This document provides Common Core assessment tasks for first grade mathematics. It includes tasks related to counting, addition, subtraction, word problems, place value, measurement, and data analysis. The tasks are broken into benchmarks 1 and 2. For benchmark 1, problems involve numbers less than or equal to 10 and adding or subtracting 0-1. Benchmark 2 extends this to problems within 20. The tasks provide concrete examples and questions to develop students' understanding of key first grade math concepts.
This document provides a series of mathematics assessment tasks for kindergarten students addressing common core standards for counting, cardinality, operations and algebraic thinking. The tasks involve counting objects, comparing quantities, addition and subtraction word problems, and missing addend problems. Teachers are instructed to observe students' strategies and accuracy in completing the tasks. The tasks increase in difficulty level across the school year quarters.
This document provides a curriculum guide for a third grade mathematics unit on equal groups involving multiplication and division. The unit focuses on helping students understand multiplication and division as the grouping and ungrouping of objects to solve real-world problems. It includes essential questions, vocabulary, and standards aligned to specific mathematical practices. Students are expected to interpret and represent multiplication and division problems using various models like arrays, pictures, and equations. They also solve word problems involving equal groups and measurement quantities using multiplication and division within 100.
The document provides an overview of a third grade mathematics unit on fractions and decimals that is 16 sessions long. It includes the big ideas, essential questions, unit vocabulary, and Arizona math standards covered. It also provides explanations and examples for key concepts like representing fractions as parts of a whole, using models to demonstrate equivalent fractions, comparing fractions, and representing fractions on a number line.
These are the unpacking documents to better help you understand the expectations for Third gradestudents under the Common Core State Standards for Math. The examples should be very helpful.
Activities and Strategies to Teach KS Standardsmflaming
The document provides an agenda and overview for a workshop on teaching math state standards to elementary learners. It includes activities, discussions, and examples to help participants understand concepts like numbers and operations, algebra, geometry, data, and problem solving. Cognitive categories for different levels of math skills are defined. Sample word problems assess addition, subtraction, multiplication, division, and multi-step reasoning abilities.
This document provides guidance for teaching basic math operations like addition, subtraction, multiplication and division to students. It emphasizes applying concepts to real-life situations to motivate students. Teachers should focus on conceptual understanding rather than rote memorization and provide examples for students to apply the operations. Using manipulatives, word problems, number lines and flashcards can help reinforce skills in an engaging way. Specific suggestions are also given for teaching addition and subtraction concepts.
Here are some possible mathematical problems that could be posed from the given situation:
1) The master worker can paint 1 square meter of the billboard per hour. The apprentice can paint 0.5 square meters per hour. If they work for 8 hours, how many square meters of the billboard can they paint?
2) The billboard measures 20 square meters. If the master worker and apprentice work together for x hours, write an equation to represent the relationship between the number of hours worked (x) and the area painted (y).
3) The billboard measures 20 square meters. The master worker and apprentice work together for 8 hours. How much of the billboard do they paint?
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 a series of mathematics assessment tasks for kindergarten students addressing common core standards for counting, cardinality, operations and algebraic thinking. The tasks involve counting objects, comparing quantities, addition and subtraction word problems, and missing addend problems. Teachers are instructed to observe students' strategies and accuracy in completing the tasks. The tasks increase in difficulty level across the school year quarters.
This document provides a curriculum guide for a third grade mathematics unit on equal groups involving multiplication and division. The unit focuses on helping students understand multiplication and division as the grouping and ungrouping of objects to solve real-world problems. It includes essential questions, vocabulary, and standards aligned to specific mathematical practices. Students are expected to interpret and represent multiplication and division problems using various models like arrays, pictures, and equations. They also solve word problems involving equal groups and measurement quantities using multiplication and division within 100.
The document provides an overview of a third grade mathematics unit on fractions and decimals that is 16 sessions long. It includes the big ideas, essential questions, unit vocabulary, and Arizona math standards covered. It also provides explanations and examples for key concepts like representing fractions as parts of a whole, using models to demonstrate equivalent fractions, comparing fractions, and representing fractions on a number line.
These are the unpacking documents to better help you understand the expectations for Third gradestudents under the Common Core State Standards for Math. The examples should be very helpful.
Activities and Strategies to Teach KS Standardsmflaming
The document provides an agenda and overview for a workshop on teaching math state standards to elementary learners. It includes activities, discussions, and examples to help participants understand concepts like numbers and operations, algebra, geometry, data, and problem solving. Cognitive categories for different levels of math skills are defined. Sample word problems assess addition, subtraction, multiplication, division, and multi-step reasoning abilities.
This document provides guidance for teaching basic math operations like addition, subtraction, multiplication and division to students. It emphasizes applying concepts to real-life situations to motivate students. Teachers should focus on conceptual understanding rather than rote memorization and provide examples for students to apply the operations. Using manipulatives, word problems, number lines and flashcards can help reinforce skills in an engaging way. Specific suggestions are also given for teaching addition and subtraction concepts.
Here are some possible mathematical problems that could be posed from the given situation:
1) The master worker can paint 1 square meter of the billboard per hour. The apprentice can paint 0.5 square meters per hour. If they work for 8 hours, how many square meters of the billboard can they paint?
2) The billboard measures 20 square meters. If the master worker and apprentice work together for x hours, write an equation to represent the relationship between the number of hours worked (x) and the area painted (y).
3) The billboard measures 20 square meters. The master worker and apprentice work together for 8 hours. How much of the billboard do they paint?
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.
These are the unpacking documents to better help you understand the expectations for Kindergartenstudents under the Common Core State Standards for Math.
The document discusses issues with how fractions are currently taught in US schools and recommends improvements. It notes that students struggle with fractions and this hinders later success in algebra. A presidential panel recommends schools focus more on mastering the basics like fractions, in addition to geometry. It emphasizes fractions are a major obstacle and schools should teach them in a more in-depth way.
This document provides a curriculum guide for a third grade mathematics unit on solids and boxes. The unit focuses on understanding two-dimensional and three-dimensional figures and their attributes. Students will learn about prisms, pyramids, edges, faces, and vertices. They will represent and solve word problems involving multiplication and division up to 10x10. Students will also measure and estimate liquid volumes and masses using standard units like grams, kilograms, and liters. They will recognize area as an attribute of plane figures and understand concepts of area measurement using unit squares.
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.
Teaching multiplication of numbers from 1 to 10 stkip surya students using ma...Sulistiawati .
This document outlines the research methodology for a study on teaching multiplication of numbers 1 to 10 using the Matematika GASING approach. The study uses a design research methodology with 14 undergraduate students. It presents an overview of the conjectured learning trajectory, including concrete, abstract, and mental stages for teaching key concepts like the concept of multiplication, multiplication of number 1, and multiplication of same numbers. The goal is to analyze students' learning and develop theories to effectively teach multiplication using this approach.
This document provides an overview of scaffolding instruction for addition and subtraction. It discusses using graphic organizers and manipulatives to build conceptual understanding from concrete to abstract levels. Specific lessons are outlined for pre-kindergarten through second grade that model addition and subtraction using objects, pictures, and number sentences. Representational tools like linking cubes, part-part-whole mats, and base ten blocks are employed to scaffold learning.
Place value and numeration is a crucial mathematical element that children develop an understanding of from a young age. It provides the foundation for skills like reading, writing, calculating and discussing numbers accurately. Teachers should offer varied individual and group activities to help students make sense of numbers in different contexts. A strong foundation in place value enables students to extend their knowledge and solve more complex problems. Common problems children face include neglecting renaming, lack of pattern with teen numbers, and reversing digits. Activities like using collections, comparing numbers, and trading can help support correct learning of place value concepts. Key patterns are the role of tens and composing/decomposing numbers. Concrete models, large numbers, and real-life situations can help develop understanding
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.
