Rev Notes A
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The document provides instructions for a partner activity called "Boards-Up!" where students will answer math equation and graphing questions by writing their answers on whiteboards and holding them up to be checked. The activity includes 10 questions involving writing equations of lines with given slopes and y-intercepts or through two given points, as well as graphing various linear equations.
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Pattern and algebra
This document outlines patterns and algebra topics for years 5 and 6, including describing, continuing, and creating patterns using fractions, decimals, whole numbers, and shapes. It also covers solving equations using multiplication, division, and order of operations (BEDMAS). Students are presented with example patterns and equations to explore.
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The document is a student's math benchmark assessment scores. It includes 3 sentences summarizing the content:
The benchmark assessment contains 5 sections on topics including radicals, simplifying radical expressions, adding and subtracting radicals, solving quadratics by completing the square, using the quadratic formula to solve equations, solving rate problems, and finding the roots of quadratic equations. The student scored 14, 11, 11, 13, and 13 points respectively on each section. The student's final score on the benchmark assessment was 20.0 out of a possible 21 points.
Multiplication and Division of Integers
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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The document provides an overview of adding integers and examples worked through step-by-step. It discusses the rules for adding integers with the same sign versus different signs. Specifically, it states that for the same sign you add the numbers and keep the sign, and for different signs you subtract the numbers and keep the sign of the number with the larger absolute value. Examples are provided to demonstrate applying these rules to evaluate integer expressions.
Absolute Value of a Number
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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The document discusses the rule for subtracting integers. The rule states that to subtract, you add the opposite. So for example, 5 - (-3) means 5 + 3, since the opposite of -3 is 3. It provides examples of subtracting integers like -5 - (-3) and -8 - (-4) using the rule. It also has practice problems for students to evaluate expressions with variables like finding a - b - (-6) when a = 8 and b = -15.
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The document is a student's math benchmark assessment scores. It includes 3 sentences summarizing the content:
The benchmark assessment contains 5 sections on topics including radicals, simplifying radical expressions, adding and subtracting radicals, solving quadratics by completing the square, using the quadratic formula to solve equations, solving rate problems, and finding the roots of quadratic equations. The student scored 14, 11, 11, 13, and 13 points respectively on each section. The student's final score on the benchmark assessment was 20.0 out of a possible 21 points.
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For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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The document provides an overview of adding integers and examples worked through step-by-step. It discusses the rules for adding integers with the same sign versus different signs. Specifically, it states that for the same sign you add the numbers and keep the sign, and for different signs you subtract the numbers and keep the sign of the number with the larger absolute value. Examples are provided to demonstrate applying these rules to evaluate integer expressions.
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For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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The document provides information about integers and inequalities:
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2. It explains the concepts of absolute value and inequalities, defining absolute value as the distance from 0 and inequality symbols.
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square and square roots
1) The document discusses squares and square roots, including definitions and properties. It defines a square number as a number that can be expressed as the product of a natural number with itself.
2) It provides examples of square numbers and explores patterns in their ones digits. Only certain digits (0,1,4,5,6,9) can end square numbers.
3) The document also covers finding square roots through prime factorization and the long division method, including examples of finding square roots of decimals. Pythagorean triplets and their relationships to squares are also discussed.
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The document introduces how to add and subtract directed numbers on a number line. It explains that if the directed numbers have the same sign, you add their values, and if they have different signs, you subtract. It provides examples of adding 6 + -3 and subtracting -4 - -9, illustrating starting at the first number on the number line and moving the corresponding number of places based on the operation and second number. The answer is found by labeling the final location.
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This document provides an overview of adding and subtracting integers. It defines a number line and absolute value. It presents rules for adding and subtracting integers, including same sign add and keep, different sign subtract, and copying the sign of the higher number. Examples are given using algebra tiles and the number line. The document concludes with an activity called "Roll to Win" that has students practice adding and subtracting integers by rolling a die and flipping a coin to determine positive or negative values.
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The document discusses square roots including:
1. Defining square roots and the radical symbol, and that the square root of a number can be positive or negative.
2. Explaining that the principal square root is always positive and how to identify squares of integers from 1 to 20.
3. Giving examples of simplifying square root expressions and identifying numbers as rational or irrational.
4. Discussing estimating square roots by finding what two consecutive integers a square root lies between.
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The document defines integers and their properties like positive and negative numbers. It introduces rules for adding and subtracting integers, such as adding numbers with the same sign and subtracting numbers with different signs. It also explains how to use a number line to demonstrate adding integers and proves that subtracting a negative number is the same as adding a positive number.
