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I think that from a cognitive learning side, what you've done is wonderful. It's helping them to look at numbers in a logical way, so that when the get to their math class, they understand better what their math teacher is saying.

Teacher, Hawaii

It teaches you new things, in new steps. Like in video games, when you explore new levels – and this is the same thing… except you learn…

Student Grade 5, Rhode Island

I didn't feel very confident in Math. I just kind of guessed all the answers, I didn't really know them. After I tried Symphony Math, it really helped, and when I did paper work, it made it much easier.

Student, Grade 4, Massachusetts

I really hated math, because I didn't understand it. You have to think more, and it really helped me alot. When you put the bars in, the numbers show up, and sometimes when you put the numbers in, the bars show up. It' really helpful that way.

Student Grade 5, Rhode Island

… to drill and drill and drill with flashcards was not working for us. There will be some doors that will be open to her because she has been able to establish a solid foundation in math.

Parent, Florida

I got better with my multiplication facts, and we just started long division, and it's helping me understand it more, because it helps you with your math a lot, and it helps you understand it more.

Student Grade 3, Florida

I put my 25 worst performing students in a pilot program using Symphony Math... Their test scores improved by double digits, and one student raised his scores by 40%.

Middle School Teacher, Hawaii

I’m very happy with the program… I’ve seen improvements with their math skills, and being able to apply {them}… especially with place value, which is hard concept for them… this is another venue for them to explore place value, and actually any of the topics that are taught.

Teacher, Massachusetts

I have been excited by the gains my students have made. The kindergarten students really understand the basic concepts. The program allows the student to progress at his own developmental rate.

Principal, Wyoming

It's so refreshing to work with you and Symphony Math. I really appreciate your dedication to education.

Teacher, New York

It was so much fun. It made me a lot happier in math and a made me a lot more confident to do things.

