations equal to each other (Method 1), or substituting values from one equation into the other (Method 2).
2) An example problem demonstrates Method 1 to find the intersection points of the equations x2+y=4 and y=2x+1. The solutions are x=-3, y=-5 and x=1, y=3.
3) Practice problems provide opportunities to use both Method 1 and Method 2 to solve systems of equations and find their intersection points.
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This document provides an overview of solving systems of linear equations through graphing and algebra. It defines a system of equations as a set of two or more equations and describes the different types of solutions as unique (intersecting lines), inconsistent (parallel lines with no solution), or dependent (same line with infinitely many solutions). Students are given examples to solve systems of equations through both graphing and algebraic methods.
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This document provides instruction on subtracting positive and negative numbers. It begins by explaining that addition must be understood first. Positive numbers are represented by black tiles, and negative numbers by red tiles. Examples of adding positive and negative numbers are worked through. The document then covers subtracting positive numbers by relating it to addition. Finally, subtracting negative numbers is explained as being equivalent to adding a positive number of the same value. Several examples are shown step-by-step to reinforce the concepts.
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This document discusses solving one-step and two-step equations using integers. It reviews solving one-step equations by isolating the variable and provides examples such as 3x = 9 and m - 4 = 13. It then introduces solving a two-step equation involving combining like terms such as 3(x – 4)+ 6x = 51 and -4 2x -7 -1/2 = 42. The objective is to teach how to use integer rules to solve problems involving variables in one-step and two-step equations.
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This document provides lesson notes on rational numbers and equivalent fractions. The objectives are for students to identify rational numbers and find equivalent fractions. It defines different types of numbers like rational, integer, whole and natural. It demonstrates how to find equivalent fractions through multiplication or division of the numerator and denominator. It also shows how to reduce or simplify fractions using a calculator. Finally, it defines improper fractions as those where the numerator is larger than the denominator and shows how to convert improper fractions to mixed numbers.
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The lesson teaches students how to calculate the perimeter and area of different objects. It defines perimeter as the distance around an object found by adding up all the sides, and area as the surface measurement found by multiplying length by width. Students are instructed to measure their textbook, desk, and a room to practice finding the perimeter and area.
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The document provides notes on calculating square roots. It discusses square roots, radicands, and radical symbols. It lists perfect squares from 1 to 100 and their corresponding square roots. It shows how to estimate square roots that fall between whole numbers. Examples are given for adding, subtracting, and finding the side of a square based on the area.
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The document provides examples and explanations for students to practice finding fractional parts of numbers and comparing and ordering fractions. It includes examples of finding fractional parts of quantities like time, distance, amounts, and numbers of questions on tests. Students are asked to solve word problems that involve identifying fractional relationships and performing calculations with fractions.
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The document contains a series of math problems involving adding and subtracting real numbers. The problems progress from single to multiple-step operations with fractions, decimals, and negatives. Students are prompted to solve problems and then check their work. The objective is for students to practice adding and subtracting real numbers.
8th grade lesson 3
This document provides examples and practice problems for addition and subtraction word problems. It begins with notes defining key terms like increase, total, decrease, difference, and more/less than. It then gives 4 examples of word problems involving adding and subtracting amounts to find a missing value. The examples include finding points scored in the second half of a game, calculating money spent at a store, determining elevation gain from a trailhead to a summit, and figuring out the year someone was born based on their age in a given year. It concludes by posing 3 additional word problems for students to practice solving.
Lesson 2
This lesson introduces students to basic arithmetic operations like identity, commutative, and associative properties. It provides examples of applying these properties to multiplication and addition. Students are asked to simplify expressions using the different properties and solve systems of equations to find the values of variables.
Lesson 5 alg
Lesson 5 teaches students about absolute value and adding signed numbers. It explains that absolute value is the distance of a number from 0 on the number line. Students then practice calculating absolute values and adding positive and negative numbers, solving expressions both inside and outside of absolute value bars.
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This document provides a lesson on converting between different units of measurement for both customary and metric systems. It includes examples of converting between units like inches to feet, quarts to pints, centimeters to meters, and others. Students are given practice problems to convert between units for distances, areas, volumes, currencies and more. Step-by-step solutions are provided for each problem.
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Alg lesson 12
This lesson introduces students to using properties of real numbers to simplify expressions. It discusses the inverse, identity, commutative, and associative properties of addition and multiplication. Examples are provided to demonstrate the identity property of multiplication and addition, the commutative properties of multiplication and addition, and the associative properties of multiplication and addition. The objective is for students to use these properties to simplify expressions involving real numbers.
