This interactive Flash applet helps students develop number sense and fluency with addition and subtraction facts within 10. Okta hides some bubbles under a shell, and then either adds more bubbles or takes some away. Students determine how many bubbles are left under the shell. Users can choose a specific one-digit starting number or let the applet choose randomly. Users can select addition, subtraction or both.

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

KenKen is a puzzle game that helps students develop whole number calculation skills, logical thinking and perseverance. Users complete the interactive grid with the digits 1-4 (or 1-6) so that each digit appears exactly once in each row or column, while also forming a target number using a specific operation. This page provides four new KenKen puzzles daily with a range of difficulty. Each puzzle includes instructions, rules, and a print option.

This 5-lesson unit is intended to help children who already understand the meanings of addition to develop fluency with addition facts. The activities and games take advantage of commutativity, the additive identity, doubles, and number patterns to develop operation sense and foster retention. Lessons include student materials, questions for students and teachers, assessment ideas, and links to interactive applets.

In this unit plan, primary learners explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using concrete (links), pictorial, and verbal representations to develop an understanding of symbolic notations. Students also investigate fact families, including those where one addend is 0 and where the addends are alike and also learn that the order (commutative) property) does not hold for subtraction. A brief bibliography of related books for children is provided. Instead of using hands on manipulatives and balances, links to Java applets: Pan Balance-Shapes and Pan Balance-Numbers ( both cataloged separately) are included. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to down load all student resources.

In this 6-lesson unit students use pasta shapes to explore the take away model of subtraction in several different contexts (counting, sets, number line, balanced equations, and inverse of addition). They decompose numbers, explore the zero property, act out subtraction situations with objects and pictures, record differences with vertical and in horizontal notation, create fact families, find differences with a calculator, and compose and solve problems involving subtraction. The lessons include student activity sheets (pdf), questions for student discussion and teacher reflection, assessment options, and links to online applets.

In this lesson students find and record addends that sum to ten in three different activities, using ten frames, linking cubes, two-sided counters, and a concentration game. The lesson includes suggestions for assessment and extension, reflection questions for students and teachers, links to related resources, and printable materials (pdf).

In this math lesson, learners use yarn to measure lengths such as arm span and height. This gives learners practice measuring with nonstandard units. Pairs of learners also compare their height and arm spans. They practice problem-solving and reasoning skills by discussing why there are similarities and differences between the lengths of yarn that represent arm spans and height. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

This 4-lesson unit assumes student understanding of multiplication; it uses patterns, properties of the operation, and games to develop fact fluency. The unit included student recording sheets, questions for students and teachers, links to online applets, and suggestions for assessment and extension.

Students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and align paper-and-pencil calculations with the arrays. The lessons provide conceptual understanding of what occurs in a 2-digit multiplication problem. Partial product models serve as transitions to understanding the standard multiplication algorithm.

In this lesson designed to enhance literacy skills, students examine how to multiply fractions by whole numbers in the context of a recipe.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

En el módulo 2, los estudiantes aplican patrones del sistema Base Ten a las estrategias mentales y un estudio secuencial de multiplicación a través de diagramas de área y la propiedad distributiva que conduce a la fluidez con el algoritmo estándar. Los estudiantes se mueven de números enteros a multiplicación con decimales, nuevamente utilizando el valor del lugar como guía para la razón y hacer estimaciones sobre los productos. La multiplicación se explora como un método para expresar medidas equivalentes tanto en el número entero como en las formas decimales. Una secuencia similar para la división comienza concretamente con discos numéricos como una introducción a la división con divisores de múltiples dígitos y lleva al estudiante a dividir los dividendos de número entero y decimales de múltiples dígitos por divisores de dos dígitos utilizando un método escrito vertical. Además, los estudiantes evalúan y escriben expresiones, registrando sus cálculos utilizando la propiedad asociativa y los paréntesis. Los estudiantes aplican el trabajo del módulo para resolver problemas de palabras de varios pasos utilizando multiplicación y división de múltiples dígitos con incógnitas que representan el tamaño del grupo o el número de grupos. El énfasis en la razonabilidad de los productos y los cocientes, la interpretación de los restos y el razonamiento sobre la colocación de decimales se basa en las habilidades aprendidas en todo el módulo, incluido el conocimiento del valor del lugar, el redondeo y la estimación.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
In Module 2 students apply patterns of the base ten system  to mental strategies and a sequential study of multiplication via area diagrams and the distributive property leading to fluency with the standard algorithm.  Students move from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products. Multiplication is explored as a method for expressing equivalent measures in both whole number and decimal forms.  A similar sequence for division begins concretely with number disks as an introduction to division with multi-digit divisors and leads student to divide multi-digit whole number and decimal dividends by two-digit divisors using a vertical written method.  In addition, students evaluate and write expressions, recording their calculations using the associative property and parentheses.  Students apply the work of the module to solve multi-step word problems using multi-digit multiplication and division with unknowns representing either the group size or number of groups.  An emphasis on the reasonableness of both products and quotients, interpretation of remainders and reasoning about the placement of decimals draws on skills learned throughout the module, including refining knowledge of place value, rounding, and estimation.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