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.
The document provides an interview summary of a lesson on solving various types of inequalities:
1) The lesson covers linear, quadratic, and rational inequalities, explaining the steps to solve each type.
2) Examples are worked through demonstrating how to identify intervals on the number line and use test values to determine the solution set of inequalities.
3) Applications involving break-even points and projectile motion are presented to show real-world examples.
This document contains a semi-detailed lesson plan for teaching students how to multiply 2 to 4 digit numbers by 1 to 2 digit numbers without regrouping. The lesson plan includes learning objectives, materials, and a sequence of activities: practicing multiplication facts with flash cards, reviewing key concepts, presenting sample problems, allowing students to practice problems in groups and individually, evaluating students abilities, and assigning additional problems as homework. The overall goal is for students to learn and demonstrate accurate and careful multiplication of multi-digit numbers.
1) The document provides guidance on using the backwards approach to lesson planning, which involves first identifying the learning outcomes and then planning assessments, instruction, and the learning environment.
2) It gives an example of a math lesson on addition and subtraction using a hundreds chart, including an entrance slip, game activity, and discussion questions to assess learning.
3) Suggestions are made to address gaps in students' understanding of subtracting 8 by relating it to subtracting 10 and adding the difference.
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.
This document outlines the first grade math curriculum which focuses on developing students' understanding of key math concepts like basic algebra, geometry, problem solving and reasoning. The curriculum covers topics like addition, subtraction, data analysis, measurement, patterns and shapes over 9 units. It aims for students to become proficient in computation and able to apply math concepts. The summary also notes that students will receive homework help materials to work on math skills at home with their families.
A Case Study of Teaching the Concept of Differential in Mathematics Teacher T...theijes
In high schools of Viet Nam, teaching calculus includes the knowledge of the real function with a real variable. A mathematics educator in France, Artigue (1996) has shown that the methods and approximate techniques are the centers of the major problems (including number approximation and function approximation...) in calculus. However, in teaching mathematics in Vietnam, the problems of approximation almost do not appear. With the task of training mathematics teachers in high schools under the new orientations, we present a part of our research with the goal of improving the contents and methods of teacher training
This lesson guide discusses joining sets with 1 to 9 objects. It provides examples of joining sets such as an apple and a mango, and joining other sets using picture cards. The key learning points are:
- Joining two sets involves putting the sets together to form a new set.
- The word "and" is used to show the joining of sets.
- Matching joined sets to their corresponding new sets helps students understand set addition.
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 document provides a curriculum guide for a 5th grade mathematics unit on multiplication and division. It includes big ideas, essential questions, vocabulary, standards, and examples for content covering writing and interpreting numerical expressions, understanding place value systems, and performing operations with multi-digit whole numbers and decimals. The unit aims to help students understand algebraic problem solving and number representations, as well as master skills with operations and place value.
1) Students will collect data on favorite fast foods in their class and grade to create bar graphs. They will write a report sharing their findings.
2) Fraction concepts are explored through examples of parts of wholes, such as one-third and two-sixths being equivalent.
3) A problem solving activity involves arranging digits 1-9 in groups so the sum is the same in each group, with discussion of multiple solutions.
The song expresses melancholy about the end of celebrations for the new year and decade. It hopes that in the coming years people will maintain visions of a peaceful world and the hopes and will to build a better future together, otherwise humankind may give up. The lyrics reflect on the passage of time and the fleeting nature of dreams while looking ahead to the unknowns of the next decade.
1) The document discusses high-frequency oscillatory ventilation (HFOV), a lung-protective ventilation strategy that uses small, high-frequency breaths to ventilate patients with acute respiratory distress syndrome (ARDS).
2) Two randomized controlled trials (MOAT and Bollen) compared HFOV to conventional ventilation in adults with ARDS but found no significant differences in mortality between the groups.
3) The trials were underpowered and had some limitations in their ventilation protocols, so more research is still needed to determine if HFOV provides benefits over conventional lung-protective ventilation for adults with ARDS.
These are the unpacking documents to better help you understand the expectations for Kindergartenstudents under the Common Core State Standards for Math.
The document discusses issues with how fractions are currently taught in US schools and recommends improvements. It notes that students struggle with fractions and this hinders later success in algebra. A presidential panel recommends schools focus more on mastering the basics like fractions, in addition to geometry. It emphasizes fractions are a major obstacle and schools should teach them in a more in-depth way.
This document provides a curriculum guide for a third grade mathematics unit on solids and boxes. The unit focuses on understanding two-dimensional and three-dimensional figures and their attributes. Students will learn about prisms, pyramids, edges, faces, and vertices. They will represent and solve word problems involving multiplication and division up to 10x10. Students will also measure and estimate liquid volumes and masses using standard units like grams, kilograms, and liters. They will recognize area as an attribute of plane figures and understand concepts of area measurement using unit squares.
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.
Teaching multiplication of numbers from 1 to 10 stkip surya students using ma...Sulistiawati .
This document outlines the research methodology for a study on teaching multiplication of numbers 1 to 10 using the Matematika GASING approach. The study uses a design research methodology with 14 undergraduate students. It presents an overview of the conjectured learning trajectory, including concrete, abstract, and mental stages for teaching key concepts like the concept of multiplication, multiplication of number 1, and multiplication of same numbers. The goal is to analyze students' learning and develop theories to effectively teach multiplication using this approach.
This document provides an overview of scaffolding instruction for addition and subtraction. It discusses using graphic organizers and manipulatives to build conceptual understanding from concrete to abstract levels. Specific lessons are outlined for pre-kindergarten through second grade that model addition and subtraction using objects, pictures, and number sentences. Representational tools like linking cubes, part-part-whole mats, and base ten blocks are employed to scaffold learning.
Place value and numeration is a crucial mathematical element that children develop an understanding of from a young age. It provides the foundation for skills like reading, writing, calculating and discussing numbers accurately. Teachers should offer varied individual and group activities to help students make sense of numbers in different contexts. A strong foundation in place value enables students to extend their knowledge and solve more complex problems. Common problems children face include neglecting renaming, lack of pattern with teen numbers, and reversing digits. Activities like using collections, comparing numbers, and trading can help support correct learning of place value concepts. Key patterns are the role of tens and composing/decomposing numbers. Concrete models, large numbers, and real-life situations can help develop understanding
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.
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.
The document provides an interview summary of a lesson on solving various types of inequalities:
1) The lesson covers linear, quadratic, and rational inequalities, explaining the steps to solve each type.
2) Examples are worked through demonstrating how to identify intervals on the number line and use test values to determine the solution set of inequalities.
3) Applications involving break-even points and projectile motion are presented to show real-world examples.
This document contains a semi-detailed lesson plan for teaching students how to multiply 2 to 4 digit numbers by 1 to 2 digit numbers without regrouping. The lesson plan includes learning objectives, materials, and a sequence of activities: practicing multiplication facts with flash cards, reviewing key concepts, presenting sample problems, allowing students to practice problems in groups and individually, evaluating students abilities, and assigning additional problems as homework. The overall goal is for students to learn and demonstrate accurate and careful multiplication of multi-digit numbers.
1) The document provides guidance on using the backwards approach to lesson planning, which involves first identifying the learning outcomes and then planning assessments, instruction, and the learning environment.
