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 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.

The goal of this task is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table.

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.

This instructional guide (PDF) is for the mobile app Pick-a-Path (both iOS and Android platforms). The guide provides professional development by discussing the math in each level of the game, giving suggestions for classroom use, and recommending related resources from Illuminations. The Pick-a-Path app is cataloged separately and listed as a related resource.

In this online version of the popular card game, students combine five given number cards, using the four arithmetic operations (addition, subtraction, multiplication, division), to arrive at a target number. This version uses the numbers 1–10 only. Users may ask for a hint or view a possible solution, although there are often multiple solutions.

This interactive game for one or two players develops students' fluency with multiplication facts, understanding of the relationship between factors and products, and strategic thinking. Players take turns moving markers on a factor list and claiming their products on a board displaying all the products of the numbers 1-9. The first player to claim four in a row wins the game. The factors and number needed to win are customizable. The resource includes links to related lessons.

This interactive Java application helps students understand the partial quotients algorithm of division in the context of dividing food equally. Students select a character and a type of food as well as the quantities of characters (divisor, 1-50) and food (dividend, 1-500) – or have the applet make selections randomly. The applet creates a story problem and leads users through the algorithm one step at a time, using questions related to the meaning of each step, and displays graphics illustrating the steps. Remainders can be expressed as whole numbers or fractions. An online calculator is available to help with calculations.

This task helps students understand that when you multiply by a number you always get a bigger number.

This interactive activity adapted from the Wisconsin Online Resource Center challenges you to plan, measure, and calculate the correct amount of roofing material needed to reroof a house.

The purpose of this task is to give students practice representing two digit numbers with concrete objects to reinforce the meaning of the tens digit and the ones digit. This task works best in partners, however it can played individually. The teacher should show the students how to play using an overhead projector or the white board before the students start.

In this unit of five lessons from Illuminations, learners begin with a number-line model and extend it to investigate linear relationships with the Distance, Speed, and Time Simulation from NCTM's E-Examples. Students then progress to plotting points and graphing linear functions while continually learning and reinforcing basic multiplication facts. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to download all student resources.

The purpose of this task is to help students see that 4_(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without evaluating it.

This 2-lesson unit offers a variety of activities and games to help students master multiplication facts with 6 and 7 as factors. It is intended for students who understand the process of multiplication and have mastered the facts where 0, 1, 2, 3, 4, and 5 are factors. Students make use of the effects and properties of multiplication, write and solve story problems, and develop materials and strategies to assist in becoming fluent with the facts. The unit includes questions for students and teachers, a printable multiplication chart, extension ideas, and link to a Virtual Spinner and an online Times Table applet (both catalogued separately).

This article focuses on automaticity and conceptual understanding of multiplication versus memorization of facts. The video, along with the dot cards (linked) allow students to see multiplication as "groups of" before introduction of the multiplication expression, (i.e. 5 x 7). This activity provides students with the conceptual understanding of multiplication and allows for student discourse around strategies for finding the total (counting up, decomposing). Here are a few guiding questions for educators to consider before implementing the activity:
When do students practice multiplication that's not written as AxB? (for the purpose of automaticity) When/how is multiplicative reasoning fostered?When do multiplication strategies become automatized?When do number strategies become number knowledge?

This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.

This Java applet allows a user to practice multiplying numbers by clicking on any of the blue squares to show a product or to double-clicking on any displayed product to hide it behind a blue square again. Exploration questions are included to help the learner see patterns in the table.

This lesson plan provides the teacher with an activity to help students calculate the Greatest Common Factor of two or more positive integers and develop a definition based on their exploration. Students find the prime factorization of two positive numbers using factor trees and Venn diagrams to sort the prime factors. The plan includes learning objectives, materials needed, questions to ask students, assessment options, extensions, teacher self-reflection questions, and further references.