Chapter 5 Sections 1 And 2 Review
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Chapter 5, Sections 1 and 2 Review. Comparing and ordering fractions. Finding Multiples using factor trees.
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The divisibility rules for 3, 4, 6, 9, 10 are: a number is divisible by 3 if the sum of its digits is divisible by 3; a number is divisible by 4 if the last two digits are divisible by 4; a number is divisible by 6 if it is divisible by both 2 and 3; a number is divisible by 9 if the sum of its digits is divisible by 9; a number is divisible by 10 if
Math-Unit 7 Review
This document provides a summary of lessons from a 4th grade everyday math unit on fractions. It covers fraction concepts like numerators, denominators, and mixed numbers. It also discusses fractions of sets, probabilities, equivalent fractions, comparing fractions, and solving fraction word problems using manipulatives like pattern blocks and counters. Students are asked to show work solving sample fraction addition, subtraction, and equivalence questions.
Lesson 6
This document provides an overview of a mathematics lesson that teaches students to interpret division using array models. The lesson includes fluency practice with group counting and adding equal groups. Students work on an application problem involving dividing 20 children into teams of 5. They draw array models to represent different division problems, such as 15 divided by 3 equals 5 groups of 3. Students are asked to write multiplication and division sentences from the array models. The lesson concludes with students solving problems involving skip counting and relating division to the unknown factor in a multiplication equation.
Ratios And Proportions Notes
This document provides information on ratios, proportions, rates and unit analysis. It defines key terms like ratio, proportion, and rate. It provides examples of how to set up and solve proportions using the reciprocal and cross product properties. It also gives examples of unit analysis and converting between units of measurement using conversion factors.
G4ww5 8
This document provides materials for a 4th grade mathematics unit. It includes lessons, activities, practice problems and games related to fractions, data analysis, geometry, measurement, number sense, and problem solving. Some key lessons include dividing objects into halves or other fractions, collecting and graphing data, solving word problems, and playing numerical games like a dice game called "Corn Shucks." The document offers guidance for teachers on discussing concepts and assessing student understanding.
4.5 comparing fractions updated
The document contains instructions and examples for comparing fractions using the least common denominator (LCD) method. It explains how to find the LCD and write fractions with a common denominator to allow for direct comparison. Examples are provided for comparing proper, improper and mixed fractions. Students are given practice problems to order fractions from least to greatest.
Chapter 4 Review Part 2
Chapter 4 Review, Part 2: October 22, 2008 Lecture Notes. Covers Rational Numbers, Multiplying, Dividing and taking Power of a Power, Scientific Notation, and Word Problems.
Basic Math review sheet.pdf
The document provides review sheets for a basic mathematics course covering key concepts in whole numbers, fractions, decimals, and mixed numbers. It lists over 60 review questions addressing skills like operations, word problems, rounding, order of operations, exponents, prime factorization, and conversions between fractions and decimals. The purpose is to help students refresh their math skills and determine the appropriate level course to begin study.
Mth10revsheets (1)
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
Quantitative aptitude h.c.f & l.c.m
The document discusses concepts related to factors, multiples, highest common factors (HCF), and least common multiples (LCM) of numbers. It provides definitions and examples of factors, multiples, HCF, and LCM. Several examples of finding the HCF and LCM of numbers using factorization and other methods are shown. The document also presents solutions to example problems involving HCF, LCM, ratios, remainders, and word problems related to these concepts.
Ciii. lesson-4-least-common-multiple
This document discusses finding the least common multiple (LCM) of sets of numbers. It begins with examples of finding the LCM of various number pairs and sets. These examples illustrate finding the prime factors of each number and identifying the smallest number that is a multiple of all numbers as their LCM. The document then provides practice problems for readers to identify the LCM of additional number sets. It concludes by recapping that the LCM is the smallest number that is divisible by all numbers in the set.