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Students will use their understanding of square numbers to evaluate square roots. Remember, square roots, quite literally mean going from square numbers, back to the root - the number which you multiplied in the first place to get the square number. Example: The square root of 49 is 7.
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1. It defines integers as the set of natural numbers, whole numbers, and their opposites, and illustrates integers on a number line.
2. It explains the concepts of absolute value and inequalities, defining absolute value as the distance from 0 and inequality symbols.
3. It provides examples of marking points on a number line, writing inequalities, and comparing integers using inequality symbols.
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The document discusses expanding and simplifying expressions within brackets. It provides examples of multiplying out terms within brackets for expressions like (2a + 3)(4a + 2) and (3b + 2)(4b - 6). The key steps are to multiply out each corresponding term, then collect like terms. Distributing negatives requires being careful about the signs of multiplied terms. The document encourages practicing expanding several example expressions within time limits to check understanding.
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1) The document shows patterns of multiples of numbers (2, 3, 4, etc.) on 6x6 grids.
2) It examines patterns in the sums of consecutive numbers, finding that sums of 3 consecutive numbers are multiples of 3, and sums of 4 consecutive numbers increase by 4s.
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Similar to Rev Notes A
November 30, 2015
The document provides an introduction and overview of inequalities for a math class. It includes:
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2) Examples of how to write inequalities using appropriate symbols (<, >, ≤, ≥) and an explanation of open vs. closed circles on a number line.
3) Steps for solving linear inequalities, with the reminder that the inequality sign must be flipped when multiplying or dividing both sides by a negative number.
4) Practice problems for students to solve and graph inequalities on a number line.
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This document contains 10 practice questions similar to those that may appear on a mastery assignment. It provides the questions, step-by-step solutions and explanations, and final answers in standard form when required. The questions cover topics such as finding the equation of a line given two points, determining if lines are parallel, perpendicular or neither, describing line graphs, finding intercepts of lines, and rewriting equations in standard form.
The real number system
John scored 17 points (4x4 + 0x1 + -1x3 = 17)
Mary scored 20 points (4x5 = 20)
Adam scored 18 points (4x4 + -1x2 = 18)
Lisa scored 30 points (4x7 + 0x1 + -1x2 = 30)
Kim scored 31 points (4x7 + 4x1 = 31)
Jenny scored 32 points (4x8 = 32)
Zack scored 27 points (4x6 + 4x1 = 27)
Amy scored 25 points (4x5 + 4x1 = 25)
The students sorted from highest to lowest scores are:
1
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This document contains notes from a math class that covered inequalities. It begins with warm-up questions involving order of operations and solving equations. It then introduces inequalities, explaining that they can have multiple solutions rather than a single value. Examples are given of inequality signs for height, drinking age, and speed limits. The rules for solving inequalities are explained, including that the inequality sign must be flipped when multiplying or dividing by a negative number. Students are provided practice problems solving and graphing inequalities on a number line.
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1. The document provides instructions for a multi-step math problem involving picking numbers, operations, and years. It has the reader choose numbers and perform calculations like multiplication, addition, subtraction on them.
2. Key steps include: picking a number 2-9, multiplying by 2 and adding 5, then multiplying the result by 50 and adding or subtracting based on whether the reader's birthday has passed for the current year.
3. The final step is to subtract the 4 digit number from the year the reader was born. The document then has some other random math questions and word problems involving indices.
Math Gr4 Ch12
The document is about algebra and graphing. It contains 12 lessons: negative numbers, finding points on a grid, graphing ordered pairs, problem-solving strategies using logical reasoning, functions, and graphing functions. The lessons include examples and practice problems related to these algebra and graphing topics.
Math Gr4 Ch12
The document is about algebra and graphing. It contains 7 lessons: negative numbers, finding points on a grid, graphing ordered pairs, problem-solving strategies using logical reasoning, functions, graphing functions, and a problem-solving investigation. Each lesson contains examples and practice problems to teach the concepts and standards covered in that lesson.
January 21, 2015
1. The document provides information on linear functions and how to determine if an equation represents a linear function. It discusses using standard form (Ax + By = C) to identify linear equations and determine intercepts.
2. The document contains examples of writing equations of lines given points and slopes in various forms. It discusses using point-slope form and converting between slope-intercept and standard form.