2) It gives an example of a math lesson on addition and subtraction using a hundreds chart, including an entrance slip, game activity, and discussion questions to assess learning.
3) Suggestions are made to address gaps in students' understanding of subtracting 8 by relating it to subtracting 10 and adding the difference.
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.
This document outlines the first grade math curriculum which focuses on developing students' understanding of key math concepts like basic algebra, geometry, problem solving and reasoning. The curriculum covers topics like addition, subtraction, data analysis, measurement, patterns and shapes over 9 units. It aims for students to become proficient in computation and able to apply math concepts. The summary also notes that students will receive homework help materials to work on math skills at home with their families.
A Case Study of Teaching the Concept of Differential in Mathematics Teacher T...theijes
In high schools of Viet Nam, teaching calculus includes the knowledge of the real function with a real variable. A mathematics educator in France, Artigue (1996) has shown that the methods and approximate techniques are the centers of the major problems (including number approximation and function approximation...) in calculus. However, in teaching mathematics in Vietnam, the problems of approximation almost do not appear. With the task of training mathematics teachers in high schools under the new orientations, we present a part of our research with the goal of improving the contents and methods of teacher training
This lesson guide discusses joining sets with 1 to 9 objects. It provides examples of joining sets such as an apple and a mango, and joining other sets using picture cards. The key learning points are:
- Joining two sets involves putting the sets together to form a new set.
- The word "and" is used to show the joining of sets.
- Matching joined sets to their corresponding new sets helps students understand set addition.
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 document provides a curriculum guide for a 5th grade mathematics unit on multiplication and division. It includes big ideas, essential questions, vocabulary, standards, and examples for content covering writing and interpreting numerical expressions, understanding place value systems, and performing operations with multi-digit whole numbers and decimals. The unit aims to help students understand algebraic problem solving and number representations, as well as master skills with operations and place value.
1) Students will collect data on favorite fast foods in their class and grade to create bar graphs. They will write a report sharing their findings.
2) Fraction concepts are explored through examples of parts of wholes, such as one-third and two-sixths being equivalent.
3) A problem solving activity involves arranging digits 1-9 in groups so the sum is the same in each group, with discussion of multiple solutions.
The song expresses melancholy about the end of celebrations for the new year and decade. It hopes that in the coming years people will maintain visions of a peaceful world and the hopes and will to build a better future together, otherwise humankind may give up. The lyrics reflect on the passage of time and the fleeting nature of dreams while looking ahead to the unknowns of the next decade.
1) The document discusses high-frequency oscillatory ventilation (HFOV), a lung-protective ventilation strategy that uses small, high-frequency breaths to ventilate patients with acute respiratory distress syndrome (ARDS).
2) Two randomized controlled trials (MOAT and Bollen) compared HFOV to conventional ventilation in adults with ARDS but found no significant differences in mortality between the groups.
3) The trials were underpowered and had some limitations in their ventilation protocols, so more research is still needed to determine if HFOV provides benefits over conventional lung-protective ventilation for adults with ARDS.
Vietnam is located in Southeast Asia and has a shape resembling the letter S. It has a long coastline and over 3,000 islands off its coast. Vietnam has diverse terrain ranging from mountains and forests to rivers, seas, and plateaus. Some of Vietnam's most scenic natural attractions include Sapa, Da Lat, Halong Bay, and Nha Trang. The climate varies between tropical in the south and four distinct seasons in the north. Vietnam has a population of over 82 million people and a culture influenced by Confucianism. The Vietnamese are generally warm and friendly people who respect elders and independence. Vietnam has a long history and was previously occupied by China for over 1,000 years and then France for
This document provides instructions for an exam on media studies focusing on TV drama. It outlines that candidates will watch a 5 minute extract from an episode of Doctor Who and answer questions about it. The first question analyzes the extract's representation of gender through techniques like camera shots, editing, sound, and mise-en-scene. The second question discusses the importance of technological convergence for institutions and audiences in one of several listed media areas, using examples from the candidate's case study research.
Commencement is the formal graduation ceremony where students receive their diplomas and any awards they have earned. While students are not required to attend, it is an important celebration of their achievement and a chance to see classmates and thank teachers. The commencement ceremony for this class will take place on June 28, 2011 at 3:45 pm at The Meeting House, an air-conditioned facility with parking and nearby restaurants. Students are encouraged to apply for any awards they feel they qualify for by the April 29 deadline.
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.
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.
This document provides a scheme of work for teaching mathematics at Stage 8. It includes 3 units per term that each focus on a different topic area like number, algebra, or data handling. Each unit lists learning objectives, example activities, and resources for teaching key concepts. It also provides problem-solving activities that can be incorporated across each unit to develop problem-solving skills. The purpose is to illustrate one way the curriculum could be planned and delivered over the school year in 3 terms with flexibility for teachers.
The document contains 4 math word problems involving operations of subtraction, addition, multiplication, and division. It also provides hints and answers for each problem. The problems involve counting and combining sets of instruments, splitting instruments between students, and calculating the total number of instruments in groups. The document concludes with 1st grade math standards related to representing, comparing, and operating on numbers up to 100.
The document contains 4 math word problems involving operations of subtraction, addition, multiplication, and division. It also provides hints and answers for each problem. The problems involve counting and combining sets of instruments, splitting instruments between students, and calculating the total number of instruments in groups. The document concludes with 1st grade math standards related to representing, comparing, and operating on numbers up to 100, as well as collecting and displaying data.
The document provides a mathematics curriculum guide for third grade students in the Isaac School District. It focuses on unit 8 which covers addition, subtraction, and number systems over 3 sessions. The unit teaches students that numbers can be represented in many ways and used to solve problems. Students will learn about relationships between numbers, place value, and comparing and ordering whole numbers. They will solve 2-step word problems using the four operations and identify arithmetic patterns. Students will also learn to fluently add and subtract within 1000 using strategies based on place value.
Kindergarten NK.5 lesson fishing one more one lesssusan70
The document provides guidance on using the backwards approach to plan lessons for the kindergarten math outcome of comparing quantities from 0 to 10. It includes identifying the outcome, determining how learning will be observed, planning instructional opportunities and assessing prior knowledge, carrying out the lesson, and assessing student learning and next steps. Sample lesson plans are provided focusing on using ten frames and counters to build and compare numbers, as well as unifix cube riddles.
This document discusses teaching numbers from 0 to 10. It begins by outlining the learning outcomes, which are to recognize mathematical skills and concepts involving whole numbers from 0 to 10, understand place value and strategies for teaching numbers. It then discusses pre-number concepts like classification, counting, and patterns that form the basis for understanding whole numbers. Two sample teaching activities are described in detail: one on classifying objects by properties, and another on comparing quantities in two sets using terms like "more than" and "less than". The document emphasizes giving students opportunities to interact with objects and develop number sense before learning numerals.
- 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.
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 guidance on using the backwards approach to lesson planning. It involves identifying the learning outcomes, determining how learning will be observed and assessed, planning the learning environment and instruction, and assessing student learning and following up.
As an example, it outlines a lesson plan focused on representing whole numbers 1-10 concretely and pictorially in two parts. The plan includes a listening activity to introduce numbers 0-10, ordering number cards, representing numbers on a two-part math mat, and a sharing portion to assess learning. Follow up may include a journal activity for students to represent their own number.
