The document provides an overview of operations and algebraic thinking standards from kindergarten through 8th grade. It shows that in the early grades, standards focus on representing numbers, addition, subtraction and basic multiplication/division. In later grades, standards expand the scope of numbers and introduce concepts like ratios, proportions, expressions and patterns. Students are expected to apply mathematical operations to increasingly complex word problems and equations over time.
This document provides a curriculum map for 8th grade mathematics for the first quarter. Students will develop an understanding of irrational numbers by approximating them with rational numbers. They will use square roots and cube roots to solve equations. Students will also apply the Pythagorean theorem and its converse to solve problems involving right triangles. Additionally, they will learn to solve linear equations with rational number coefficients.
This document provides the Texas Essential Knowledge and Skills (TEKS) for mathematics in middle school (grades 6-8). It outlines the key concepts and skills students should master in each grade level, including number operations, algebraic thinking, geometry, measurement, probability, statistics, and problem solving. The TEKS ensure students build foundational math understanding and make connections within and outside of mathematics.
The document discusses understanding the TEKS (Texas Essential Knowledge and Skills) standards to identify gaps in curriculum. It explains how to analyze specific TEKS objectives to determine the depth of thinking, content, and context of a lesson. Key aspects to identify include the cognitive verbs, concepts, and context based on the TEKS objective. Together this informs the design, content, and assessment of the lesson to ensure all parts of the TEKS are taught. Examples from a math TEKS on volume are provided to demonstrate this process.
The document discusses hands-on math activities for kindergarten students focusing on number sense, patterns, and algebraic thinking. It describes activities using manipulatives to help students represent, compare, and order numbers. Other activities address identifying, duplicating, and extending patterns using objects. The document emphasizes building foundations for algebraic concepts like functions through concrete experiences with patterns, relationships between numbers, and using math language.
1) The document provides a mathematics curriculum guide for first grade addition, subtraction, and number systems. It outlines big ideas, essential questions, unit vocabulary, and Arizona state standards to be covered.
2) Key concepts include counting quantities, comparing numbers, and composing and decomposing numbers. Students will learn strategies for addition and subtraction word problems involving combining, separating, and comparing quantities.
3) The guide provides examples and explanations for how students can use objects, drawings, and equations to represent addition and subtraction word problems involving unknown values in different positions. It emphasizes developing fluency with addition and subtraction facts to 10.
- Students with number sense have an awareness of numbers and their relationships, intuition about magnitudes, understanding of equivalence and operations.
- The document outlines critical areas of focus in number and operations for kindergarten through second grade including counting, addition, subtraction, place value and measurement.
- Developing number sense in the early grades is important for later mathematics achievement including fluency with addition and subtraction facts.
Number sense involves understanding numbers and their relationships rather than just following algorithms. It has five key components and is important for skills like mental math, estimation, and problem solving. Developing number sense requires experiences with counting, magnitude, operations, and referents for quantities using a variety of manipulatives and representations.
This document provides a curriculum map for 8th grade mathematics for the first quarter. Students will develop an understanding of irrational numbers by approximating them with rational numbers. They will use square roots and cube roots to solve equations. Students will also apply the Pythagorean theorem and its converse to solve problems involving right triangles. Additionally, they will learn to solve linear equations with rational number coefficients.
This document provides the Texas Essential Knowledge and Skills (TEKS) for mathematics in middle school (grades 6-8). It outlines the key concepts and skills students should master in each grade level, including number operations, algebraic thinking, geometry, measurement, probability, statistics, and problem solving. The TEKS ensure students build foundational math understanding and make connections within and outside of mathematics.
The document discusses understanding the TEKS (Texas Essential Knowledge and Skills) standards to identify gaps in curriculum. It explains how to analyze specific TEKS objectives to determine the depth of thinking, content, and context of a lesson. Key aspects to identify include the cognitive verbs, concepts, and context based on the TEKS objective. Together this informs the design, content, and assessment of the lesson to ensure all parts of the TEKS are taught. Examples from a math TEKS on volume are provided to demonstrate this process.
The document discusses hands-on math activities for kindergarten students focusing on number sense, patterns, and algebraic thinking. It describes activities using manipulatives to help students represent, compare, and order numbers. Other activities address identifying, duplicating, and extending patterns using objects. The document emphasizes building foundations for algebraic concepts like functions through concrete experiences with patterns, relationships between numbers, and using math language.
1) The document provides a mathematics curriculum guide for first grade addition, subtraction, and number systems. It outlines big ideas, essential questions, unit vocabulary, and Arizona state standards to be covered.
2) Key concepts include counting quantities, comparing numbers, and composing and decomposing numbers. Students will learn strategies for addition and subtraction word problems involving combining, separating, and comparing quantities.
3) The guide provides examples and explanations for how students can use objects, drawings, and equations to represent addition and subtraction word problems involving unknown values in different positions. It emphasizes developing fluency with addition and subtraction facts to 10.
- Students with number sense have an awareness of numbers and their relationships, intuition about magnitudes, understanding of equivalence and operations.
- The document outlines critical areas of focus in number and operations for kindergarten through second grade including counting, addition, subtraction, place value and measurement.
- Developing number sense in the early grades is important for later mathematics achievement including fluency with addition and subtraction facts.
Number sense involves understanding numbers and their relationships rather than just following algorithms. It has five key components and is important for skills like mental math, estimation, and problem solving. Developing number sense requires experiences with counting, magnitude, operations, and referents for quantities using a variety of manipulatives and representations.