3. The document provides practice problems determining if graphs are functions, whether equations represent lines, finding rates of change, intercepts, and writing equations in different forms. It aims to help students work with linear functions and equations.
G8-Math-Q1-Week-5-Linear-Equations.pptx
This document discusses linear equations in two variables. It defines linear equations, shows how to determine if an equation is linear and how to write it in standard form. It also discusses solving linear equations by finding ordered pairs that satisfy the equation. Finally, it demonstrates different methods for graphing linear equations on a Cartesian plane using tables of values, x- and y-intercepts, and slope-intercept form.
4.1 notes(8th grade)
This document discusses solving inequalities using addition and subtraction. It provides examples of writing inequalities from words and graphs, as well as solving inequalities algebraically. Specifically, it shows how to write an inequality describing a speed limit of 45 mph or a child needing to be taller than 40 inches. It also demonstrates how to write inequalities from graphs and solve examples algebraically such as 9 ≥ x + 7 and -2 < y + 15, graphing the solutions.
Imaginary numbers ppt.
The document discusses imaginary numbers. Imaginary numbers are represented by i, where i = √-1. Standard form for imaginary numbers is a + bi. Rules for adding, subtracting, multiplying and dividing imaginary numbers are provided. When multiplying or dividing, terms with i must be distributed or the fraction simplified to avoid having i in the denominator. The quadratic formula can produce imaginary number solutions when the expression under the square root is negative.
Imaginary numbers ppt.
The document discusses imaginary numbers. Imaginary numbers are represented by the symbol i, where i = √-1. Standard form for imaginary numbers is a + bi. Rules for adding, subtracting, multiplying, and dividing imaginary numbers are provided. When dividing, terms cannot have i in the denominator, and the expression must be multiplied by the same term with the opposite sign. The quadratic formula can produce imaginary number solutions when the expression under the square root is negative.
Imaginary numbers ppt.
The document discusses imaginary numbers. Imaginary numbers are represented by the symbol i, where i = √-1. Standard form for imaginary numbers is a + bi. Rules for adding, subtracting, multiplying and dividing imaginary numbers are provided. When dividing, terms cannot have i in the denominator, and the expression must be multiplied by the same term with the opposite sign. The quadratic formula can produce imaginary number solutions when the expression under the square root is negative.
Imaginary numbers ppt.
The document discusses imaginary numbers. Imaginary numbers are represented by the symbol i, where i = √-1. Standard form for imaginary numbers is a + bi. Rules for adding, subtracting, multiplying, and dividing imaginary numbers are provided. When dividing, terms cannot have i in the denominator, and the expression must be multiplied by the same term with the opposite sign. The quadratic formula can produce imaginary number solutions when the expression under the square root is negative.
Solving Absolute Value Equations and Inequalities.ppt
This document provides information and examples for solving absolute value equations and inequalities. It begins with definitions of absolute value and discusses how absolute value equations can have two solutions since the expression inside the absolute value can be positive or negative. Examples are provided for solving absolute value equations by setting the expression equal to both its positive and negative values. The document also discusses how to solve absolute value inequalities by splitting them into "and" or "or" statements and provides examples of solving and graphing various absolute value inequalities.
October 21, 2013
The document provides information about inequalities:
1. It discusses the meaning of inequalities and how they differ from equations by having a range of possible solutions rather than a single solution.
2. Examples of common signs involving inequalities are presented, such as signs for minimum heights or drinking ages, and how they should be written using inequality symbols.
3. The basic rules for solving and graphing inequalities on a number line are introduced, such as using open or closed circles to represent < or ≤, and how the inequality sign must be flipped when multiplying or dividing by a negative number to maintain the relationship.
Similar to Rev Notes A (20)
Solving Absolute Value Equations and Inequalities.ppt
Solving Absolute Value Equations and Inequalities.ppt
Rev Notes A
- 1. Boards‐Up! ‐ Your goal is to answer the following questions with your partner and write your answers on your white boards. ‐ When I say "Boards Up!" you'll put your answer in the air. ‐ If it's right, you get a point; if it's wrong, you don't. ‐ For all problems, you must use the best form possible. 1. Write an equation of a line with slope of 6 and y‐intercept (0, ‐5). 2. Graph the equation y = ‐3x + 4. 3. Write an equation of a line with slope of ‐4 through (8, ‐2). 1
- 3. 3
- 4. 4
- 5. 5
- 6. Homework: pg. 402 #4, 5, 8, 9 pg. 404 #3, 9 Worksheet 6