This document provides an overview of the 2nd grade mathematics curriculum for the Isaac School District. The curriculum guide outlines key ideas, essential questions, vocabulary, standards, and examples for Unit 1, which focuses on counting, coins, addition, subtraction, and place value. The unit aims to help students understand different strategies for counting, solving addition and subtraction problems, and communicating their mathematical thinking. It provides standards and examples for representing and solving word problems involving addition and subtraction, fluently adding and subtracting within 20, working with equal groups to understand multiplication, and understanding place value in three-digit numbers.
This document outlines the first grade math curriculum which focuses on developing students' understanding of key math concepts like basic algebra, geometry, problem solving and reasoning. The curriculum covers topics like addition, subtraction, data analysis, measurement, patterns and shapes over 9 units. It provides examples of math problems and activities students will experience to build their skills in a hands-on way. The document also notes that students will receive materials like math bookmarks and handbooks to use at home for homework.
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 to find factor pairs, determine if numbers are multiples, and identify prime and composite numbers between 1-100.
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.
First New Teachers' Conference, Manila, 10 September 2011Jimmy Keng
This document contains summaries from presentations given at various schools around the world on teaching mathematics. It discusses lessons from Chile, Japan, and the Philippines on public lessons, as well as a LEAP program in Manila. Participants at Keys Grade School in Manila provided methods for finding the difference between two numbers. At De Tweemaster in the Netherlands, participants demonstrated methods for finding the area of polygons by counting dots. The document outlines three main points about teaching mathematics through visualization, generalization, and communication. It provides further examples and solutions for percentage and angle problems.
- Module 1 focuses on building fluency with addition and subtraction within 100 by practicing mental strategies and using place value understanding.
- Topic A reviews foundational skills like decompositions within 10 and partners to 10 to prepare students for more complex problems.
- Topic B introduces strategies for subtracting single-digit numbers from multiples of ten and two-digit numbers, like taking from ten.
- The module aims to set students up for mastery of sums and differences within 100 by the end of Grade 2.
The document provides a daily lesson log for a 5th grade mathematics class that focuses on ratios. Over the course of the week, students will:
1) Learn about ratios and how to express them using fractions, decimals, and proportions. Examples used include comparing numbers of circles to squares.
2) Practice skills like writing ratios in different forms using real objects and visual examples from daily life. Ratios compared may involve numbers of students, fruits, or classroom supplies.
3) Apply their understanding of ratios to solve word problems involving costs, quantities for sale, and family demographics to strengthen comprehension of ratios in practical scenarios. Assessment occurs through ratio identification, expression, and application exercises.
The document outlines the indicators used in Georgia's 2013 College and Career Ready Performance Index (CCRPI) for elementary schools, middle schools, and high schools. It provides details on the content mastery, post-education readiness, and other indicators measured for each level. It also lists supplemental "Exceeding the Bar" indicators that schools can earn additional points for achieving.
This professional development plan outlines goals and actions to improve teacher understanding and implementation of Depth of Knowledge (DOK) levels in lesson planning, instruction, and assessment. The plan includes:
1) Training teachers on DOK levels and assessment; 2) Having teacher teams decompose standards to identify DOK levels; 3) Having teachers match identified DOK levels to standards when assessing orally, formatively, and summatively.
4) Observing teachers during instruction to show improvement across observations. 5) Having teacher teams analyze formative and summative assessments for DOK alignment to standards. 6) Revising assessments based on teacher examination and analysis of data to improve assessments and teacher confidence.
This document provides a template for schools to analyze data, identify training needs, justify needs using data, plan actions to address problems, measure results of training, and assign responsibilities. The template is intended as a tool to help schools, teachers, and parents plan rigorous and relevant professional development using data.
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Graphic organizers are visual displays that depict relationships between facts, terms, and ideas to improve learning outcomes. There are many types of graphic organizers suited to different types of information. Research shows graphic organizers effectively improve comprehension and vocabulary, especially when used after reading with teacher instruction on how to use them. Their effectiveness depends on factors like grade level, implementation point, and instructional context.
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Funding agencies consider several factors when reviewing grant applications, including whether the proposed project: fits the goals of the board and system; has documented need and support from administration, community, and parents; is sustainable and replicable; can be completed on time; and does not compete with previously funded projects. Appropriate personnel and reporting requirements must also be in place.
This document provides guidance for writing successful grant proposals in 3 parts: planning, research, and the proposal. It outlines key questions to consider in each area, including needs, goals, objectives, activities, timelines, budgets, and evaluations. The guidance emphasizes aligning all aspects of the proposal, having a clear need supported by data, strong planning, measurable objectives, and specifically describing how funds would be used to meet goals. Overall, it advises thoroughly addressing common proposal components to clearly demonstrate the merits of a project to reviewers.
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This document provides an agenda and overview for the first week of an education course. It includes assignments to complete such as viewing PowerPoints, writing a paper, replying to classmates, watching videos, and submitting a reflection. Students are asked to select a content area of focus and review the schedule for next week which will include creating headers and footers and learning about watermarks. Contact information is provided for any questions.
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Assessment
1. Common Core Grade 1
Assessment Tasks
Charlotte Area Mathematics Consortium, 2011
2. Common Core Assessment
Tasks
First Grade
Benchmark 1
1.OA.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.
What’s in the Bag? (Change Unknown)
Place one to ten objects in a paper bag. The student reaches in a takes some counters out.
Ask ―How many are left in the bag? How did you figure out your answer?‖
Example: Pulled 3 out and 7 remain in the bag. 3 + ___ = 10
or 10 – 3 = ___. (The algorithm is not the focus with this activity in benchmark 1.)
What’s in the Bag? ( Result Unknown)
Gather ten objects. Ask the student to choose an amount of objects to put in a paper bag,
Charlotte Area Mathematics Consortium, 2011
3. naming the number. The teacher does the same from the remaining amount, naming the
number. The student determines how many objects are in the bag. Ask: What did you do to
figure out the answer? (The total number of objects should not exceed ten for benchmark 1.)
What’s in the Bag? (Start Unknown)
Gather ten objects. The teacher places some of the objects in a bag without the child’s
knowledge (use a partition, close your eyes). The student places some more objects from the
objects remaining in the bag, naming the number. Remove any remaining objects to eliminate
confusion. The student empties the bag and counts of all the objects. A teacher asks ―How
many objects where in the bag to start with? What did you to figure out your answer?‖
1.OA.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.
Ice Cream Treats
Use ten frames, number line, or hundreds chart to solve problems. Students may also draw a
picture to solve problem. (For benchmark 1 students are expected to add 2 numbers with a sum
less than or equal to 10.)
Example: 2 children eat chocolate ice cream. 4 children eat vanilla ice cream. Ask: How
many children are eating ice cream? How did you figure out your answer? Show me.
(Provide a variety of materials for child choose which to use.)
Charlotte Area Mathematics Consortium, 2011
4. 1.OA.3 Apply properties of operations as strategies to add and
subtract.2Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.
(Commutative property of addition.) To add 2 + 6 + 4, the second two
numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.)
Missing Cubes
+ = +
____________________
Student should complete this task with pictures or objects. Ask: How many cubes are needed
to make the sets equal? (For benchmark 1, sets should not be greater than 10.)
1.OA.4 Understand subtraction as an unknown addend
problem.
Picking Apples
Jan picked three apples from the tree. Jan needs 10 apples in all. How many more apples
does Jan need to pick? (Use storyboards, ten frames or other objects to demonstrate. For
benchmark 1 the total number of objects used should be less than or equal to 10.)
Charlotte Area Mathematics Consortium, 2011
5. 1.OA.5 Relate counting to addition and subtraction (e.g.,
by counting on 2 to add 2.