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Students will learn to subtract real numbers by understanding that adding two positive numbers results in a positive number, adding two negative numbers results in a negative number, and adding a positive and negative number requires subtracting the numbers and using the sign of the larger number. Practice problems are provided to apply these rules for subtracting real numbers.
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The document provides notes and practice problems on multiplying and dividing real numbers. It covers the following key points:
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2) Numbers can be positive or negative, and the sign of the result of multiplication or division depends on whether the signs of the numbers are the same or different.
3) Worked examples are provided to demonstrate multiplying, dividing, and evaluating expressions involving positive and negative real numbers.
Lesson 35
Students will learn to identify similar and congruent polygons. Similar polygons have the same shape but different sizes, with corresponding angles that are equal and sides that are proportional. Congruent polygons have the same shape and size, with both corresponding angles and sides that are equal. Examples are provided to demonstrate side-side-side similarity, angle-angle-angle similarity, finding missing sides, and using scale factors to determine actual lengths and widths from a drawing.
Lesson 31
Students will practice adding integers by combining like terms. Examples are provided of combining terms with variables such as adding 3x + 2 - x + 3, which combines to 2x + 3. More examples are given of combining terms with multiple variables such as x + 2y + 3x + y and 5r + 7w - 3r - 5w. The lesson reviews the concepts of terms and coefficients before practicing combining like terms with various variables.
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The document contains 5 word problems involving dividing quantities into equal groups or sets. The problems include: dividing 360 chairs into rows of 15 chairs each; dividing $28.75 cost for 5 student tickets to find the cost of each ticket; dividing 375 quarters into groups of 40 to find the number of rolls; multiplying 30 rows with 32 tiles each to find the total number of ceiling tiles; and dividing $95 cost for 4 student tickets to find the cost of each ticket. The final problem divides 632 dimes into groups of 50 to find the number of rolls.
8th lesson 8
The lesson teaches students how to calculate the perimeter and area of different objects. It defines perimeter as the distance around an object found by adding up all the sides, and area as the surface measurement found by multiplying length by width. Students are instructed to measure their textbook, desk, and a room to practice finding the perimeter and area.
8th gr lesson 9
Prime numbers are only divisible by 1 and themselves, while composite numbers can be divided into multiple factors. The document asks the reader to use tiles to represent the factorization of various numbers as either prime or composite, and determine if additional numbers provided are prime or composite as well.
Lesson 3 alg
This document provides an introduction to simplifying exponential expressions. It defines the base and exponent of a power, and gives examples of evaluating small exponential expressions. It also introduces expressions and equations, explaining that expressions are math problems without an equal sign while equations contain an equal sign.
Alg lesson 9
1) The objective is for students to evaluate algebraic expressions.
2) Examples are provided of substituting values into expressions and evaluating them.
3) Students are given practice problems evaluating expressions where values are given for variables.
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Lesson 1 alg
- 1. Lesson 1 Objective: Students will be able to identify subsets of real numbers.
- 2. Set = collection of objects Empty Set = nothing, . , o Finite Set = specific #s, 12,13,24 Infinite Set = numbers that can go on forever … 123 …
- 3. Irrational ퟑ ퟒ ퟐ 흅 .2574965 4… CRAZY Rational ½, .123123123, .75, ퟐퟓ Integers: …-3,-2,-1,0,1,2,3… (number line) Whole: 0,1,2,3… (Starts with 0) Natural: 1,2,3… (counting numbers)
- 4. 2
- 5. 5
- 6. ¾
- 7. 2휋
- 8. 0
- 9. …the value of bills in your wallet?
- 10. …the balance of a checking account
- 11. …the circumference of a circular table
- 12. Intersection of sets = same #s ∩ A = ퟐ, ퟒ, ퟔ, ퟖ, ퟏퟎ, ퟏퟐ B = ퟑ, ퟔ, ퟗ, ퟏퟐ A ∩ B = ퟔ, ퟏퟐ Union of sets = list numbers together, no repeats ∪ A = ퟐ, ퟒ, ퟔ, ퟖ, ퟏퟎ, ퟏퟐ B = ퟑ, ퟔ, ퟗ, ퟏퟐ A ∪ 푩 = ퟐ, ퟑ, ퟒ, ퟔ, ퟖ, ퟗ, ퟏퟎ, ퟏퟐ
Editor's Notes
- Now Practice, before next slide.