Developing Number Concepts in K-2 Learnersmflaming
This document discusses developing number sense in students and outlines several key building blocks or components of number sense, including rote counting, one-to-one correspondence, subitizing, tens frames, keeping track, conservation of number, hierarchical inclusion, compensation, part-whole relationships, unitizing/place value, and relationships between operations. It provides definitions and examples for each concept and suggests they take time and experience to build. A numerically powerful child can decompose numbers flexibly, understand relationships between numbers and operations, and connect numerals to real-life situations.
CPPS Gr 4 Math Pacing Guide EnNY state standardsBob Fidler
This document provides a grade 4 math pacing guide for Comstock Park Public Schools. It outlines 7 modules to be covered over the school year, with each module lasting approximately 25 days. Module 1 focuses on place value, rounding, and algorithms for addition and subtraction of multi-digit whole numbers. Each module includes state standards, major topics, lessons, and assessments. The pacing guide provides an overview of the essential math content and skills to be taught at each grade level.
The new national curriculum in England introduced in 2014 raises expectations and standards such that children in year 4 are now expected to be working at the same level as year 5 students previously. The document outlines the key areas and objectives covered in the year 4 curriculum including higher level objectives in number, calculation, geometry, measurement, fractions and decimals. It also describes the structure of math lessons and focus on developing mental math skills daily.
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
This lesson introduces students to the relationship between addition and subtraction using tape diagrams and algebraic expressions. Students represent addition and subtraction expressions using tape diagrams with squares and explore how adding and then subtracting the same number results in the original amount. They realize this is true regardless of the specific numbers used. Students then write number sentences with variables to represent these identities, like w + x - x = w. The lesson aims to build students' understanding that identities will be true for any numbers substituted into the variables.
This document provides a lesson on the concept of opposites of numbers. It includes:
1) An opening exercise asking students to identify relationships between sets of opposites words.
2) Examples of locating numbers and their opposites on a number line. The key points are that opposites are the same distance from zero but on opposite sides, and zero is its own opposite.
3) A word problem example modeling a real-world situation involving opposites on a number line, with questions to discuss the representation.
The lesson emphasizes that opposites are equidistant from zero but on opposite sides, and that zero represents the point of reference or no change in various contexts.
Number sense refers to an intuitive understanding of numbers and their relationships. It develops through exploring numbers in various contexts and relating them in flexible ways. The document discusses key components of number sense development in early grades, including prenumber concepts like patterning and sorting, counting principles like one-to-one correspondence and cardinality, rational counting strategies, and understanding relationships among numbers through benchmarks and part-whole relationships. Effective instruction focuses on developing these foundations of number sense through clear models, guided practice, and review.
Writing and solving equations can be abstract and confusing for students. Learn nonconventional ways to encourage flexible thinking and develop a deeper understanding of inverse relationships, fact families, and variables representation. Walk away with three easy-to-use activities to expand students' toolkit for solving equations.
This document provides information about Advanced Math I and II summer school courses for rising 6th and 7th grade students. It outlines the eligibility requirements, placement criteria, curriculum topics, and contact information. Students have the option to take the courses online or in-class. The curriculum covers advanced topics in number and operations, computation, measurement, geometry, probability, statistics, patterns/functions, and algebra. Students who successfully complete the courses will be placed in a higher-level math class for the upcoming school year.
The document is a curriculum guide for 4th grade mathematics that outlines the key concepts and standards for Unit 1 on factors, multiples, and arrays involving multiplication and division. The unit focuses on helping students understand relationships between multiplication and division and strategies for solving word problems using the four operations. It provides examples of how students can find factor pairs, determine if numbers are multiples, and identify prime and composite numbers between 1-100. The unit aims to build students' abstract reasoning skills and ability to model mathematical concepts.
This document provides an overview of key concepts in algebra including:
- Evaluating algebraic expressions and using variables, formulas, and mathematical models.
- Foundational concepts of sets such as intersections, unions, and subsets of real numbers.
- Properties and applications of real numbers including the number line, inequalities, absolute value, and distance.
- Simplifying algebraic expressions by combining like terms.
This document provides a lesson on positive and negative numbers on the number line. It begins with an opening exercise reviewing number lines numbered 0-10. Students then construct number lines using a compass to locate positive and negative whole numbers. The lesson defines the opposite of a number as being on the other side of 0 and being the same distance from 0. Examples are used to demonstrate locating positive and negative numbers on horizontal and vertical number lines. Students work in groups to locate given numbers and their opposites on number lines.
The document provides an overview of the fourth grade mathematics curriculum for Unit 8 on multiplication and division. It includes 3 key ideas: that there are multiple strategies for multiplying and dividing whole numbers, that multiplication and division are related, and that learning these skills has value. The unit covers multiplying up to 4-digit numbers by 1-digit numbers and dividing up to 4-digit dividends by 1-digit divisors. Students will represent and solve multi-step word problems involving all four operations. They will also generate and analyze number patterns that follow given rules.
This document introduces continued fraction expansions by discussing rational approximations of real numbers using the mediant, or Farey sum, of two fractions. It describes an activity where students explore continued fractions by drawing and analyzing paths on a Farey diagram, which represents rational numbers as endpoints. The activity aims to reinforce fraction addition and introduce patterns in continued fractions that relate to operations on the path endpoints.
