Manipulatives provide a concrete representation of foundational math concepts.

The meaning of mathematical symbols becomes clear by making the connection to manipulatives.

Students use language, symbols and manipulatives to solve everyday problems.

Students develop immediate recall of number relationships AFTER building the conceptual foundation.

1Number Sense2Introduction to Addition & Subtraction3Ones, Tens & Hundreds4Intermediate Addition & Subtraction5Two-Digit & Three-Digit Numbers6Advanced Addition & Subtraction7Adding & Subtracting One-digit Numbers8Introduction to Multiplication & Division9Adding & Subtracting Two-digit Numbers10Three Part Addition & Subtraction11Adding & Subtracting Three-digit Numbers12Introduction to Fractions13Intermediate Multiplication & Division14Unit Fractions15Non-Unit Fractions16Not Greater & Not Less17Improper Fractions

Classroom instruction is informed by the status of each student using Symphony Math.

Symphony Math is an educational software intervention that is designed to provide students with a solid understanding of the most important foundational concepts for math. In a time when students and teachers are pressed to cover a vast amount of math topics in so little time, Symphony Math offers students the opportunity to practice independently the most important math concepts in-depth. The program can be used as an intervention for older students or as a regular ed supplement to a schools existing curriculum.Symphony Math uses on-screen manipulatives to provide students with a visual model of important math concepts. These visual models help students see what the concept looks like which leads to improved understanding. The on screen manipulatives can be used to build problems and receive immediate visual feedback.

This screen shows that five two-bars are equal to one ten-bar. This helps students mentally picture what multiplication and division looks like. 5x2 is seen as five groups of two which equals one group of ten. While many students can memorize their multiplication facts, some students need to work with visual models in order to understand what multiplication facts mean.Symphony Math explicitly makes the connection between the visual models and the symbols that are used to represent math concepts. Once students have developed a basic understanding of the concept with manipulatives, the symbols are introduced. Just as students need to learn that sounds that are represented by the letters of the alphabet, they also need to learn the ideas represented by the numerals and symbols of mathematics.

This screen shows a problem where the student must make the connection between the concrete visual model and the abstract symbols. The symbols show 4+1=5. In this screen the student has correctly created the matching problem with manipulatives. A four-bar combined with a one-bar are the same length as a five-bar.As students become proficient with manipulatives, symbols and language, story problems are introduced. Story problems give students the opportunity to extend their understanding of fundamental concepts to another context.Once students have developed an understanding of a concept with both manipulatives and symbols they work in a timed environment to develop automatic recall of basic number relationships. Students need to answer number relationship questions in five seconds or less to achieve mastery. Detailed reports show which number relationships have been mastered fluently and which have not.Both the National Council of Teachers of Mathematics and the National Mathematics Advisory Panel advocate for teaching a streamlined curriculum that emphasizes the most important mathematical concepts. Symphony Math matches this approach by guiding students through a scope & sequence of the most important mathematical concepts.

Students move through these 17 stages at their own pace. An advanced student might finish the entire program in three hours. A first grade student might spend the entire school year working on stages one, two and three.Symphony Math offers a comprehensive data reporting system to help inform classroom instruction. The dashboard (pictured on this slide) provides real-time updates on student progress and brings important issues to the teachers attention. Questions like, Who needs help? and What do they need help with? are quickly answered on the dashboard. More detailed information can be found in the reports section.This slide illustrates how Symphony Math fits within the three tier model. For tier one students who are on benchmark level with their math skills, Symphony Math can be used three times a week for fifteen minutes each time. At the tier one level, Symphony Math helps students deepen their understanding of important mathematical concepts.

For tier two students, who are below benchmark level with their math skills, Symphony Math can be used 4 times a week for fifteen to twenty minutes each time. The program will provide extra practice mastering fundamental concepts and skills. The program will continually assess which skills a student needs to master, direct the student to those parts of the program, and then progress at that student's level of readiness.

For tier three students, who need intensive intervention with their math skills, Symphony Math can be used five times a week for twenty minutes each time. These students are often struggling in math because they have not mastered fundamental prerequisite concepts. Symphony Math provides students who need considerably more time working with important concepts at their developmental level the opportunity to progress at their own pace.