Student, Grade 4, Massachusetts

Scope & Sequence

Stage / Concept	Example
Stage 1: Number Sense	4 < ? < 7
Equal	3 = ?
Greater	8 > ?
Less	5 < ?
Between	4 < ? < 9
Missing Comparison	2 ? 5 ? 7
Not Equal	7 ? ?
Stage 2: Introduction to Addition & Subtraction	2 + 1 = ?
Introduction to Addition	2 + 1 = ?
Introduction to Missing Addend	2 + ? = 3
Introduction to Subtraction	3 – 1 = ?
Introduction to Missing Subtrahend	3 – ? = 2
Stage 3: Ones, Tens & Hundreds	100+100+100 = ?
Introduction To 1s	1+1+1+1=4
Compose 1s	4 + 5 = 9
Decompose 1s	? + 5 = 9
Comparing 1s	9 > 6
Introduction To 10s	10+10+10+10=40
Compose 10s	40 + 50 = 90
Decompose 10s	? + 50 = 90
Comparing 10s	90 > 60
Introduction To 100s	100+100+100=300
Compose 1s/10s/100s	400 + 500 = 900
Decompose 100s	? + 500 = 900
Comparing 100s	900 > 600
Stage 4: Intermediate Addition & Subtraction	5 + 6 = ?
Intermediate Addition	5 + 6 = ?
Intermediate Missing Addend	5 + ? = 11
Intermediate Missing Addends	? + ? = 11
Intermediate Subtraction	11 – 5 = ?
Intermediate Missing Subtrahend	11 – ? = 6
Intermediate Missing Subtrahend And Minuend	? – ? = 6
Stage 5: Two-Digit & Three-Digit Numbers	300 + 40 + 1 = ?
Composing Two-Digit Numbers	3 + 30 = ?
Decomposing Two-Digit Numbers	? + 30 = 33
Comparing Two-Digit Numbers	45 < ? < 60
Composing Three-Digit Numbers	300 + 40 + 1 = ?
Decomposing Three-Digit Numbers	? + 300 + 40 = 341
Comparing Three-Digit Numbers	542 > ? > 498
Stage 6: Advanced Addition & Subtraction	9 + 8 = ?
Advanced Addition	9 + 8 = ?
Advanced Missing Addend	9 + ? = 17
Advanced Subtraction	17 – 8 = ?
Advanced Missing Subtrahend	17 – ? = 9
Stage 7: Adding & Subtracting One-Digit Numbers	8 + 7 = ? (vertical)
Adding One-Digit Numbers	5 + 4 = ?
Missing Addend One-Digit Numbers	5 + ? = 9
Subtracting One-Digit Numbers	9 – 4 = ?
Missing Subtrahend One-Digit Numbers	9 – ? = 5
Adding One-Digit Numbers With Regrouping	8 + 9 = ?
Missing Addend One-Digit Numbers With Regrouping	8 + ? = 17
Subtracting One-Digit Numbers With Regrouping	12 – 8 = ?
Missing Subtrahend One-Digit Numbers With Regrouping	12 – ? = 4
Stage 8: Introduction to Multiplication & Division	2 x 1 = ?
Introduction to Multiplication	2 x 1 = ?
Introduction to Missing Multiplier	? x 2 = 2
Introduction to Missing Multiplicand	2 x ? = 2
Introduction To Division	2 ÷ 1 = ?
Introduction to Missing Dividend	? ÷ 1 = 2
Introduction to Missing Divisor	2 ÷ ? = 2
Stage 9: Adding & Subtracting Two-Digit Numbers	56 + 75 = ? (vertical)
Adding Two-Digit Numbers	12 + 45 = ?
Missing Addend Two-Digit Numbers	12 + ? = 57
Subtracting Two-Digit Numbers	57 – 12 = ?
Missing Subtrahend Two-Digit Numbers	57 – ? = 45
Adding Two Digit-Numbers With Regrouping	56 + 75 = ?
Missing Addend Two-Digit Numbers With Regrouping	56 + ? = 131
Subtracting Two-Digit Numbers With Regrouping	131 – 75 = ?
Missing Subtrahend Two-Digit Numbers With Regrouping	131 – ? = 56
Stage 10: Three Part Addition & Subtraction	8 + 5 + 2 = ?
Three-Part Addition	3 + 2 + 5 = ?
Three-Part Missing Addend	3+2+?=5
Missing Part Of Sum	2 + 3 = ? + 4
Three-Part Subtraction	10 – 3 – 2 = ?
Three-Part Missing Subtrahend	10 – 3 – ? = 5
Stage 11: Adding & Subtracting Three-Digit Numbers	342+237=? (vertical)
Adding Three-Digit Numbers	342 + 237 = ?
Missing Addend Three-Digit Numbers	342 + ? = 579
Subtracting Three-Digit Numbers	579 – 237 = ?
Missing Subtrahend Three-Digit Numbers	579 – ? = 342
Adding Three-Digit Numbers With Regrouping	679 + 834 = ?
Missing Addend Three-Digit Numbers With Regrouping	679 + ? = 1513
Subtracting Three-Digit Numbers With Regrouping	1513 – 834 = ?
Missing Subtrahend Three-Digit Numbers With Regrouping	1513 – ? = 679
Stage 12: Introduction to Fractions	1/2 of 2 = ?
Unit Fractions: Missing Part	1/2 of 2 = ?
Unit Fractions: Missing Whole	1/2 of ? = 1
Unit Fractions: Missing Relationship	?/? of 2 = 1
Non-Unit Fractions: Missing Part	2/3 of 3 = ?
Non-Unit Fractions: Missing Whole	2/3 of ? = 2
Non-Unit Fractions: Missing Relationship	?/? of 3 = 2
Whole Fractions: Missing Part	4/4 of 4 = ?
Whole Fractions: Missing Whole	4/4 of ? = 4
Whole Fractions: Missing Relationship	?/? of 4 = 4
Stage 13: Intermediate Multiplication & Division	3 x 9 = ?
Intro To Missing Multiplier And Multiplicand	? x ? = 2
Intermediate Multiplication	3 x 9 = ?
Intermediate Missing Multiplier	? x 9 = 27
Intermediate Missing Multiplicand	3 x ? = 27
Intermediate Division	27 ÷ 9 = ?
Intermediate Missing Dividend	? ÷ 9 = 3
Intermediate Missing Divisor	27 ÷ ? = 3
Intermediate Missing Divisor And Quotient	27 ÷ ? = ?
Stage 14: Unit Fractions	1/2 of 4 = ?
Advanced Unit Fractions: Missing Part	1/2 of 4 = ?
Advanced Unit Fractions: Missing Whole	1/2 of ? = 2
Advanced Unit Fractions: Missing Relationship	?/? of 4 = 2
Comparing Unit Fractions	1/2 > ? > 1/4
Comparing Unit Fractions: Missing Comparison	1/2 ? 1/3
Stage 15: Non-Unit Fractions	2/3 of 9 = ?
Advanced Non-Unit Fractions: Missing Part	2/3 of 9 = ?
Advanced Non-Unit Fractions: Missing Whole	2/3 of ? = 6
Advanced Non-Unit Fractions: Missing Relationship	?/? of 9 = 6
Comparing Non-Unit Fractions	3/3 > ? > 1/3
Comparing Non-Unit Fractions: Missing Comparison	2/3 ? 4/5
Stage 16: Not Greater & Not Less	4 NOT > ?
Not Greater Than	4 NOT > ?
Not Less Than	4 NOT < ?
Negative Inequalities	4 NOT < ? NOT < 2
Missing Comparisons (Negation)	4 ? 6 ? 8
Stage 17: Improper Fractions	3/2/ of 4 = ?
Improper Fractions: Missing Part	3/2 of 4 = ?
Improper Fractions: Missing Whole	3/2 of ? = 6
Improper Fractions: Missing Relationship	?/? of 4 = 6
Comparing Improper Fractions	3/2 < ? < 6/2
Comparing Improper Fractions: Missing Operator	3/2 ? 5/3

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