This interactive Flash puzzle helps children develop number sense and an understanding of our decimal number system. A 0-99 square has been cut into 11 irregular pieces which the user re-assembles. A printable (pdf) version is included along with questions for Getting Started and a Teachers' Resources page with implementation suggestions.

In this 5.5 minute video Dr James Grime (Cambridge University, UK) explains why mathematicians don't classify the number 1 as a prime. He includes historical background and an explanation of the Fundamental Theorem of Arithmetic.

This web page provides links to resources aligned to the CCSS that guide and support first grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) and Problems of the Month, (POM home page is cataloged separately) developed by the Noyce Foundation are included. The activities were designed to measure students' ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. Resources are listed for specific grade 1 standards and are also organized by progression for an alternate search route.

This page hosts a collection of geometric tasks in pdf format that are aligned to the CCSS standards 1.G1 through 1.G3. It also has links to supplementary literature and learning materials.

This page provides examples of 1st Grade Measurement and Data activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group, or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for 1st Grade Measurement and Data Activities listed are in PDF format.

This blog page offers more than 25 activities and games that use a Hundred Chart to develop students' skills and concepts in a variety of math topics: basic operations, number sense, patterns, number theory, fractions, decimals, and logic. The suggestions include links to materials and to other websites.

This problem with multiple solutions offers an opportunity for students to practice simple addition and subtraction, work with number sentences (equations), and develop systematic work habits. Given cards containing the addition, subtraction and equal signs along with the digits 2, 4, 6, and 8. solvers are challenged to find as many ways as possible to arrange some or all seven cards to create true statements. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, printable cards (pdf) and a link to an interactive Flash applet.

This Java applet game promotes mental math and strategic thinking skills using a card from Suntex's 24 Game. The player is presented with four numbers (1-9) on a card. The goal is to manipulate each of the four numbers only once so that the end result is 24. Addition, subtraction, multiplication, division and/or parentheses maybe used and the player must be able to enter the expression using the online calculator.

This number challenge is an opportunity to reinforce mental arithmetic and order of operations while developing systematic work habits. Students are asked to use the numbers 4, 6, 6, and 8 (exactly once each) and the four basic operations to find as many ways as they can to represent the number 24. There are over 60 different ways! The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for support, and a link to a related article, Opening Out. (cataloged separately).

In this open-ended investigation, students use visualizing skill and work systematically to explore surface area. Learners use linking cubes to build three-dimensional objects with exactly 28 faces exposed. Ideas for implementation, extension and support are included.

In this 7-minute video astronomer Dr Meghan Gray explains the relationship of the Earth's rotation and its revolution around the Sun, resulting in the need to add an extra day to our calendar every four years. She describes additional adjustments required to keep our calendar aligned with the Earth's movements. Dr Gray explains the Julian date and its usefulness.

This activity helps students develop concepts and language related to position by experimenting with the size and relationships between two circles in a qualitative way. They use terms such as outside, touching and overlapping. The Teachers' Notes page includes suggestions for implementation and discussion questions. Students then can move to a follow-up activity, 3 Rings, cataloged separately.

This web page provides links to resources aligned to the CCSS that guide and support second grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS), Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks developed by the Noyce Foundation are included. The tasks were designed to measure students’ ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. They include the scoring rubric, student responses, and discussion of student understanding and misconceptions. Resources are listed for specific grade 2 standards and are also organized by progression for an alternate search route.

This page hosts a collection of geometric tasks in pdf format that are aligned to the CCSS standards 2.G1 through 2.G3. It also has links to supplementary literature and learning materials.

This page provides examples of 2nd Grade Measurement and Data activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group, or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for 2nd Grade Measurement and Data Activities listed are in PDF format.

This interactive Flash applet provides a Concentration-type game (called pelmanism in the UK) in which students must discern the properties of three-dimensional solids and their colors in order to match them in pairs. Spheres, cones, prisms and other standard 3-D shapes are hidden face down on cards. Time and number of trials needed to solve are recorded.

This activity helps students develop concepts and language regarding the size and positional relationship possibilities of three circles in the plane in a qualitative manner. They use terms such as overlapping, inside, and touching as they work systematically to find all possible arrangements. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension. This activity can be a follow-up to "2 Rings" cataloged separately.

