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 interactive Flash game learners use their knowledge of coordinates on a grid to move Plotter the penguin and avoid trouble. The game includes three levels of difficulty, a story mode, and a choice of five different games to play. Each game provides instruction as well as in-depth help in linked PDF documents.

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 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.

In this challenging instructional task students relate addition and subtraction problems to money and to situations and goals related to saving money.

This word problem may be used for instructional or assessment purposes, depending on where students are in their understanding of addition and how the teacher supports them.

The purpose of this task is for students to select 2 numbers from a set that sum to 5 (or any other number).

Students gain experience and practice with three types of word problems using the "Take From" context: result unknown, change unknown, and start unknown.

This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. However, students should not be discouraged from using individual counting to start if they are stuck. Often students will get tired of counting and devise the shortcut method themselves.

In this lesson plan students create graphs and analyze data based on the data provided by the United States Census Bureau. Students choose five states to focus on and create a bar graph for each, then students compare the data represented in the graphs and answer questions about the data. The lesson includes student activity sheet, the link to the U.S. Census Bureau is no longer active, please follow this link instead: http://www.census.gov/population/projections/files/stateproj/stpjpop.txt

This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.

Students develop a physical understanding for the meaning of equality by trying to find equal lengths using rods.

This task helps students broaden and deepen their understanding of the equals sign and equality.

This lesson from Illuminations provides an introduction to the use of variables, and develops students' algebraic thinking. Students create variable machines to discover the value of words by assigning each letter of the alphabet a unique number value. Learning objectives, a materials list, a pdf file of the student worksheet, an instructional plan, questions for the students, assessment options, extensions, and teacher reflections are provided.

The words compose and decompose are used to describe actions that young students learn as they acquire knowledge of small numbers by putting them together and taking them apart. This understanding is a bridge between counting and knowing number combinations. It is how instant recognition of small numbers develops and leads naturally to later understanding of fact families. This task helps them develop an understanding of number combinations.

This lesson builds on student understanding of how to perform addition and subtraction equatiions by using the concept of math mountains.  Students will be able to find the unknown number by using the part, part, whole strategy.  This concept is foundational for second grade students to experience the connection between subtraction and addtion problems.  Students will explain their understanding by the using diagrams of math mountains.  They will explain how they deternimined the unknown by the part, part, whole system.