This document discusses math standards, curriculum, and assessment at Canterbury School. It compares the school's math curriculum, which is based on national standards and specific math content, to the Educational Records Bureau (ERB) test, which measures math proficiency. Graphs show Canterbury students significantly outperforming national norms in grades 5-8 on the ERB assessments in number systems, geometry, and statistics. The document concludes the school's strong alignment of standards-based content and curriculum taught by excellent teachers results in well-prepared math students.
Students will learn about decimals including:
- Understanding place value of decimals and comparing decimal values
- Performing computations of addition, subtraction, multiplication and division of decimals
- Solving problems involving combined operations with decimals
Key points include representing decimals on a number line, using calculators to explore decimals, and limiting operations to no more than three decimal numbers. Students will be able to perform calculations and solve real-world problems involving decimals.
This curriculum map outlines the essential concepts, skills, activities, and assessments for 3rd grade mathematics over the school year. From September to October, students will learn addition and subtraction of 3-digit numbers through strategies like rounding, estimating, and regrouping. From October to December, the focus is on multiplication and division, including interpreting situations, properties, and solving word problems. Students will also learn to measure area from December to January by finding the area of rectangles and composing figures. Fractions will be covered from January to March, where students will describe, compare, and represent fractions. Finally, measurement and data will be addressed in two parts, with graphing and data displayed covered from March to April, and geometry and
Algebraic thinking involves recognizing patterns, modeling situations with symbols, and analyzing change. It relies on understanding variables to represent unknown quantities. The document traces the evolution of algebraic thinking from simple equations to more complex concepts like functions, composite functions, and properties of equations. It provides examples of how algebraic reasoning and symbols can be used to represent and solve real-world problems.
1. The document discusses the importance of integrating thinking across subjects using conceptual lenses to facilitate deeper understanding and knowledge transfer.
2. It provides examples of conceptual lenses like conflict, complexity, and systems that can be applied across topics to engage students at higher cognitive levels.
3. The integration of thinking involves using conceptual lenses to make connections between factual information and broader concepts, allowing students to develop generalizations and enduring understandings.
The document outlines the five strands of the National Council of Teachers of Mathematics (NCTM): Number and Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability. It then provides more details on the four process standards within the Algebra strand: understanding patterns and relationships, representing and analyzing mathematical situations, using mathematical models, and analyzing change.
Developing Number Concepts in K-2 Learnersmflaming
This document discusses developing number sense in students and outlines several key building blocks or components of number sense, including rote counting, one-to-one correspondence, subitizing, tens frames, keeping track, conservation of number, hierarchical inclusion, compensation, part-whole relationships, unitizing/place value, and relationships between operations. It provides definitions and examples for each concept and suggests they take time and experience to build. A numerically powerful child can decompose numbers flexibly, understand relationships between numbers and operations, and connect numerals to real-life situations.
CPPS Gr 4 Math Pacing Guide EnNY state standardsBob Fidler
This document provides a grade 4 math pacing guide for Comstock Park Public Schools. It outlines 7 modules to be covered over the school year, with each module lasting approximately 25 days. Module 1 focuses on place value, rounding, and algorithms for addition and subtraction of multi-digit whole numbers. Each module includes state standards, major topics, lessons, and assessments. The pacing guide provides an overview of the essential math content and skills to be taught at each grade level.
The new national curriculum in England introduced in 2014 raises expectations and standards such that children in year 4 are now expected to be working at the same level as year 5 students previously. The document outlines the key areas and objectives covered in the year 4 curriculum including higher level objectives in number, calculation, geometry, measurement, fractions and decimals. It also describes the structure of math lessons and focus on developing mental math skills daily.
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
This lesson introduces students to the relationship between addition and subtraction using tape diagrams and algebraic expressions. Students represent addition and subtraction expressions using tape diagrams with squares and explore how adding and then subtracting the same number results in the original amount. They realize this is true regardless of the specific numbers used. Students then write number sentences with variables to represent these identities, like w + x - x = w. The lesson aims to build students' understanding that identities will be true for any numbers substituted into the variables.
This document provides a lesson on the concept of opposites of numbers. It includes:
1) An opening exercise asking students to identify relationships between sets of opposites words.
2) Examples of locating numbers and their opposites on a number line. The key points are that opposites are the same distance from zero but on opposite sides, and zero is its own opposite.
3) A word problem example modeling a real-world situation involving opposites on a number line, with questions to discuss the representation.
The lesson emphasizes that opposites are equidistant from zero but on opposite sides, and that zero represents the point of reference or no change in various contexts.
Number sense refers to an intuitive understanding of numbers and their relationships. It develops through exploring numbers in various contexts and relating them in flexible ways. The document discusses key components of number sense development in early grades, including prenumber concepts like patterning and sorting, counting principles like one-to-one correspondence and cardinality, rational counting strategies, and understanding relationships among numbers through benchmarks and part-whole relationships. Effective instruction focuses on developing these foundations of number sense through clear models, guided practice, and review.
Writing and solving equations can be abstract and confusing for students. Learn nonconventional ways to encourage flexible thinking and develop a deeper understanding of inverse relationships, fact families, and variables representation. Walk away with three easy-to-use activities to expand students' toolkit for solving equations.