This web page provides links to resources aligned to the CCSS that guide and support third grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) and Problems of the Month, (POM home page is cataloged separately) developed by the Noyce Foundation are included. The tasks were designed to measure students’ ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. They include the scoring rubric, student responses, and discussion of student understanding and misconceptions. Resources are listed for specific grade 3 standards and are also organized by progression for an alternate search route.

This page hosts a collection of geometric tasks in pdf format that are aligned to the CCSS standards 3.G1 and 3.G2. It also has links to supplementary literature and learning materials.

This page provides examples of 3rd Grade Measurement and Data activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group, or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for 3rd Grade Measurement and Data Activities listed are in PDF format.

This flexible, interactive Flash applet allows students to explore number patterns and to develop number sense and fluency with addition, subtraction, and multiplication. The student or teacher enters a starting number and a step increment. Both values may be up to 4 digits and either positive or negative. The user then mentally carries out the sequence and enters the resulting 10th and 11th terms. The first 9 terms are color-coded in groups of 3 and may be shown or hidden one group at a time. Users have the option of hiding or showing the starting number and/or the increment.

This web page provides links to resources aligned to the CCSS that guide and support fourth grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) for the Noyce Foundation, Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks developed by the Noyce Foundation are also included. The performance tasks were originally designed to measure students' ability to solve non-routine problems and then to explain and justify their solutions. The task scoring rubric, student responses, and discussion of student understanding and misconceptions are provided to improve instruction. Resources are listed for specific grade 4 standards and are also organized by progression for an alternate search route.

This page hosts a collection of geometric tasks in pdf format that are aligned to the CCSS standards 4.G1 through 4.G3. It also has links to supplementary literature and learning materials.

This page provides examples of 4th Grade Measurement and Data activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group, or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for 4th Grade Measurement and Data Activities listed are in PDF format.

This math app intended for upper elementary students using the addition and subtraction level and middle school students using all four operations helps players practice their order of operations. This interactive game encourages students to use higher order thinking to use the five numbers and given operations to solve the "target" number by working backwards given the answer but not the equation. The best feature about this math game is that teachers are able to receive immediate feedback of their students’ progress through email. Students do not have to provide an email address in order to play.

This blog entry identifies five Pinterest boards for mathematics. Each board is represented by a picture, link, and brief description. This web blog contains a link to "10 Pinterest Boards Every Teacher Must Know About".

This blog post contains links to resources intended to help teachers and parents prepare for and engage in successful parent-teacher conferences.

This problem reinforces the telling of time on a digital clock, and it requires students to work systematically. The number of 'times' the digit 5 appears in a 24-hour period is a matter of a solver's assumptions. Ideas for implementation, extension and support are included along with a printable poster. A link to an interactive Class Clock (cataloged separately) is provided.

This web page provides links to resources aligned to the CCSS that guide and support fifth grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS), Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks developed by the Noyce Foundation are included. The tasks were designed to measure students' ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. They include the scoring rubric, student responses, and discussion of student understanding and misconceptions. Resources are listed for specific grade 5 standards and are also organized by progression for an alternate search route.

This page hosts a collection of geometric tasks in pdf format that are aligned to the CCSS standards 5.G1 through 5.G4. It also has links to supplementary literature and learning materials.

This page provides examples of 5th Grade Measurement and Data activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for 5th Grade Measurement and Data Activities listed are in PDF format.

This webpage provides free resources to educators wanting to know more about the CCSS standards for reading and mathematics. The resources fall under 3 categories "Steal these Tools" (lessons and activities that can be implemented in your classroom), "You've got to read this" (research, articles, and webpages for professional development), and "By teachers for teachers" (information about teachers making contributions to the field of education).

This web page presents information about using math templates during instruction to keep each student actively involved and to allow the teacher to informally assess each student's proficiency with the skills and concepts addressed throughout the lesson. The web page provides suggestions for using templates and explanations for why templates should be used. There is a link to the template library, which includes available templates (in PDF format) for the following categories: Number and Operation, Patterns and Algebra, Geometry and Measurement, Data Analysis and Probability, Discrete Math and Logic and Problem Solving.

In this article eight guidelines are detailed for making adaptations to the general reading and math curriculum. Each principal is explained and a link is provided to a chart that lists these guidelines and questions to ask yourself before selecting the adaptation. A link to similar articles on adapting curriculum is also provided.