Counting All
Instructional Task 1 (Counting all)
Provide the child with two dot dice. Roll the dot dice and count all to obtain the total value of the
two dice.
(For benchmark 1 the total number used should be less than or equal to 12.)
1.OA.6 Add and subtract within 20, demonstrating
Charlotte Area Mathematics Consortium, 2011
6. fluency for addition and subtraction within 10. Use
strategies such as counting on; making ten (e.g., 8 + 6 = 8
+ 2 + 4 = 10 + 4 = 14); decomposing a number leading to
a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the
relationship between addition and subtraction (e.g.,
knowing that 8 +4 = 12, one knows 12 – 8 = 4); and
creating equivalent but easier or known sums (e.g., adding
6 + 7 by creating the known equivalent 6 + 6 + 1 = 13).
Figuring Fun
Provide a student with an addition or subtraction problem and ask them to explain how they
solved the number sentence. For benchmark 1 students work with problems involving numbers
within 10 only adding and subtracting 0 or 1. Students should be able to figure out the
sum/difference within 5 seconds. Ask students to explain their thinking process to figure out
the answer. No manipulatives should be used. Students should demonstrate of one of the
following strategies; counting on or counting back, 1 more, 1 less, using an addition fact to solve
subtraction or vice versa, etc…)
1.OA.7 Understand the meaning of the equal sign, and
determine if equations involving addition and subtraction
are true or false. For example, which of the following
equations are true and which are false? 6 = 6, 7 = 8 – 1, 5
+ 2 = 2 + 5, 4 + 1 = 5 + 2.
True or Not?
For benchmark 1 use objects/pictures to demonstrate the following (do not show equations):
Charlotte Area Mathematics Consortium, 2011
7. Determine which of the following examples are true and explain:
2+7=9
10 = 9 + 1
4+3=1+8
1 + 3 = 13
1.NBT.1 Count to 120, starting at any number less than
120. In this range, read and write numerals and represent
a number of objects with a written numeral.
What Comes Next?
Rote count from a number less than 30 up to 30.
Name That Number
Give a number 0 – 30, students represent that number with objects, tally marks, picture sets,
etc…
Charlotte Area Mathematics Consortium, 2011
8. 1.NBT.2 Understand that the two digits of a two-digit
number represent amounts of tens and ones. Understand
the following as special cases: a. 10 can be thought of as
a bundle of ten ones — called a ―ten‖.
Making Tens
(2a) Given a set of objects less than or equal to 30, (e.g. 24 cubes), how many groups of 10 did
you make? (For benchmark 1 students do not have to count leftovers on this task. Students
should only recognize they made 1,2 or 3 groups of ten and the leftovers are not a group of ten.
Students are also not required to tell the total amount of objects, only count the number of
groups of ten.)
Charlotte Area Mathematics Consortium, 2011
9. 1.MD.1 Order three objects by length; compare the
lengths of two objects indirectly by using a third object.
Measuring Around the Room
Given three objects of different size/lengths, student should be able to organize them in order
from smallest to largest.
1.MD.4 Organize, represent and interpret data with up to
three categories; ask and answer questions about the total
number of data points, how many in each category, and
how many more or less are in one category than in
another.
Air, Land, and Sea
Prompt students to look at several pictures of living things (see examples).
What question can you ask that will allow you to sort the pictures into groups? Sort the pictures
based on your question/categories. Prompt student to record his/her data on a chart. A chart
example is provided.
Sea Land
Air
Charlotte Area Mathematics Consortium, 2011
10. Common Core Assessment
Tasks
First Grade
Benchmark 2
1.OA.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.
What’s in the Bag? (Change Unknown)
Place one to ten objects in a paper bag. The student reaches in a takes some counters out.
Ask ―How many are left in the bag? How did you figure out your answer?‖
Example: Pulled 3 out and 7 remain in the bag. 3 + ___ = 10
Charlotte Area Mathematics Consortium, 2011
11. or 10 – 3 = ___. Write a number sentence to show what you did to figure out the answer.
What’s in the Bag? ( Result Unknown)
Gather ten objects. Ask the student to choose an amount of objects to put in a paper bag,
naming the number. The teacher does the same from the remaining amount, naming the
number. The student determines how many objects are in the bag. Ask: What did you do to
figure out the answer? Write a number sentence to show what you did to figure out the answer.
(The total number of objects should not exceed ten for benchmark 2.)
What’s in the Bag? (Start Unknown)
Gather ten objects. The teacher places some of the objects in a bag without the child’s
knowledge (use a partition, close your eyes). The student places some more objects from the
objects remaining in the bag, naming the number. Remove any remaining objects to eliminate
confusion. The student empties the bag and counts of all the objects. A teacher asks ―How
many objects where in the bag to start with? What did you to figure out your answer? Write a
number sentence to show what you did to figure out the answer.‖ (The total number of objects
should not exceed ten for benchmark 2.)
1.OA.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.
Ice Cream Treats
Use ten frames, number line, or hundreds chart to solve problems. Students may also draw a
picture to solve problem. (For benchmark 2 students are expected to add 3 numbers with a sum
less than or equal to 10.)
Example: 2 children eat chocolate ice cream. 4 children eat vanilla ice cream. 1 child eats
strawberry ice cream. Ask: How many children are eating ice cream? How did you figure out
your answer? Show me. (Provide a variety of materials for child choose which to use.)
Charlotte Area Mathematics Consortium, 2011
12. 1.OA.3 Apply properties of operations as strategies to add and subtract.
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.
(Commutative property of addition.) To add 2 + 6 + 4, the second two
numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.)
Missing Numbers
3 + 4 = 4 + ____
6 + ____ = 2 + 6
Student should complete this task using an equation and/or symbols. Ask: What number is
needed to make the sets equal? (For benchmark 2, sets should not be greater than 10.)
1.OA.4 Understand subtraction as an unknown addend
problem.
Picking Apples
Jan picked three apples from the tree. Jan needs 10 apples in all. How many more apples
does Jan need to pick? (Use storyboards, ten frames or other objects to demonstrate. Write an
addition and subtraction number sentence to match your story. (For benchmark 2 the total
number of objects used should be less than or equal to 10.)
Charlotte Area Mathematics Consortium, 2011
13. 1.OA.5 Relate counting to addition and subtraction (e.g.,
by counting on 2 to add 2.
Count On and Count Back
Instructional Task 1 (Counting on)
Provide the child with a numeral die and a dot die. Roll the numeral die first. Then roll the dot
die and count on to obtain the total value of the two dice.
Instructional Task 2 (Counting back)
Provide the students with a numeral card or a spinner with numbers 5 to 10. The student
should also have a spinner with dots representing numbers 0 - 5. Students will count back the
value of the dots from the numeral on the card or original spinner.
Instructional Task 3 (Counting on and back)
Given a group of 6 counters, ask students to make the pile contain 10. Observe how student
changes the pile. To meet standard, the student should count on from 6 to get 10, …7 8 9 10.
. Then ask the student to make the pile contain 7 counters. The student should count back
from 10 to 7. Observe the child and ask them to orally explain how they are changing the pile
of counters.
(These tasks are progressive in nature. By the end of benchmark 2, students should be able to
complete task 3. For benchmark 2 the total number used should be less than or equal to 12.)
