Scope & Sequence
Symphony Math focuses on the foundations for success in mathematics. The following Scope & Sequence provides an overview of the main concepts that are addressed in each Stage and SubStage, along with the main Common Core State Standard that applies to each concept. Mastery Round Levels (MR), or timed mastery rounds that practice math facts, are activated when students master particular Stages. Students work on the Mastery Rounds separately from their work in the conceptual Stages.
Stage  Concept  Standard  Example  
1  The Number Sequence  K  1,2,3,4,?  
1.1  Sequencing  K.CC.4  1,2,3,4,?  
1.2  Identifying Numbers  K.CC.3  Find ’3′  
1.3  Counting Forward  K.CC.2  4,5,6,?  
1.4  Counting Backward  K.CC.2  7,6,5,?  
2  More/Less/Same  K  Find ’1′ more than 6.  
2.1  Find ‘One More’  K.CC.5  Find ’1′ more than 6.  
2.2  Find ‘One Less’  K.CC.4  Find ’1′ less than 5.  
2.3  Find ‘More’  K.CC.5  Find ‘Taller.’  
2.4  Find ‘Less’  K.CC.4  Find ‘Less’.  
2.5  Same  K.CC.6  4 = ?  
3  Add & Subtract to 5  K  3 + 2 = ?  
3.1  Beginning Addition: Missing Result  K.OA.2  3 + 2 = ?  
3.2  Beginning Addition: Missing Change  K.OA.2  ? + 1 = 5  
3.3  Beginning Subtraction: Missing Result  K.OA.2  5 – 1 = ?  
3.4  Beginning Subtraction: Missing Change  K.OA.2  4 – 2 = ?  
3.5  Adding 0 and 1  K.OA.5  6 + 0 = ?  
3.6  Subtracting 0 and 1  K.OA.5  7 – 1 = ?  
3.7  Commutative Property  K.OA.2  7 + 1 = 1 + ?  
MR 1  Add & Subtract Within 5  K.OA.5  1 + 2 = ? (timed)  
MR 2  Add & Subtract Within 5 (Missing Change)  K.OA.5  1 + ? = 3 (timed)  
4  Ten as a Unit  K  8 + 2 = ?  
4.1  Introducing 10  K.OA.4  8 + 2 = ?  
4.2  Making 10  K.OA.4  ? + 7 = 10  
4.3  10 Plus  K.OA.4  10 + 3 = ?  
4.4  Subtracting with 10  K.OA.4  10 – 4 = ?  
MR 3  Add & Subtract Within 10  1.OA.6  2 + 8 = ? (timed)  
MR 4  Add & Subtract Within 10(Missing Change)  1.OA.6  2 + ? = 10 (timed)  
5  Comparing Numbers  K  ? = 13  
5.1  Equals  K.CC.7  ? = 13  
5.2  Greater Than  K.CC.7  8 > ?  
5.3  Less Than  K.CC.7  8 < ?  
6  Add & Subtract to 20  1  6 + 8 = ?  
6.1  Advanced Addition: Missing Result  1.OA.1  6 + 8 = ?  
6.2  Advanced Addition: Missing Change  1.OA.2  6 + ? = 14  
6.3  Advanced Subtraction: Missing Result  1.OA.2  18 – 9 = ?  
6.4  Advanced Subtraction: Missing Change  1.OA.1  18 – ? = 9  
6.5  Fact Families  1.OA.3  3 + 5, 5 + 3, 8 – 3, 8 – 5  
6.6  Threepart Addition & Subtraction  1.OA.3  14 = 8 + ? + 4  
MR 5  Add & Subtract Within 20  2.OA.2  8 + 9 = ? (timed)  
MR 6  Add & Subtract Within 20 (Missing Change)  2.OA.2  8 + ? = 17 (timed)  