This 440-page report explores how students in pre-K through grade 8 learn mathematics, with a focus on number and operations, and recommends how teaching, curricula, and teacher education should change to improve mathematics learning. (A 39-page summary, Helping Children Learn Mathematics, is catalogued separately.) The authors identify five interdependent components of mathematical proficiency and describe how students develop this proficiency. The report presents a portrait of mathematics learning: research findings on what children know about numbers before they arrive in pre-K and the implications for instruction; details on the processes by which students acquire mathematical proficiency; what is known from research about teaching for mathematics proficiency and developing proficiency in teaching. Visitors to this website may read the full text online, download a copy (pdf), or purchase a hard copy.

This page provides a problem solving resource for teachers to use with their students in the days leading up to Christmas. Twenty-four math problems from the NRICH collection have been included in this advent problem set based on the theme of Planet Earth; each problem includes teacher resources, a printable page, and a solution

This virtual manipulative allows a teacher or student to represent a linear equation and solve it through the use of a balance beam. Unit blocks (representing 1s) and x-boxes (representing the unknown), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, the learner can choose to perform any arithmetic operation to both sides of the equation keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance thus giving the value of x. There is also the option of creating your own equations to solve.

This problem introduces repeated doubling in the context of a plant with branches that split into 2 more branches every week. The problem lays the foundation for understanding exponential growth and lends itself to a variety of representations. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

In this problem learners practice addition, subtraction and multiplication while developing logical reasoning. Solvers apply the given clues along with their understanding of the domino numbering system to determine which dominoes are missing from a set. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, printable sheets of dominoes (pdf), and a link to an interactive Dominoes Environment (cataloged separately).

This interactive Flash applet enables students, using estimation and measurement skills, to investigate angles. Teachers can use this page for demonstrating how to read a protractor, and the protractor can be hidden to give students practice in estimating angle measures. The size of the angle can be controlled or chosen randomly.

In this blog entry, the author explains the importance of identifying the learning goal before choosing any type of digital tool. Typical uses of digital devices and applications are described as the author suggests the necessary steps in planning and implementing them in the classroom. Cost considerations and links to suggested sites providing details about available apps are included. While this blog post does not address teaching mathematics specifically, the information is useful to elementary teachers of all subjects as they make decisions about the implementation of technology in their classrooms.

This NCTM resource presents a problem involving distance, rate and time. The challenge asks students to determine the number of days it would take a tern to migrate from the Arctic to the Antarctic given a constant rate of speed. Hints and prompts for students and additional "Try These" challenges about distance and speed are also included. Students may also check their answer and see steps to solve the problem. PDF files of the challenges are linked from the site for printing.

Learn the relationship between perimeter and area. A shape will be automatically generated with the perimeter that you choose. Calculate the area of this shape. Area Explorer is one of the Interactivate assessment explorers.

This lesson plan helps students understand multi-digit division by constructing area models. The included interactive provides two example problems and helps connect the model to the traditional long division algorithm. Students solve their own problems using graph paper and/or base-10 blocks and progress toward mental strategies.

This activity reinforces the concepts of area and perimeter and their independent relationship. Students analyze and compose shapes made from unit squares that satisfy area and perimeter specifications. Ideas for implementation, extension and support are included along with printable sheets and shape cards.

This interactive Wolfram Demonstration helps students visualize the relationship between multiplication and the area of a rectangle. On a 10x10 multiplication table, with 1 in the lower left and 100 in the upper right, users adjust the size of a rectangle by dragging a vertex or sliders, or by choosing a product from a pulldown list. The resulting rectangle highlights the width, height and area (factors and product) as well as other equivalent areas (products) on the board, illustrating commutativity and multiple factor pairs. Wolfram CDF Player, a free download, is required to view this resource.

Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.

This weblog by Elena Aguilar details important issues about coaching teachers. The topics in the entries vary in content, but are always centered around the idea of transforming instruction through coaching.

This brief article describes how one elementary school uses visual arts, dance, drama, or music to teach other subjects like mathematics, social studies, language arts, and science. Students learn geometry kinesthetically with flexible bands called “stretchies.” The integrated activities not only help students retain knowledge but also teach them to work together cooperatively. Guided by ASU Public Events and the Peoria Unified School District Arts Education Department, this model was adapted from the Changing Education Through the Arts (CETA) model developed by the John F. Kennedy Center for the Performing Arts in Washington D.C. and Partners in Education Department.