Charlotte Area Mathematics Consortium, 2011
14. 1.OA.6 Add and subtract within 20, demonstrating
fluency for addition and subtraction within 10. Use
strategies such as counting on; making ten (e.g., 8 + 6 = 8
+ 2 + 4 = 10 + 4 = 14); decomposing a number leading to
a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the
relationship between addition and subtraction (e.g.,
knowing that 8 +4 = 12, one knows 12 – 8 = 4); and
creating equivalent but easier or known sums (e.g., adding
6 + 7 by creating the known equivalent 6 + 6 + 1 = 13).
Figuring Fun
Provide a student with an addition or subtraction problem and ask them to explain how they
solved the number sentence. For benchmark 2 students work with problems involving numbers
within 10. Students should be able to figure out the sum/difference within 5 seconds. Ask
students to explain their thinking process to figure out the answer. No manipulatives should be
used. Students should demonstrate of one of the following strategies; making 10,
decomposing, counting on or counting back, doubles, 1 more, 1 less, using an addition fact to
solve subtraction or vice versa, etc…)
1.OA.7 Understand the meaning of the equal sign, and
determine if equations involving addition and subtraction
are true or false. For example, which of the following
equations are true and which are false? 6 = 6, 7 = 8 – 1, 5
Charlotte Area Mathematics Consortium, 2011
15. + 2 = 2 + 5, 4 + 1 = 5 + 2.
True or Not?
For benchmark 2 use objects/pictures/equations to demonstrate the following (the focus for
benchmark 2 is understanding the equations):
Determine which of the following examples are true and explain:
2+7=9
10 = 9 + 1
4+3=1+8
1 + 3 = 13
1.OA.8 Determine the unknown whole number in an
addition or subtraction equation relating three whole
numbers.
All in the Family
Given a fact family (4 + 3 = 7), students will be able to supply any unknown number to make the
equation true.
(7 = __ + 4, 7 - __ = 4, __ = 4 + 3)
Sample instructional strategies or tools might include fact triangles, number-bond cards,
part-whole cards, dominoes)
(For benchmark 2, students should work with sums within 10.)
Charlotte Area Mathematics Consortium, 2011
16. 1.NBT.1 Count to 120, starting at any number less than
120. In this range, read and write numerals and represent
a number of objects with a written numeral.
What Comes Next?
Rote count from a number less than 50 up to 50.
Name That Number
Give a number 0 – 50, students represent that number with objects, tally marks, picture sets,
etc…
1.NBT.2 Understand that the two digits of a two-digit
number represent amounts of tens and ones. Understand
the following as special cases: a. 10 can be thought of as
a bundle of ten ones — called a ―ten‖.
Charlotte Area Mathematics Consortium, 2011
17. Making Tens
(2b) For the numbers 11-19, how many groups of 10 can you make? Would you have any
leftovers? If so, how many leftovers would you have? What would the number be?
(2c) Given a set of 50 or less objects (decades only, no leftovers), have the students put the
objects into groups of 10. How many groups of 10 do you have? How many total objects do
you have?
1.MD.1 Order three objects by length; compare the
lengths of two objects indirectly by using a third object.
Measuring Around the Room
Give student stick that is about 4 inches long. Ask student to find an object in the room that is
shorter than and longer than the measuring tool. Student is asked to determine which object is
longer/shorter and explain reasoning. Observe: Can student relate reasoning to the original
measuring tool?
Charlotte Area Mathematics Consortium, 2011
18. 1.MD.2 Express lengths of an object as a whole number
of length units, by laying multiple copies of a shorter object
end to end; understand that the length measurement of an
object is the number of same-size length units that span it
with no gaps or overlaps.
Measuring Lengths
Provide a bag with assorted units of different sizes (Cuisenaire rod or paper clips)
Prompt student to use the materials in the box to measure the length of a given object
Observe:
o Does the student understand that all units must be the same size?
o If student uses different lengths, ask how the student would describe his/her measurement
Charlotte Area Mathematics Consortium, 2011
19. 1.MD.3 Tell and write time in hours and half-hours using
analog and digital clocks.
Broken Clock
Show student an image of a clock with the minute hand missing.
Ask the student to predict the position of the minute hand and the corresponding time. Explain
reasoning.
Repeat assessment with another example where hour hand is between two numbers.
Observe:
o Does the student understand what happens to the minute hand when the hour hand is
pointing directly to a number
o Does the student can approximate time based on the location of the hour hand
o When the time is at the half-hour, does the student know that the hour is the number that is
located before the hour hand.
1.MD.4 Organize, represent and interpret data with up to
three categories; ask and answer questions about the total
number of data points, how many in each category, and
how many more or less are in one category than in
another.
What’s the Weather?
Prompt students to look at a calendar with the weather shown for each day.
Ask: ―How would you sort the weather displayed on this calendar? Could you use numbers or
symbols (tally marks) to show me how you could organize this information?‖
Charlotte Area Mathematics Consortium, 2011
20. Common Core Assessment
Tasks
First Grade
Benchmark 3
1.OA.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.
What’s in the Bag? (Change Unknown)
Place ten to twenty objects in a paper bag. The student reaches in a takes some counters out.
Ask ―How many are left in the bag? How did you figure out your answer?‖
Example: Pulled 3 out and 7 remain in the bag. 3 + ___ = 10
or 10 – 3 = ___. Write a number sentence to show what you did to figure out the answer.
Charlotte Area Mathematics Consortium, 2011
21. What’s in the Bag? ( Result Unknown)
Gather ten to twenty objects. Ask the student to choose an amount of objects to put in a paper
bag, naming the number. The teacher does the same from the remaining amount, naming the
number. The student determines how many objects are in the bag. Ask: What did you do to
figure out the answer? Write a number sentence to show what you did to figure out the answer.
(The total number of objects should not exceed 20 for benchmark 3.)
What’s in the Bag? (Start Unknown)
Gather ten to twenty objects. The teacher places some of the objects in a bag without the child’s
knowledge (use a partition, close your eyes). The student places some more objects from the
objects remaining in the bag, naming the number. Remove any remaining objects to eliminate
confusion. The student empties the bag and counts of all the objects. A teacher asks ―How
many objects where in the bag to start with? What did you to figure out your answer? Write a
number sentence to show what you did to figure out the answer.‖ (The total number of objects
should not exceed 20 for benchmark 3.)
1.OA.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.
Ice Cream Treats
Use ten frames, number line, or hundreds chart to solve problems. Students may also draw a
picture to solve problem. (For benchmark 3 students are expected to add 2 numbers with a sum
less than or equal to 20.)
Example: 5 children eat chocolate ice cream. 9 children eat vanilla ice cream. Ask: How
many children are eating ice cream? How did you figure out your answer? Show me.
(Provide a variety of materials for child choose which to use.)
Charlotte Area Mathematics Consortium, 2011
22. 1.OA.3 Apply properties of operations as strategies to add and subtract.
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.
(Commutative property of addition.) To add 2 + 6 + 4, the second two
numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.)
Mixed Up Numbers
Say: ―Susie solved the following problem: 6 + 2 + 4 = 12 First she added 6 + 2 and got
eight. Then she counted up 4 more and got an answer of 12. Is there a different way to solve
this problem?‖
Observe
- Does the child realize that 6 and 4 can be grouped first into 10 and then add
the leftover 2?
Student should complete this task using objects, drawings, equations and symbols. (For
benchmark 3, sets should not be greater than 20.)
1.OA.4 Understand subtraction as an unknown addend
problem.
Picking Apples
Jan picked three apples from the tree. Jan needs 10 apples in all. How many more apples
does Jan need to pick? (Use storyboards, ten frames or other objects to demonstrate.) Write
an addition and subtraction number sentence to match your story. (For benchmark 3 the total
number of objects used should be less than or equal to 20.)