7  Tens  1  Create ’80.’  
7.1  Identifying 10s  1.NBT.2  Create ’80.’  
7.2  Ordering 10s  1.NBT.2  20, 30, 40, ?  
7.3  Counting Backward by 10s  1.NBT.2  70, 60, 50, ?  
7.4  Find ‘Ten More’  1.NBT.5  Make ’10 more’ than 50.  
7.5  Find ‘Ten Less’  1.NBT.5  Make ’10 less’ than 40.  
7.6  Related 1s and 10s  2.NBT.5  20 + 50 = ?  
7.7  Combinations of 100  1.NBT.4  100 = 30 + ?  
7.8  Add/Subtract Teens and Ones  1.OA.6  12 + 5 = ?  
7.9  Compare Tens  1.NBT.3  30 ? 50  
8  Add & Subtract with 10s  1  20 + 3 = ?  
8.1  Place Value Addition: Missing Result  1.OA.8  20 + 3 = ?  
8.2  Place Value Addition: Missing Change  1.NBT.4  20 +? = 23  
8.3  Place Value Subtraction: Missing Result  1.OA.4  23 – 3 = ?  
8.4  Place Value Subtraction: Missing Change  1.OA.8  23 – ? = 20  
8.5  PartWhole with 1s and 10s  2.NBT.5  56 = 20 + ? +?  
8.6  PartWhole with 1s and 10s (+10)  1.NBT.5  69 + 10 = ?  
8.7  PartWhole with 1s and 10s (10)  1.NBT.5  56 10 = ?  
8.8  Adding With Multiples of 10 (No Regroup)  1.NBT.4  37 + 40 = ?  
8.9  Compare TwoDigit Numbers  1.NBT.3  67 ? 82  
9  Hundreds  2  Make ’700.’  
9.1  Identifying 100s  2.NBT.1  Make ’700.’  
9.2  Ordering 100s  2.NBT.2  200, 300, 400, ?  
9.3  Counting Backward by 100s  2.NBT.2  700, 600, 500, ?  
9.4  Find ’100 More’  2.NBT.2  Make ’100 more’ than 400.  
9.5  Find ’100 Less’  2.NBT.2  Make ’100 less’ than 600.  
9.6  Related 1s, 10s, 100s  2.MD.6  2 + 5, 20 + 50, 200 + 500  
9.7  Add/Subtract Hundreds and Tens  2.MD.6  730 + 50 = ?  
9.8  Compare Hundreds  2.NBT.4  300 ? 500  
MR 7  Add & Subtract Within 200  3.NBT.2  160 + 50 = ? (timed)  
MR 8  Add & Subtract Within 200 (Missing Change)  3.NBT.2  160 + ? = 210 (timed)  
10  Add & Subtract with 100s  2  200 + 30 = ?  
10.1  Place Value Addition: Missing Result  2.NBT.7  200 + 30 = ?  
10.2  Place Value Addition: Missing Change  2.MD.6  200 + ? = 230  
10.3  Place Value Subtraction: Missing Result  2.NBT.7  230 – 30 = ?  
10.4  Place Value Subtraction: Missing Change  2.MDF.6  230 – ? = 200  
10.5  Part to Whole (1s,10s,100s)  2.NBT.1  563 = ? + 30 + ?  
10.6  PartWhole: 1s, 10s, and 100s (+100)  2.NBT.8  692 + 100 = ?  
10.7  PartWhole: 1s, 10s, and 100s (100)  2.NBT.8  564 – 100 = ?  
10.8  Compare ThreeDigit Numbers  2.NBT.4  697 ? 903  
11  Foundations for Multiplication  2  2, 4, 6, ?, ?  
11.1  Skip Counting  2.NBT.2  2, 4, 6, ?, ?  
11.2  Adding 2s, 3s, and 4s  2.OA.4  3+3+3+3+3=?  
11.3  Equal Groupings  2.OA.4  ‘Create 4 groups of 2’  
12  Regrouping with 2 and 3 digits  2  19 + 5 = 20 + ?  
12.1  Regrouping with 1 and 2 Digits  2.OA.1  19 + 5 = 20 + ?  
12.2  Regrouping to 100  2.NBT.5  47 + 19 = 60 + ?  
12.3  Regrouping with 2 Digits: Subtraction  2.NBT.5  33 – 5 = 20 + ?  
12.4  Regrouping with 2 Digits: Missing Change  2.NBT.5  39 + ? = 60 + 8  
12.5  Regrouping with 2 Digits: Subtraction, Missing Change  2.NBT.5  71 – ? = 50 + 7  
12.6  Regrouping to 1,000: Addition  2.NBT.7  247 + 386 = 600 + ? + 3  
12.7  Regrouping to 1,000: Subtraction  2.NBT.7  712 – 30 = 600 + ? + 2  
13  Multiplication and Division  3  2 x 4 = ?  
13.1  Intro to Multiplication: Missing Product  3.OA.1  2 x 4 = ?  
13.2  Intro to Multiplication: Unknown Number of Groups  3.OA.3  ? x 2 = 12  
13.3  Intro to Multiplication: Size of Group Unknown  3.OA.4  2 x ? = 20  
13.4  Intro to Division  3.OA.2  12 ÷ 3 = ?  
13.5  Intro to Missing Dividend  3.OA.4  ? ÷ 5 = 2  
13.6  Intro to Missing Divisor  3.OA.6  10 ÷ ? = 2  
MR 9  Multiply & Divide Within 30  3.OA.7  3 x 8 = ? (timed)  
MR 10  Multiply & Divide Within 100  3.OA.7  9 x 8 = ? (timed)  