This 8-page monograph offers strategies for effective questioning that engages students and that deepens their conceptual understanding in mathematics. It suggests questions and prompts that help students progress through various stages of the problem solving process and that help teachers assess the thinking of students. The article describes the purposes of questions at different stages of a lesson and describes situations when it is appropriate to convey information to students. A list of references is included.

In this practice guide the Institute of Education Sciences (IES) provides reseach based guidelines for implementing a school or system wide intervention program. The guide identifies eight recommendations to help educators use response to intervention practices, provides a brief description of each, establishes the relative strength of the research base, and discusses difficulties that may occur in implementing these interventions.

This interactive Java applet gives students practice in sorting attribute blocks by color, shape, or size. In each problem students are presented with a set of objects that share a common attribute, and they must identify objects from another set that have the same attribute. Students can check their solution, and have another try or request a new problem. Teacher information about the blocks and their classroom implementation is included.

This interactive Java applet helps students learn about sequences and patterns through analysis of attributes. The user analyzes the existing pattern and must complete the "train" by dragging the appropriate shapes into place. The user is required to discern which attribute is used to create the pattern (color, shape, or number) as well as determine how to extend it.

This problem, from the collection of Aunty Mathilda challenges, promotes algebraic thinking and problem solving strategies. When Mathilda was ten years old her rich aunties wanted to give her a gift of money for her birthday but she must first decide if she would rather have one more silver dollar then she received last year on her birthday or twice as many dimes then she received last year. Aunty Mathilda's nephew believes she made the wrong decision. Included are links to an easier challenge and to a harder one, and additional background support: alignment to the CCSS standards, explanations, literature connections and extensions regarding the challenge.

This problem, from the collection of Aunty Mathilda challenges, promotes algebraic thinking and problem solving strategies. Aunty Math must determine the individual weight of her two nephews and niece given clues about their combined weight. Included are links to an easier challenge and to a harder one, depending on the level of the solver, and a link to a page for parents and teachers with additional background support, alignment to the CCSS, explanations and extensions.

This problem builds on simple sorting skills and gives children the opportunity to use logical reasoning. Students describe the characteristics of ten marbles using their different color markings and then design a color scheme for marbles to show specific attributes. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.

This 8-page monograph explains bansho, a research-informed instructional strategy for mathematical communication and collective problem-solving. Following a brief overview, the article outlines how bansho can be used to plan and implement an effective three-part problem-solving lesson. Bansho can be incorporated into collaborative planning sessions, in which teachers work with partners or in groups within communities of practice to learn about mathematics for teaching. The author provides a sample grade 2 lesson on the development of multiplication concepts and a list of references.

Enter data to create a bar graph, then change many settings for the graph's appearance.

Sort colored shapes into a bar graph. Practice sorting by shape or by color. Appropriate for elementary grades. Bar Graph Sorter is one of the Interactivate assessment explorers.

This Java applet allows students to practice adding and subtracting whole numbers, decimals, or integers. Students use base blocks in blue to represent positive numbers, and red to represent either negative numbers or subtraction. The applet offers up to three decimal places, 2 to 4 columns, and bases from 2 through 5 and 10. Applet instructions and teaching ideas are available through the links at the top of the page.

This interactive Java applet helps users develop place value concepts involving subtraction of numbers with 1, 2, 3, or 4 digits. The virtual blocks are manipulated to model regrouping in order to solve whole number subtraction problems posed by the applet. Users also may create and solve their own problems with whole numbers or with up to 3 decimal places. When creating problems a user may change the default of base 10 to any of the bases 2, 3, 4, or 5.

This collection from NRICH provides activities to help learners think and work like a mathematician. Tasks have students exploring, questioning, working systematically, visualizing, conjecturing, explaining, generalizing and justifying. Activities are organized under specific strategies and processes.

This collection from NRICH provides activities to help learners think and work like a mathematician. Tasks have students exploring, questioning, working systematically, visualizing, conjecturing, explaining, generalizing and justifying. Activities are listed under strategies and processes.

In this formative assessment lesson students identify patterns (both linear and exponential) in a realistic context. They may solve this problem through a variety of strategies, providing opportunities for groups of students to share and critique various problem solving approaches.