Charlotte Area Mathematics Consortium, 2011
23. 1.OA.5 Relate counting to addition and subtraction (e.g.,
by counting on 2 to add 2.
Count On and Count Back
Instructional Task 1 (Counting on)
Provide the child with a numeral die and a dot die. Roll the numeral die first. Then roll the dot
die and count on to obtain the total value of the two dice.
Instructional Task 2 (Counting back)
Provide the students with a numeral card or a spinner with numbers 5 to 10. The student
should also have a spinner with dots representing numbers 0 - 5. Students will count back the
value of the dots from the numeral on the card or original spinner.
Instructional Task 3 (Counting on and back)
Given a group of 6 counters, ask students to make the pile contain 10. Observe how student
changes the pile. To meet standard, the student should count on from 6 to get 10, …7 8 9 10.
. Then ask the student to make the pile contain 7 counters. The student should count back
from 10 to 7. Observe the child and ask them to orally explain how they are changing the pile
of counters.
(For benchmark 3 the total number used should be less than or equal to 20.)
Charlotte Area Mathematics Consortium, 2011
24. 1.OA.6 Add and subtract within 20, demonstrating
fluency for addition and subtraction within 10. Use
strategies such as counting on; making ten (e.g., 8 + 6 = 8
+ 2 + 4 = 10 + 4 = 14); decomposing a number leading to
a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the
relationship between addition and subtraction (e.g.,
knowing that 8 +4 = 12, one knows 12 – 8 = 4); and
creating equivalent but easier or known sums (e.g., adding
6 + 7 by creating the known equivalent 6 + 6 + 1 = 13).
Figuring Fun
Provide a student with an addition or subtraction problem and ask them to explain how they
solved the number sentence. For benchmark 3 students work with problems involving numbers
within 20. Students should be able to figure out the sum/difference within 5 seconds. Ask
students to explain their thinking process to figure out the answer. No manipulatives should be
used. Students should demonstrate of one of the following strategies; making 10,
decomposing, counting on or counting back, doubles, 1 more, 1 less, using an addition fact to
solve subtraction or vice versa, etc…)
1.OA.7 Understand the meaning of the equal sign, and
determine if equations involving addition and subtraction
are true or false. For example, which of the following
equations are true and which are false? 6 = 6, 7 = 8 – 1, 5
+ 2 = 2 + 5, 4 + 1 = 5 + 2.
Charlotte Area Mathematics Consortium, 2011
25. True or Not?
For benchmark 3 use equations only to demonstrate the following:
Determine which of the following examples are true and explain:
2+7=9
10 = 9 + 1
4+3=1+8
1 + 3 = 13
1.NBT.1 Count to 120, starting at any number less than
120. In this range, read and write numerals and represent
a number of objects with a written numeral.
What Comes Next?
Rote count from a number less than 100 up to 100.
Name That Number
Give a number 0 – 100, students represent that number with objects, tally marks, picture sets,
etc…
Charlotte Area Mathematics Consortium, 2011
26. 1.NBT.3 Compare two two-digit numbers based on
meanings of the tens and ones digits, recording the results
of comparisons with the symbols >,=,<.
What’s your Sign?
Use the symbols to make the number sentence true. Draw a picture (base 10 blocks, 10
frames, number lines) and explain your reasoning.
42 __ 45
76 __ 51
22 __ 22
1.NBT.4 Add within 100, including adding a two-digit
number and a one-digit number, and adding a two-digit
number and a multiple of ten, using concrete models or
drawings and strategies based on place value, properties
of operations, and/or the relationship between addition
and subtraction; relate the strategy to a written method
and explain reasoning used. Understand that in adding
Charlotte Area Mathematics Consortium, 2011
27. two-digit numbers, one adds tens and tens and ones and
ones; and sometimes it is necessary to compose a ten.
All About Kids
Task 1
There are 25 jump ropes in the gym and 8 basketballs. How many total jump ropes and
basketball do we have altogether? Explain your answer through pictures, numbers or words.
Task 2
There are 16 students sitting at a table in the cafeteria. There are 20 students sitting at the
next table. How many total students are sitting at the tables in the cafeteria? Explain how you
solved the problem using pictures, numbers or words.
1.NBT.5 Given a two-digit number, mentally find 10 more
or less than the number, without having to count; explain
the reasoning used.
Take It or Leave It
Given a set of objects 0- 90, (e.g. 34 cubes), how many groups of 10 can you make? Are there
any leftovers? How many will there be if we add 10 more? What if we take 10 away?
*can be done in combination with assessment 1.NBT.2
Charlotte Area Mathematics Consortium, 2011
28. 1.MD.4 Organize, represent and interpret data with up to
three categories; ask and answer questions about the total
number of data points, how many in each category, and
how many more or less are in one category than in
another.
Air, Land, and Sea
Prompt students to look at several pictures of living things (see examples).
What question can you ask that will allow you to sort the pictures into groups? Sort the pictures
based on your question/categories. Prompt student to record his/her data on a chart. A chart
example is provided.
Student provide at least three relevant statements to interpret data.
Teacher observation:
Does the student use specific vocabulary (ex: more/less than, most/least)
Sample Chart
Where do these animals live?
Air (numbers or tallies)
Land (numbers or tallies)
Water (numbers or tallies)
Sea Land
Air
Charlotte Area Mathematics Consortium, 2011
29. 1.G.1 Distinguish between defining attributes versus
non-defining attributes; build and draw shapes to possess
defining attributes.
Hide ‘n Seek
Student reaches into a bag and feels the hidden shape
Student describes the hidden shape using defining attributes
Teacher should listen for use of specific vocabulary
o Do children use formal or informal language?
o Do children use defining or non-defining attributes (―The shape has three corners.‖ vs ―The
shape feels like a witch’s hat.‖)
1.G.2 Compose two-dimensional shapes or
three-dimensional shapes to create a composite shape,
and compose new shapes from the composite shape.
Cover Up
Give student a simple pattern block or tangram puzzle
Ask student, ―How many different ways can you cover the puzzle?‖
Observe student:
o Does student strategically manipulate shapes to fit puzzle?
o Does student flip and rotate shapes to make them fit?
o Does student pay attention to boundaries?
Charlotte Area Mathematics Consortium, 2011
30. Common Core Assessment
Tasks
First Grade
Benchmark 4
1.OA.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.
What’s in the Bag? (Change Unknown)
Place ten to twenty objects in a paper bag. The student reaches in a takes some counters out.
Ask ―How many are left in the bag? How did you figure out your answer?‖
Example: Pulled 3 out and 7 remain in the bag. 3 + ___ = 10
or 10 – 3 = ___. Write a number sentence to show what you did to figure out the answer.
Charlotte Area Mathematics Consortium, 2011
31. What’s in the Bag? ( Result Unknown)
Gather ten to twenty objects. Ask the student to choose an amount of objects to put in a paper
bag, naming the number. The teacher does the same from the remaining amount, naming the
number. The student determines how many objects are in the bag. Ask: What did you do to
figure out the answer? Write a number sentence to show what you did to figure out the answer.
(The total number of objects should not exceed 20 for benchmark 4.)
What’s in the Bag? (Start Unknown)
Gather ten to twenty objects. The teacher places some of the objects in a bag without the child’s
knowledge (use a partition, close your eyes). The student places some more objects from the
objects remaining in the bag, naming the number. Remove any remaining objects to eliminate
confusion. The student empties the bag and counts of all the objects. A teacher asks ―How
many objects where in the bag to start with? What did you to figure out your answer? Write a
number sentence to show what you did to figure out the answer.‖ (The total number of objects
should not exceed 20 for benchmark 4.)