This document provides information about Advanced Math I and II summer school courses for rising 6th and 7th grade students. It outlines the eligibility requirements, placement criteria, curriculum topics, and contact information. Students have the option to take the courses online or in-class. The curriculum covers advanced topics in number and operations, computation, measurement, geometry, probability, statistics, patterns/functions, and algebra. Students who successfully complete the courses will be placed in a higher-level math class for the upcoming school year.
The document is a curriculum guide for 4th grade mathematics that outlines the key concepts and standards for Unit 1 on factors, multiples, and arrays involving multiplication and division. The unit focuses on helping students understand relationships between multiplication and division and strategies for solving word problems using the four operations. It provides examples of how students can find factor pairs, determine if numbers are multiples, and identify prime and composite numbers between 1-100. The unit aims to build students' abstract reasoning skills and ability to model mathematical concepts.
This document provides an overview of key concepts in algebra including:
- Evaluating algebraic expressions and using variables, formulas, and mathematical models.
- Foundational concepts of sets such as intersections, unions, and subsets of real numbers.
- Properties and applications of real numbers including the number line, inequalities, absolute value, and distance.
- Simplifying algebraic expressions by combining like terms.
This document provides a lesson on positive and negative numbers on the number line. It begins with an opening exercise reviewing number lines numbered 0-10. Students then construct number lines using a compass to locate positive and negative whole numbers. The lesson defines the opposite of a number as being on the other side of 0 and being the same distance from 0. Examples are used to demonstrate locating positive and negative numbers on horizontal and vertical number lines. Students work in groups to locate given numbers and their opposites on number lines.
The document provides an overview of the fourth grade mathematics curriculum for Unit 8 on multiplication and division. It includes 3 key ideas: that there are multiple strategies for multiplying and dividing whole numbers, that multiplication and division are related, and that learning these skills has value. The unit covers multiplying up to 4-digit numbers by 1-digit numbers and dividing up to 4-digit dividends by 1-digit divisors. Students will represent and solve multi-step word problems involving all four operations. They will also generate and analyze number patterns that follow given rules.
This document introduces continued fraction expansions by discussing rational approximations of real numbers using the mediant, or Farey sum, of two fractions. It describes an activity where students explore continued fractions by drawing and analyzing paths on a Farey diagram, which represents rational numbers as endpoints. The activity aims to reinforce fraction addition and introduce patterns in continued fractions that relate to operations on the path endpoints.
This document discusses math standards, curriculum, and assessment at Canterbury School. It compares the school's math curriculum, which is based on national standards and specific math content, to the Educational Records Bureau (ERB) test, which measures math proficiency. Graphs show Canterbury students significantly outperforming national norms in grades 5-8 on the ERB assessments in number systems, geometry, and statistics. The document concludes the school's strong alignment of standards-based content and curriculum taught by excellent teachers results in well-prepared math students.
Students will learn about decimals including:
- Understanding place value of decimals and comparing decimal values
- Performing computations of addition, subtraction, multiplication and division of decimals
- Solving problems involving combined operations with decimals
Key points include representing decimals on a number line, using calculators to explore decimals, and limiting operations to no more than three decimal numbers. Students will be able to perform calculations and solve real-world problems involving decimals.
This curriculum map outlines the essential concepts, skills, activities, and assessments for 3rd grade mathematics over the school year. From September to October, students will learn addition and subtraction of 3-digit numbers through strategies like rounding, estimating, and regrouping. From October to December, the focus is on multiplication and division, including interpreting situations, properties, and solving word problems. Students will also learn to measure area from December to January by finding the area of rectangles and composing figures. Fractions will be covered from January to March, where students will describe, compare, and represent fractions. Finally, measurement and data will be addressed in two parts, with graphing and data displayed covered from March to April, and geometry and
Algebraic thinking involves recognizing patterns, modeling situations with symbols, and analyzing change. It relies on understanding variables to represent unknown quantities. The document traces the evolution of algebraic thinking from simple equations to more complex concepts like functions, composite functions, and properties of equations. It provides examples of how algebraic reasoning and symbols can be used to represent and solve real-world problems.
1. The document discusses the importance of integrating thinking across subjects using conceptual lenses to facilitate deeper understanding and knowledge transfer.
2. It provides examples of conceptual lenses like conflict, complexity, and systems that can be applied across topics to engage students at higher cognitive levels.
3. The integration of thinking involves using conceptual lenses to make connections between factual information and broader concepts, allowing students to develop generalizations and enduring understandings.
The document outlines the five strands of the National Council of Teachers of Mathematics (NCTM): Number and Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability. It then provides more details on the four process standards within the Algebra strand: understanding patterns and relationships, representing and analyzing mathematical situations, using mathematical models, and analyzing change.
Concept: The document discusses teaching algebra concepts to primary school students.
Skill: Students learn algebra through understanding patterns, relationships, and using concrete materials to represent abstract concepts.
Strategy: It is important for students to fully understand underlying concepts before moving to skills and strategies. Teachers should ensure students are confident in concepts through visual and hands-on learning before having them calculate abstract problems.
This document proposes redefining geometry and algebra education for secondary students using contemporary approaches. It suggests incorporating hands-on experiences with 3D shapes, interdisciplinary applications, and technology like graphing software. Formal proofs could be redefined through synthetic, analytic, and transformational perspectives. Contemporary geometry could introduce inductive and deductive reasoning visually. Algebra education should emphasize relationships between quantities through multiple representations like numeric, symbolic, and graphical forms. Technology can help students generalize relationships and solve various equation types, supporting 21st century workforce skills.