In this creative thinking activity students must determine how many combinations can be made when putting three beads into bags. To complete the activity students must create their own recording system to make sure they are not repeating solutions and they have found all possible solutions. Included in this resource are teacher’s notes with suggestions for introducing the activity, discussion questions, support suggestions, and a printable version.

The stated mission of this blog is "To make the nightly math problem as common as the bedtime story." Each day Laura Bilodeau Overdeck and her husband John post an interesting fact or scenario about everyday life and related math problems at three readiness levels. They include a page of suggestions for how to use these problems with children. This is a good source of problems for teachers and parents, as well as a model for adapting problems to meet different needs.

This iOS app for the online site Bedtime Math (cataloged separately) offers a problem of day as well as a database of over 400 problems that cover a range of topics that the user may explore. Each problem of the day includes background information and four levels of problem solving options (Wee Ones, Little Kids, Big Kids, and the Sky's the Limit). Each problem includes an answer.

This 2.5 minute animation introduces children to the concept of a fraction as part of a whole. It defines numerator and denominator in both slash and horizontal bar format and challenges viewers to name two fractions represented by visual models.

This blog is dedicated to sharing ideas for integrating children's literature with elementary mathematics. Entries include descriptions and commentary on specific books as well as teaching tips for using them. The author includes external links to lesson plans and to authors' home pages. Readers can browse for books by math topic and leave comments to share their own teaching tips.

This free iOS app helps develop spatial reasoning and strategic thinking. Users reflect seed squares (horizontally, vertically and diagonally) to grow larger pieces that eventually cover the given design space without spilling over. A graduated set of difficulty levels makes the game accessible to a wide range of ages.

This problems is an opportunity to explore triangular numbers in the familiar context of decorating a birthday cake with a number of candles corresponding to a child's age. The problem lends itself to systematic strategies and multiple representations. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

This problem provides an opportunity for students to develop problem solving skills while applying skip-counting and exploring the concepts of multiples and factors within 20. It is posed in the context of toppings on cookies ("biscuits" in the UK) and lends itself to multiple representations. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and downloadable handouts.

In this problem students explore the concept of proportion by comparing the relative strengths of different mixes of juice flavor and water in a visual context. Given four mixtures represented by purple and white rectangles, students order the drinks from strongest to weakest flavor and explain their reasoning. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support.

This problem requires a sound understanding of the fraction relationship between part and whole and can be used for finding fractions of numbers and quantities. Students are given the fractional amount of apples in a fruit bowl and the specific number of other fruit in the bowl in order to figure out how many apples are in the bowl. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension, a link to a worksheet which provides student support, and a downloadable pdf of the puzzle.

This problem introduces children to algebra by looking for a pattern and generalizing with a rule. Students explore in how many different ways can a stick of 6, 7 or 8 different colored interlocking cubes be broken into two parts. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and an idea for support and extension.

In this activity, learners decipher a page from the Dresden Codex, one of the few Mayan books still in existence. By thinking like an archaeologist, students combine their mathematical abilities with some basic logic and trial-and-error investigation to figure out what the codex means. In the course of this explorations, participants discover: How archaeologists have figured out what Mayan documents mean. How the Mayan system of counting is like ours, and how it is different. How Mayan beliefs were tied to their understanding of mathematics.

This brief article describes the historical methods of marking and measuring time. Among the instruments and methods discussed are sundials, water clocks, celestial motions, and mechanical clocks. Included are descriptions of the sources of inaccuracies of these methods. Links to related resources and a separate page of pedagogical notes are provided.

This problem promotes logical thinking and introduces learners to the trial and error (guess and check) problem solving strategy, especially with the interactive provided. In this problem children need to understand the difference between having a certain number of brothers and the number of boys in a family to answer the question, "How many children are there in the Brown family?" The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a down loadable worksheet for students to table their trials.

This lesson plan requires students to interpret line plots with scales to the nearest quarter of a unit. During the lesson students review measurement, elements of a line plot, and analyzing data. An independent activity is included for assessment and students' examples are included for comparison.

In this Cyberchase interactive simulation students help the Cybersquad gather bugs to create a bar graph by sorting the bugs into the correct columns by color. Once three graphs have been created they are prompted to answer a question comparing the graphs, all of which have different scales. The simulation includes instructions and hints.