1.OA.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.
Ice Cream Treats
Use ten frames, number line, or hundreds chart to solve problems. Students may also draw a
picture to solve problem. (For benchmark 4 students are expected to add 3 numbers with a sum
less than or equal to 20.)
Example: 5 children eat chocolate ice cream. 9 children eat vanilla ice cream. 3 children eat
strawberry ice cream. Ask: How many children are eating ice cream? How did you figure out
your answer? Show me. (Provide a variety of materials for child choose which to use.)
Charlotte Area Mathematics Consortium, 2011
32. 1.OA.3 Apply properties of operations as strategies to add and subtract.
Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.
(Commutative property of addition.) To add 2 + 6 + 4, the second two
numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.)
Mixed Up Numbers
Say: ―Susie solved the following problem: 6 + 2 + 4 = 12 First she added 6 + 2 and got
eight. Then she counted up 4 more and got an answer of 12. Is there a different way to solve
this problem?‖
Observe
- Does the child realize that 6 and 4 can be grouped first into 10 and then add
the leftover 2?
Student should complete this task using objects, drawings, equations and symbols. (For
benchmark 4, sets should not be greater than 20.)
1.OA.4 Understand subtraction as an unknown addend
problem.
Picking Apples
Jan picked three apples from the tree. Jan needs 10 apples in all. How many more apples
does Jan need to pick? (Use storyboards, ten frames or other objects to demonstrate.) Write
an addition and subtraction number sentence to match your story. (For benchmark 4 the total
number of objects used should be less than or equal to 20.)
Charlotte Area Mathematics Consortium, 2011
33. 1.OA.5 Relate counting to addition and subtraction (e.g.,
by counting on 2 to add 2.
Count On and Count Back
Instructional Task 1 (Counting on)
Provide the child with a numeral die and a dot die. Roll the numeral die first. Then roll the dot
die and count on to obtain the total value of the two dice.
Instructional Task 2 (Counting back)
Provide the students with a numeral card or a spinner with numbers 5 to 10. The student
should also have a spinner with dots representing numbers 0 - 5. Students will count back the
value of the dots from the numeral on the card or original spinner.
Instructional Task 3 (Counting on and back)
Given a group of 6 counters, ask students to make the pile contain 10. Observe how student
changes the pile. To meet standard, the student should count on from 6 to get 10, …7 8 9 10.
. Then ask the student to make the pile contain 7 counters. The student should count back
from 10 to 7. Observe the child and ask them to orally explain how they are changing the pile
of counters.
(For benchmark 4 the total number used should be less than or equal to 20.)
Charlotte Area Mathematics Consortium, 2011
34. 1.OA.6 Add and subtract within 20, demonstrating
fluency for addition and subtraction within 10. Use
strategies such as counting on; making ten (e.g., 8 + 6 = 8
+ 2 + 4 = 10 + 4 = 14); decomposing a number leading to
a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the
relationship between addition and subtraction (e.g.,
knowing that 8 +4 = 12, one knows 12 – 8 = 4); and
creating equivalent but easier or known sums (e.g., adding
6 + 7 by creating the known equivalent 6 + 6 + 1 = 13).
Figuring Fun
Provide a student with an addition or subtraction problem and ask them to explain how they
solved the number sentence. For benchmark 4 students work with problems involving numbers
within 20. Students should be able to figure out the sum/difference within 5 seconds. Ask
students to explain their thinking process to figure out the answer. No manipulatives should be
used. Students should demonstrate of one of the following strategies; making 10,
decomposing, counting on or counting back, doubles, 1 more, 1 less, using an addition fact to
solve subtraction or vice versa, etc…)
1.OA.7 Understand the meaning of the equal sign, and
determine if equations involving addition and subtraction
are true or false. For example, which of the following
equations are true and which are false? 6 = 6, 7 = 8 – 1, 5
+ 2 = 2 + 5, 4 + 1 = 5 + 2.
Charlotte Area Mathematics Consortium, 2011
35. True or Not?
For benchmark 4 use equations only to demonstrate the following:
Determine which of the following examples are true and explain:
2+7=9
10 = 9 + 1
4+3=1+8
1 + 3 = 13
1.OA.8 Determine the unknown whole number in an
addition or subtraction equation relating three whole
numbers.
All in the Family
Given a fact family (4 + 3 = 7), students will be able to supply any unknown number to make the
equation true.
(7 = __ + 4, 7 - __ = 4, __ = 4 + 3)
Sample instructional strategies or tools might include fact triangles, number-bond cards,
part-whole cards, dominoes.
(For benchmark 4, students should work with sums within 20.)
Charlotte Area Mathematics Consortium, 2011
36. 1.NBT.1 Count to 120, starting at any number less than
120. In this range, read and write numerals and represent
a number of objects with a written numeral.
What Comes Next?
Rote count from a number less than 120 up to 120.
Name That Number
Give a number 0 – 120, students represent that number with objects, tally marks, picture sets,
etc…
1.NBT.4 Add within 100, including adding a two-digit
number and a one-digit number, and adding a two-digit
number and a multiple of ten, using concrete models or
drawings and strategies based on place value, properties
of operations, and/or the relationship between addition
and subtraction; relate the strategy to a written method
Charlotte Area Mathematics Consortium, 2011
37. and explain reasoning used. Understand that in adding
two-digit numbers, one adds tens and tens and ones and
ones; and sometimes it is necessary to compose a ten.
All About Kids
Room 1 read 24 books in October. Room 4 read 37 books in October. How many books did
both rooms read? Explain your answer through pictures, numbers or words. (Student may use
hundred grids, base ten blocks, etc... to demonstrate answer.)
1.NBT.6 Subtract multiples of to in the range 10-90 from
multiples of 10 in the range 10-90 (positive or zero
differences) using concrete models or drawings and
strategies based on place value, properties of operations,
and/or the relationship between addition and subtraction;
relate the strategy to a written method and explain
reasoning used.
Decades of Fun
There are 40 children on the bus. At the first bus stop, 20 children get off. How many
students are left on the bus? Explain and show your answer using models (hundreds chart, 10
frames, number line).
Charlotte Area Mathematics Consortium, 2011
38. 1.MD.4 Organize, represent and interpret data with up to
three categories; ask and answer questions about the total
number of data points, how many in each category, and
how many more or less are in one category than in
another.
What’s the Weather?
Prompt students to look at a calendar with the weather shown for each day.
Ask: ―How would you sort the weather displayed on this calendar? Could you use numbers or
symbols (tally marks) to show me how you could organize this information?
17 9
4
Student provide at least three relevant statements to interpret data.
Teacher observation:
Does the student use specific vocabulary (ex: more/less than, most/least)
What can you tell me about the weather for this month?
Sunny (numbers or tallies)
Cloudy (numbers or tallies)
Rainy (numbers or tallies)
1.G.3 Partition circles and rectangles into two and four
equal shares, describe the shares using the words halves,
fourths, and quarters, and use the phrases half of, fourth
of, and quarter of. Describe the whole as two of or four of
the shares. Understand for these examples that
decomposing into four or more equal shares creates
Charlotte Area Mathematics Consortium, 2011
39. smaller shares.
Sharing Brownies
Joey and his three friends want to share a pan of brownies equally.
Have student identify which pans are correctly partitioned into fourths.
Ask student to explain reasoning.
*Provide various representations
Charlotte Area Mathematics Consortium, 2011