The document is a lesson plan on investigating patterns in algebra. It introduces key vocabulary terms like variable, term, coefficient, constant, and pattern. Students are asked to match these vocabulary words to algebraic representations. The lesson objective is for students to investigate patterns using algebraic tables, expressions, and equations. An example is given of a table to track water lost over time in drops to represent a pattern algebraically. An exit ticket asks students to reflect on what new skills they learned.
Scientix 8th SPNE Brussels 16 October 2015: Functional thinking in students a...Brussels, Belgium
Presentation of the project "Functional thinking in students at elementary education as an approximation to algebraic thinking"- Spain, held during the 8th Science Projects' Networking Event, Brussels, 16 October 2015
The document discusses strategies for promoting algebraic thinking. It presents an activity using M&Ms to model decay, describes using tiles to model functions, and discusses using spreadsheets to model relationships. Spreadsheets allow students to explore concepts through algebraic, tabular, and graphical representations. The document emphasizes that multiple representations give students powerful tools for success in mathematics.
This document summarizes key concepts about proportional reasoning. It defines proportional reasoning as a mathematical relationship between two quantities that involves a constant multiplicative relationship. It discusses proportional reasoning as developing between concrete and formal operations. It also provides examples of using proportional relationships to solve problems and discusses research on how to best teach proportional reasoning concepts to students.
This document discusses research on the relationship between students' understanding of fractions and their algebraic thinking. It describes studies that gave students fraction and algebra tasks to solve and analyzed their solutions. Some students used verbal explanations, pronumerals, or scaling fractions and whole numbers in parallel to solve fraction tasks. These flexible approaches to fractions predict stronger algebraic thinking. The document concludes that aspects like operating on fractions, understanding equivalence, and using multiplicative methods are essential for algebra success.
This document outlines algebra and pattern skills for years 5 and 6. For year 5, it includes describing patterns using words, numbers and symbols, continuing patterns for at least 5 steps, and finding unknown quantities in multiplication and division number sentences. For year 6, it adds describing patterns using rules, using order of operations to solve number sentences, and writing number sentences that apply order of operations rules. It provides examples of patterns using fractions, decimals, whole numbers and shapes, as well as solving equations and finding quotients.
Student Teaching Cooperative Learning Group Lesson Plan (Math)Joy Hoffman
This document provides a lesson plan for a 1st grade math class. The objectives are for students to sort dominoes by their total and write number models. Students will play a parking lot game using dominoes to fill number spots from 0-12, and write addition number models for each. Procedures include introducing the game, having students play in groups while the recorder writes number models, and reviewing as a class. Student understanding will be evaluated through class discussion and completed number model sheets.
The document describes activities that a classroom did to practice making repeating patterns. The students used connecting blocks, drew around shapes, used sticks and colored straws, and beads to create patterns. They listed examples of patterns they made using colors like red, yellow, blue and green in a repeating order. The students enjoyed making patterns in different ways, including on an iPad, and links to online pattern activities are provided.
The document provides examples and explanations of arithmetic and geometric sequences. It defines an arithmetic sequence as one where the difference between consecutive terms is constant, and a geometric sequence as one where the ratio between consecutive terms is constant. Examples are given to demonstrate identifying whether a sequence is arithmetic or geometric and calculating the common difference or ratio. Students are given practice problems to determine if sequences are arithmetic, geometric, or neither, and to write the next three terms. A reflection question asks to identify the non-matching sequence type from options given.
Applications and Generalizations of Goursat's Lemma PosterCaridad Arroyo
The document discusses attempts to generalize Goursat's Lemma to find the subgroups of the direct product of more than two groups. It explains how applying the lemma recursively becomes convoluted for more than two groups. The authors examined applying the lemma to the direct product of three groups but were unable to find a generalization that would create an isomorphism using coset representatives to describe all subgroups.
1. The document contains a math review game in Jeopardy format for 1st grade students covering topics like counting to 100, skip counting, identifying even and odd numbers, adding 3 numbers, numbers before and after other numbers.
2. The Jeopardy game is divided into different dollar amount questions ($100, $200, $300, $400, $500) and includes a Final Jeopardy question.
3. The questions test the students on skills like counting forward and backward, identifying patterns in skip counting, determining if numbers are even or odd, and performing addition problems.
1. Flightless birds have different uses for their wings such as swimming, flapping to scare enemies, or using them like rudders when running.
2. Ant colonies are divided into different groups including worker ants, soldier ants, and a queen ant, each with different roles to support the colony.
3. Allergies can cause a range of reactions in people from mild to severe and sometimes deadly, as the immune system overreacts to otherwise harmless substances.
The document provides information about a first grade math unit on subtraction from The Moffatt Girls math curriculum. It includes the standards covered in Unit 3, which focus on subtraction within 20, properties of operations, fluency with addition and subtraction within 10, the meaning of the equal sign, and solving word problems. It describes the unit's NO PREP practice pages and math centers to provide practice and application of skills in an engaging way. Pictures show examples of the practice pages and centers being used in the classroom.
The document summarizes the Kindergarten Kentucky Core Academic Standards for mathematics. It outlines two critical areas of instruction: (1) representing, relating, and operating on whole numbers using objects, and (2) describing shapes and space using geometric ideas and vocabulary. More time should be spent on number concepts than other topics. The standards also describe mathematical practices students should develop, such as problem solving, reasoning, communication, and making connections.