El módulo 5 es la culminación del trabajo de los niños con el número en el año previo a K. A lo largo de los módulos 1 y 3, tuvieron extensas experiencias de conteo con los números 0-10. En el módulo 4, examinaron las relaciones entre los números 1-5 hasta la comparación. En el módulo 5, los niños hacen la transición del concepto comparativo de más (4 manzanas es más de 1 manzana) al concepto de adición (3 manzanas y 1 más manzanas hacen 4 manzanas). Están listos para comenzar a trabajar con operaciones, centrándose en las historias de suma y sustracción con los números 1 a 5. Los estudiantes también aprenderán a escribir números 0-5 y explorar patrones en este módulo final.

English Description:
Module 5 is the culmination of children's work with number in the Pre-K year.  Throughout Modules 1 and 3, they had extensive counting experiences with numbers 0-10.  In Module 4, they examined the relationships between numbers 1-5 through comparison.  In Module 5, children transition from the comparative concept of more (4 apples is more than 1 apple) to the concept of addition (3 apples and 1 more apple make 4 apples).  They are ready to begin work with operations, focusing on addition and subtraction stories with numbers 1 to 5.  Students will also learn to write numerals 0-5 and explore patterns in this final module.

This Illuminations brainteaser activity promotes algebraic thinking and reasoning skills. Each letter of the alphabet has been assigned a numerical value. Solvers use given sums of the letter values of 29 names to deduce the individual values. Solvers are asked to find the value of their own names and may use an interactive applet to test their solutions.

In this six lesson unit, students recognize and explore the relationships among pennies, nickels, dimes, and quarters. They estimate and count sets of mixed coins, create equivalent sets, write story problems that involve money, and use coins to make patterns. Within the unit there is a link to US Mint. http://www.usmint.gov/kids/teachers/

This interactive pan balance allows students to enter numeric or algebraic expressions and investigate the important concept of equivalence as well as practice arithmetic and algebraic skills. Users place an expression in each of the red and blue pans. These expressions may or may not include the variable x. If the expression is algebraic, a value for x is entered or adjusted by moving the slider. As the value of x changes, the results will be weighed and graphed. Instructions and exploration directions and questions are included.

This Java tool is used to strengthen student understanding of equality and computation of numerical expressions. The applet also helps students understand that equality is a relationship, not an operation. After entering an expression in both the red and blue pan, the pans will move up and down depending on which expression is greater. When the expressions are equivalent, the pans will balance and the full equation will be entered into the Balanced Equations table. Instructions and exploration directions and questions are included.

This Java applet allows children to explore a balancing tool and thus build their algebraic thinking about equivalency. By placing shapes on each side of the balance and finding equivalent sets of weights, students discover the weight of each shape in one of six built-in sets or a random set.

This five lesson Illuminations unit gives students an opportunity to create and analyze numeric and geometric patterns with particular emphasis on growing patterns. The lesson titles are respectively, What's Next?, Patterns On Charts, Growing Patterns, Exploring Other Number Patterns and Looking Back And Moving Forward. Each lesson includes learning objectives, material list, instructional plan, linked resources and assessment options.

This mobile app (available for both iOS and Android devices) was developed by the National Council of Teachers of Mathematics with funding from Verizon Foundation. The app is based on the Decimal Maze from the popular lesson "Too Big or Too Small". The goal is to help Okta reach the target (maximum, minimum, or a specific value) by choosing a path from the top of the maze to the bottom — adding, subtracting, multiplying and dividing as the player goes. Seven levels with seven puzzles in each level test the player's skills with operation with powers of ten, negative numbers, fractions, decimals, and exponents.