1 ESO - UNIT 03 - DIVISIBILITY
1. This document discusses divisibility, prime numbers, and finding the highest common factor and least common multiple of numbers. It defines divisibility as being able to divide one number by another with no remainder. Prime numbers only have two factors, themselves and 1, while composite numbers have more than two factors. The highest common factor is the largest factor that is common to two or more numbers, while the least common multiple is the smallest number that is a multiple of the given numbers.
Lesson Presentation - Compare Fractions Final.pptx
This document provides success criteria for comparing fractions. It aims to teach students to: compare fractions with the same denominator by looking at the numerator; find the lowest common multiple to compare fractions with different denominators; and use common numerators to compare fraction sizes. The document contains examples and explanations of comparing fractions using these different methods in less than or equal to 3 sentences.
Understanding Fractions
This document provides an overview of fractions including definitions and classifications. It defines a fraction as the quotient of two rational numbers. Fractions are classified as proper, improper, or mixed numbers depending on the relationship between the numerator and denominator. It also discusses equivalent fractions, ordering fractions with like and unlike denominators, and methods for finding the least common multiple (LCM) to determine a common denominator for ordering fractions.
Lesson on Ratio and Proportion.pptx
1. The document provides a lesson on ratios that teaches learners to visualize, identify, write, and simplify ratios. It includes examples of counting objects to write ratios and determining if ratios are equivalent.
2. Methods taught for finding equivalent ratios include cross multiplication and multiplying the means and extremes. Rules are given for simplifying ratios, including using the greatest common factor.
3. The lesson emphasizes that ratios can be used in daily life, such as a cooking recipe, and provides an assessment with ratio questions and problems to simplify ratios.
Gcf Lcm Word Problems
The document provides information and examples about finding the greatest common factor (GCF) and least common multiple (LCM) of numbers. It defines prime numbers and factors. It then gives step-by-step instructions for finding the GCF and LCM of two numbers by writing them as products of their prime factors. Several word problems are provided as examples of when to use GCF versus LCM to solve problems involving dividing items into equal groups or determining when events will repeat at the same time again.
(7) Lesson 6.8
The document provides examples of solving two-step inequalities and writing and solving word problems as inequalities. It begins with six examples of solving two-step inequalities by combining like terms and then isolating the variable, including graphing the solution sets on number lines. The next examples involve writing and solving word problems as inequalities, such as writing an inequality to represent the number of magazine subscriptions needed to earn $35. The document concludes by reviewing the process of solving two-step inequalities.
MATH-UNIT-2-GRADE-3-LESSON-51-53 (1).pptx
The document provides instructions and examples for teaching students how to estimate quotients when dividing multi-digit numbers. It includes estimating strategies like rounding divisors, thinking of compatible numbers, and estimating answers. A variety of word problems, worksheets, and activities are presented to help students practice estimating quotients in different contexts.
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Finds the common multiples and the least common demo teach
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This document provides summaries and reviews of various books and titles. Some of the key points mentioned include:
- Reviews of books in popular series like The Raven Cycle and Slayer, noting whether they live up to expectations.
- Summaries of titles that portray important themes like mental illness, the criminal justice system, and LGBTQ stories in an underrepresented way.
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The document discusses using percentages and equations to solve percent problems. It provides examples of finding the percent, part, or whole given information about two of the quantities. It also gives examples of writing and solving equations to determine commission earned from sales, royalty amounts, and results of a survey where the part and percent are known.
Mark Up And Discount
The document discusses calculating markups and discounts for retail stores.
It provides examples of calculating markups based on a store's cost and its percentage markup. For a music store with a 67% markup, a CD that costs $10.50 would have a $6.80 markup.
It also discusses calculating discounts, with an example of a 20% discount on an item originally priced at $39.95 resulting in a sale price of $31.96 using either a two-step method or a one-step method.
The document concludes with assignment problems for the reader to complete related to these markup and discount calculations.