These are the unpacking documents to better help you understand the expectations for 1st grade students under the Common Core State Standards for Math. The example problems are great.
The document summarizes the key aspects of the Common Core State Standards for mathematics. It describes the development and adoption process, benefits for states, characteristics of the standards, and their focus on coherence, clarity, and rigor. It also provides examples of the mathematical practices and standards format for different grade levels.
A Problem Solving Approach To Mathematics For Elementary School TeachersKimberly Pulley
The document summarizes key concepts about addition and subtraction of whole numbers:
1) It defines addition of whole numbers using set models and as the union of two disjoint finite sets. The sum is the cardinal number of the combined set.
2) It describes the number line model for addition, showing how to represent addends as vectors on the number line and find their sum.
3) It defines less than and greater than relations using the number line, and discusses ordering whole numbers.
4) It introduces important properties of whole number addition, including closure, commutativity, associativity, and the identity property.
This document discusses integrating writing into mathematics instruction. It provides math and writing standards for 8th grade related to operations, measurement, algebra, and writing quality. It then gives an example of how to calculate the area of a rectangle by multiplying length by width. It models writing the steps and includes a student example. Finally, it provides a rubric for assessing written responses in math and discusses positives and negatives of integrating writing.
The document provides an outline for a teaching week on functional mathematics for year 7 students. It includes topics such as numbers, fractions, decimals, measurement, and area/perimeter. The topics and outcomes are listed along with instructional approaches and strategies using examples, activities, and resources to explain key concepts in numbers, operations, and measurement.
The document provides an overview of topics and learning outcomes for a 7th grade functional mathematics teaching week. It includes instruction on:
1. Numbers - reading, writing, representing, and comparing numbers up to millions.
2. Fractions - representing, comparing, adding, and subtracting fractions.
3. Combined operations - performing multi-step calculations involving addition, subtraction, multiplication, and division.
The document outlines instructional approaches and strategies as well as recommended resources for teaching each topic.
X professional learning_communities_presentation_6-27-11vroule
The document discusses professional learning communities (PLCs) and their key components, including teacher collaboration, common curricula, common assessments, and a focus on student learning. It provides examples of PLC accomplishments in a school district, including developing common curricula, learning outcomes, assessments, and analyzing assessment results at different grade levels. Specific progress examples include lists of annual learning outcomes in elementary math, sample unit-level outcomes for middle school subjects, and an analysis of a common assessment in middle school science.
This document provides an overview of high school math concepts related to rational numbers and fractions, as outlined in the Common Core State Standards. It includes:
1) A breakdown and comparison of specific standards for The Real Number System (N-RN) and Arithmetic with Polynomials and Rational Expressions (A-APR) and their alignment with Washington Performance Expectations.
2) Examples of common student misconceptions related to these standards and potential resources to address them.
3) Sample problems and online lessons for practicing skills such as rewriting expressions with rational exponents, adding and multiplying rational expressions, and creating equations to represent real-world situations.
This document contains a daily lesson log for a 7th grade mathematics class. The lesson covers algebraic expressions, properties of real numbers, linear equations, and inequalities in one variable. The lesson objectives are to differentiate between equations and inequalities, illustrate linear equations and inequalities, and find solutions to linear equations and inequalities. The lesson content includes differentiating equations and inequalities, linear equations and inequalities in one variable, and solving linear equations and inequalities. Learning resources and procedures are outlined for reviewing concepts, examples, practice, and application. Formative assessments are used to check student understanding.
This document provides an overview of the 5th grade mathematics standards for North Carolina related to the Common Core. It is intended to help educators understand what students are expected to know and be able to do under the new standards. The document explains that the standards describe the essential knowledge and skills students should master in order to be prepared for 6th grade. It also provides examples for how the standards can be unpacked to clarify their meaning and intent. Educators are encouraged to provide feedback to help improve the usefulness of the document.
The document is a daily lesson log for a 7th grade mathematics class covering algebraic expressions. It includes the objectives, content, procedures, and resources for lessons on translating phrases, algebraic expressions, classifying polynomials, and laws of exponents. The lessons introduce key concepts such as constants, variables, coefficients, terms, polynomials, monomials, binomials, and trinomials. Students practice skills like translating phrases, identifying algebraic components, classifying polynomials, and working with exponents. Formative assessments are used to check understanding of these essential algebraic concepts.
This document outlines an agenda for a presentation on teaching hands-on algebra to early grades. It discusses defining algebra, investigating patterns, variables and equations, functions, and assessing algebraic concepts. Activities are suggested to help students work with patterns, variables, equations, and functions in a concrete manner to build understanding before introducing symbolic representations. The goal is to develop algebraic reasoning and representation skills from an early age.
This document provides an overview of the 6th-8th grade Virginia SOLs and Common Core State Standards for mathematics. It summarizes the key focuses and differences between the two sets of standards, including their approaches to problem solving, use of technology, and emphasis on different mathematical concepts across grades 6-8 such as foundations of algebra, rational numbers, and geometric properties. The document also includes perspectives on the benefits and drawbacks of each set of standards.
These are the unpacking documents to better help you understand the expectations for Kindergartenstudents under the Common Core State Standards for Math.
The document provides an overview of effective instructional strategies for teaching the Common Core State Standards for Mathematics, including focusing instruction where the standards focus, thinking across grades and topics to promote coherence, and pursuing conceptual understanding, skill and fluency, and application of mathematical concepts. It discusses the three shifts in instruction required by the CCSS and examples of how to implement tasks, scaffolding, modeling and other strategies to develop students' mathematical understanding and skills.
The document outlines the conceptual framework and pedagogical approaches of the Philippines K-12 mathematics curriculum. It describes the twin goals of critical thinking and problem solving. It also explains the spiral approach where mathematical concepts increase in depth and breadth as students progress through grades, ensuring a seamless transition in learning.
The document provides guidance for a kindergarten mathematics curriculum unit on classroom routines and counting. It outlines big ideas, essential questions, unit vocabulary, Arizona state math standards, and explanations for counting to 100, writing numbers 0-20, understanding cardinality through counting objects, comparing numbers of objects, and answering "how many" questions through counting up to 20 objects. The unit focuses on developing foundational number sense and counting skills.
Mathematics Curriculum Guide Kinder 2011 2012Isaac_Schools_5
The document provides guidance for a kindergarten mathematics curriculum unit on classroom routines and counting. It outlines big ideas, essential questions, unit vocabulary, Arizona math standards, and explanations for counting to 100, writing numbers 0-20, understanding cardinality through counting objects, comparing numbers of objects, and answering "how many" questions through counting up to 20 objects. The unit focuses on developing foundational number sense and counting skills.
2. +
Kindergarten
Standards
CCSS.Math.Content.K.OA.A.1 Represent
addition and subtraction with
objects, fingers, mental
images, drawings, sounds , acting out
situations, verbal explanations, expressions, or
equations.
CCSS.Math.Content.K.OA.A.2 Solve addition
and subtraction word problems, and add and
subtract within 10, e.g., by using objects or
drawings to represent the problem.
CCSS.Math.Content.K.OA.A.3 Group numbers
less than or equal to 10 into pairs in more than
one way. Can be done by using objects or
drawings, and record each decomposition by a
drawing or equation.
CCSS.Math.Content.K.OA.A.4 For any number
from 1 to 9, find the number that makes 10
when added to the given number by using
objects or drawings, and record the answer with
a drawing or equation.
CCSS.Math.Content.K.OA.A.5 Add and subtract
within 5.
Summary
Students will be able to
represent numbers 1 through
10 using visual aids. They will
be able to add, subtract, and
group these numbers by using
objects or drawings. They will
also be able to solve addition
and subtraction word problems.
4. +
First Grade
Standards
CCSS.Math.Content.1.OA.A.1 Use addition and subtraction
within 20 to solve word problems involving situations of adding
to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using
objects, drawings, and equations with a symbol for the unknown
number to represent the problem.
CCSS.Math.Content.1.OA.A.2 Solve word problems that call for
addition of three whole numbers whose sum is less than or
equal to 20, e.g., by using objects, drawings, and equations with
a symbol for the unknown number to represent the problem.
CCSS.Math.Content.1.OA.B.3 Apply properties of operations as
strategies to add and subtract.
CCSS.Math.Content.1.OA.B.4 Understand subtraction as an
unknown-addend problem.
CCSS.Math.Content.1.OA.C.5 Relate counting to addition and
subtraction.
CCSS.Math.Content.1.OA.C.6 Add and subtract within
20, demonstrating fluency for addition and subtraction within 10.
Use strategies such as counting on; making ten, decomposing a
number leading to a ten, using the relationship between addition
and subtraction, and creating equivalent but easier or known
sums.
CCSS.Math.Content.1.OA.D.7 Understand the meaning of the
equal sign, and determine if equations involving addition and
subtraction are true or false.
CCSS.Math.Content.1.OA.D.8 Determine the unknown whole
number in an addition or subtraction equation relating three
whole numbers.
Summary
Students will continue to use
addition and subtraction to
solve word problems and
equations. They will expand
their range from 1 to 20. They
will also learn to apply
properties of operations.
Students will also use a number
of strategies to add and
subtract problems.
5. +
First Grade
Represent and solve problems involving addition and
subtraction.
Understand and apply properties of operations and the
relationship between addition and subtraction.
Add and subtract with 20.
Work with addition and subtraction equations.
6. +
Second Grade
Standards
CCSS.Math.Content.2.OA.A.1 Use addition
and subtraction within 100 to solve one- and
two-step word problems by using drawings
and equations with a symbol for the
unknown number to represent the problem.
CCSS.Math.Content.2.OA.B.2 Add and
subtract within 20 using mental strategies.
By end of Grade 2, know from memory all
sums of two one-digit numbers.
CCSS.Math.Content.2.OA.C.3 Determine
whether a group of objects (up to 20) has
an odd or even number of members; write
an equation to express an even number as
a sum of two equal addends.
CCSS.Math.Content.2.OA.C.4 Use addition
to find the total number of objects arranged
in rectangular arrays with up to 5 rows and
up to 5 columns; write an equation to
express the total as a sum of equal
addends.
Summary
Students will continue solving
word problems with more
complex numbers (within 100).
Students will also focus on
using mental strategies to add
and subtract within 20.
Students will identify odd and
even numbers and additional
structured in arrays. Students
will also practice writing
equations to demonstrate their
understanding. Students will be
introduced to multiplication.
7. +
Second Grade
Represent and solve problems involving addition and
subtraction.