Percent Of Change
This document provides examples and explanations for calculating percent of increase and percent of decrease. It defines percent of change as the amount of change divided by the original amount. Several examples are given of calculating the percent of increase or decrease in different scenarios. These include finding the percent increase from 4 to 7.5 (87.5%), the annual increase in video game production from 1960 to 1990 (about 133%), and the percent decrease when a computer costs dropped from $875 to $745 (14%).
Fractions, Decimals, And Percents
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Factors & Primes
The document defines prime numbers, composite numbers, and prime factorization. It provides examples of prime and composite numbers. It then explains how to perform prime factorization by writing a number as the product of its prime factors using a factor tree method in multiple steps.
Regrouping With Subtraction
1. The document provides examples of how to solve subtraction problems using regrouping or "borrowing" when the numbers in a column cannot be directly subtracted.
2. It explains that when subtraction is not possible in one column, you can "borrow" from the column to the left by decreasing its value by 1 and increasing the value of the column directly to its right by 10.
3. This process is demonstrated through step-by-step examples of subtracting multi-digit numbers like 745 - 527 and 621 - 345.
Chapter 4 Section 9 Scientific Notation
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Ch. 4, Sec 1: Divisability and Factors
This document provides instruction on divisibility rules and factors. It begins with warm up exercises on division and multiplication. It then covers divisibility rules for numbers 2, 5, 10, 3, and 9 based on the digits in the number. Examples are provided to demonstrate applying the rules. Factors of numbers are defined as integers that fully divide into that number. Examples of finding all the factors of various numbers are given. The document concludes with a word problem about arranging choral students in rows.
Ch. 4, Sec 2: Exponents
This document provides an overview of exponents and exponential notation:
- Exponents show repeated multiplication, with the base being the factor and the exponent showing how many times the base is multiplied by itself.
- Exponential notation compactly writes repeated multiplication, such as 2^6 representing 2 x 2 x 2 x 2 x 2 x 2.
- Negative integers raised to an even power are positive, while raised to an odd power are negative.
- A word problem example calculates 10^3 = 10 x 10 x 10 = 1,000.
- Order of operations must be followed when evaluating expressions with exponents.
Pa2 3 Simplifying Algebraic Expressions
This document discusses key concepts in simplifying algebraic expressions:
1) Any expression separated by addition or subtraction is a term. A term with no variable is a constant, and any number multiplying a variable is its coefficient.
2) Terms with identical variables and exponents are like terms. To simplify an expression, like terms can be combined by adding or subtracting them.
3) An example problem walks through identifying coefficients, like terms, and constants in expressions and combining like terms using the distributive property.
Chapter 2, Section 2: Distributive Property
The document explains the distributive property, which states that multiplying a sum or difference by a number is equivalent to multiplying each term in the sum or difference by that number. It provides examples of using the distributive property to simplify multiplication problems, including with variables. It also explains using the distributive property "backwards" by first distributing and then combining like terms.
Property Of Numbers
The document discusses properties of numbers including commutative, associative, identity properties of addition and multiplication. It provides examples of applying these properties to simplify calculations mentally. Specifically, it explains that the commutative property allows changing the order of numbers when adding or multiplying, and the associative property allows changing the grouping of numbers when adding or multiplying. It also notes that the identity for addition is 0 and for multiplication is 1.
Ch.1 Sec.7 Inductive Reasoning
This document discusses inductive reasoning and the process of making conjectures based on patterns. It explains that inductive reasoning involves making observations about a pattern, forming a conjecture to describe the pattern, and writing a rule to explain the pattern. It provides examples of patterns and questions to help observe patterns and write the corresponding rules. The document also discusses using counter-examples to determine if a conjecture is correct or incorrect.
Chapter1, Sec 9 Multiplying Dividing Integers
This document summarizes rules for multiplying and dividing integers:
1) When multiplying integers with the same sign, the product is positive. When multiplying integers with different signs, the product is negative.
2) The rules for dividing integers are the same as for multiplying - a positive result for same signs, negative result for different signs. Division by zero is undefined.
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