Add and subtract within 20.
Work with equal groups of objects to gain foundations for
multiplication.
8. +
Third Grade
Standards
CCSS.Math.Content.3.OA.A.1 Interpret
products of whole numbers, e.g., interpret 5 7
as the total number of objects in 5 groups of 7
objects each.
CCSS.Math.Content.3.OA.A.2 Interpret wholenumber quotients of whole
numbers, e.g., interpret 56 8 as the number of
objects in each share when 56 objects are
partitioned equally into 8 shares, or as a
number of shares when 56 objects are
partitioned into equal shares of 8 objects each.
CCSS.Math.Content.3.OA.A.3 Use
multiplication and division within 100 to solve
word problems in situations involving equal
groups, arrays, and measurement
quantities, e.g., by using drawings and
equations with a symbol for the unknown
number to represent the problem.1
CCSS.Math.Content.3.OA.A.4 Determine the
unknown whole number in a multiplication or
division equation relating three whole numbers.
Summary
Third grade focuses on
multiplication and division of
whole numbers. Students will
use multiplication and division
to solve problems involving
equal groups, arrays, and
measurement quantities, etc.
9. +
Third Grade
Represent and solve problems involving multiplication and
division.
Understand properties of multiplication and the relationship
between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations and ifentify and
explain patterns in arithmetic.
10. +
Fourth Grade
Standards
CCSS.Math.Content.4.OA.A.1 Interpret a
multiplication equation as a comparison.
Represent verbal statements of
multiplicative comparisons as multiplication
equations.
CCSS.Math.Content.4.OA.A.2 Multiply or
divide to solve word problems involving
multiplicative comparison, e.g., by using
drawings and equations with a symbol for
the unknown number to represent the
problem, distinguishing multiplicative
comparison from additive comparison.
CCSS.Math.Content.4.OA.A.3 Solve
multistep word problems posed with whole
numbers and having whole-number
answers using the four operations, including
problems in which remainders must be
interpreted. Represent these problems
using equations with a letter standing for the
unknown quantity. Assess the
reasonableness of answers using mental
computation and estimation strategies
including rounding
Summary
Students will continue to work
with multiplication and division.
Students will be introduced to
the x variable and be required
to complete whole number
problems in which all
operations are used and
contain an unknown quantity.
Students begin to move away
from drawings and
representations to written
equations with variables for
unknown numbers. Students
begin too generate and analyze
patterns.
11. +
Fourth Grade
Use the four operations with whole numbers to solve problems.
Gain familiarity with factors and multiples.
Generate and analyze patterns.
12. +
Fifth Grade
Standards
CCSS.Math.Content.5.OA.A.1 Use
parentheses, brackets, or braces in numerical
expressions, and evaluate expressions with
these symbols.
CCSS.Math.Content.5.OA.A.2 Write simple
expressions that record calculations with
numbers, and interpret numerical expressions
without evaluating them.
CCSS.Math.Content.5.OA.B.3 Generate two
numerical patterns using two given rules.
Identify relationships between corresponding
terms. Form ordered pairs consisting of
corresponding terms from the patterns, and
graph the ordered pairs on a grid.
Summary
Students will learn the
importance of
parentheses, brackets, and
braces and learn how to
accurately solve equations that
have them. Students will write
simple equations without
evaluating them. In
addition, students will learn to
solve problems based on set
“rules” (patterns). Students will
continue to graph the ordered
pairs on a grid.
14. +
Sixth Grade
Standards
CCSS.Math.Content.6.RP.A.1 Understand the concept
of a ratio and use ratio language to describe a ratio
relationship between two quantities.
CCSS.Math.Content.6.RP.A.2 Understand the concept
of a unit rate a/b associated with a ratio a:b with b ≠
0, and use rate language in the context of a ratio
relationship.
CCSS.Math.Content.6.RP.A.3 Use ratio and rate
reasoning to solve real-world and mathematical
problems.
CCSS.Math.Content.6.RP.A.3a Make tables of
equivalent ratios relating quantities with wholenumber measurements, find missing values in the
tables, and plot the pairs of values on the
coordinate plane. Use tables to compare ratios.
CCSS.Math.Content.6.RP.A.3b Solve unit rate
problems including those involving unit pricing and
constant speed.
CCSS.Math.Content.6.RP.A.3c Find a percent of a
quantity as a rate per 100 (e.g., 30% of a quantity
means 30/100 times the quantity); solve problems
involving finding the whole, given a part and the
percent.
CCSS.Math.Content.6.RP.A.3d Use ratio reasoning
to convert measurement units; manipulate and
transform units appropriately when multiplying or
dividing quantities.
Summary
Content shifts from Operations
and Algebraic Thinking to
Ratios and Proportional
Relationships. Students will
learn about ratios, ratio
terminology, and how ratios are
used in mathematical problems
and every day life. Students will
be able to solve different math
problems using ratios such as
problems involving unit
pricing, constant
speed, percent, etc. Students
will also know how to
manipulate ratios.
16. +
Middle School and High School
Continuum
5th grade, the standards for operations and
algebraic thinking get more specific per grade.
Grade 6 and 7 focus on ratios and proportional
relationships. All of the middle school grades focus
on non-rational numbers and how to
analyze, approximate, and rationalize them. The
high school grades focus primarily on extending the
properties of exponents to rational exponents and
using properties of rational and irrational numbers.
After