14  Introduction to Fractions  3  2/2 = 1, 3/3 = ?  
14.1  Dividing a Whole  3.NF.1  Create ‘Thirds’  
14.2  Creating Unit Fractions  3.NF.2  Make 1/4  
14.3  Creating NonUnit Fractions  3.NF.2  1/4 + 1/4 =  
14.4  Whole Numbers as Fractions  3.NF.3c  6 = 6/?  
14.5  Comparing Fractions  3.NF.3d  1/2 ? 1/3  
14.6  Equivalent Fractions  3.NF.3a  1/2 = 2/4  
15  Multiply and Divide to 100  3  5 x 12 = ?  
15.1  Multiplication to 100  3.OA.3  5 x 12 = ?  
15.2  Multiplication to 100: Missing Groups  3.OA.3  ? x 12 = 60  
15.3  Multiplication to 100: Missing Groups II  3.OA.4  12 x ? =60  
15.4  Division to 100  3.OA.4  42 ÷ 7 = ?  
15.5  Division to 100: Missing Dividend  3.OA.6  ? ÷ 6 = 7  
15.6  Division to 100: Missing Divisor  3.OA.6  42 ÷ ? = 6  
15.7  Multiplication to 100: Commutative Property  3.OA.5  14 x 6 = 6 x 14  
15.8  Multiplication to 100: Distributive Property  3.OA.5  10 x 3 + 5 x 3 = 45  
16  Multiply & Divide with 1/10/100  3  1 x 7, 10 x 7, 100 x 7  
16.1  Multiply by 1, 10, 100: Missing Result  4.NBT.1  1 x 7, 10 x 7, 100 x 7  
16.2  Multiply by 1, 10, 100: Missing Factor  4.NBT.1  ? x 8, ? x 80, ? x 800  
16.3  Divide by 1, 10, 100: Missing Result  4.NBT.1  8 ÷ 1, 80 ÷ 10, 800 ÷ 100  
16.4  Divide by 1, 10. 100: Missing Divisor  3.OA.7  9 ÷ ?, 90 ÷ ?, 900 ÷ ?  
16.5  Multiplying 1s and 10s  3.NBT.3  7 x 60 = ?  
17  Add & Subtract Unit Fractions  4  1/2 = ?/8  
17.1  Equivalent Fractions  4.NF.1  1/2 = ?/8  
17.2  Comparing Fractions  4.NF.2  3/5 ? 4/7  
17.3  Addition with Unit Fractions: Missing Result  4.NF.3a  1/4 + 1/4 = ?  
17.4  Addition with Unit Fractions: Missing Change  4.NF.3a  1/4 + ? = 2/4  
17.5  Subtraction with Fractions: Missing Result  4.NF.3a  3/4 – 1/4 = ?  
17.6  Subtraction with Fractions: Missing Change  4.NF.3a  3/4 – ? = 1/4  
MR 11  Multiply & Divide With Place Value  4.NBT.4  80 x 4 = ? (timed)  
18  NonUnit Fractions  4  2/5 + 3/5 = ?  
18.1  Addition with Non Unit Fractions: Missing Result  4.NF.3b  2/5 + 3/5 = ?  
18.2  Addition with Non Unit Fractions: Missing Change  4.NF.3b  2/6 + ? = 5/6  
18.3  Subtraction with NonUnit Fractions: Missing Result  4.NF.3b  3/3 – 2/3 = ?  
18.4  Subtraction with Non Unit Fractions: Missing Change  4.NF.3b  7/8 – ? = 3/8  
19  Decimals  4  0.4, 0.5, ?, 0.7  
19.1  Sequencing Decimals  4.NF.5  0.4, 0.5, ?, 0.7  
19.2  Identifying Decimals  4.NF.5  Find ‘36 hundredths.’  
19.3  Equivalence with 10ths and 100ths  4.NF.6  3/10 = ?/100  
19.4  Addition with 10ths and 100ths  4.NF.6  3/10 + 6/100 = ?  
19.5  Decimal Notation for 10ths and 100ths  4.NF.6  52/100 = ?  
19.6  Comparing Decimal Numbers  4.NF.7  0.76 ? 0.8  
20  Fractions Greater Than 1 Whole  4  Make ‘3/2’  
20.1  Composing Fractions Greater Than 1 Whole  4.NF.3c  Make ‘3/2’  
20.2  Composing Mixed Numbers  4.NF.3c  Make ‘2 1/3’  
20.3  Decomposing Fractions Greater Than 1 Whole  4.NF.3c  5/3 = 2/3 + ?  
20.4  Decomposing Mixed Numbers  4.NF.3b  2 1/3 = 3/3 + ?  
21  Standard Algorithm: Addition and Subtraction  4  368 + 848 = ?  
21.1  2digit and 1digit Addition  4.NBT.4  87 + 9 = ?  
21.2  2digit and 1digit Subtraction  4.NBT.4  87 – 9 = ?  
21.3  2digit and 2digit Addition  4.NBT.4  58 + 67 = ?  
21.4  2digit and 2digit Subtraction  4.NBT.4  82 – 59 = ?  
21.5  3digit and 3digit Addition  4.NBT.4  368 + 848 = ?  
21.6  3digit and 3digit Subtraction  4.NBT.4  848 – 368 = ?  
21.7  3Part Addition with Mixed Digits  4.NBT.4  368 + 7 + 56 = ?  
21.8  4digit Subtraction  4.NBT.4  1,470 – 258 = ?  
22  Expanded Mode Multiplication and Division  4  26 x 68 = ?  
22.1  1Digit x 2digit  4.NBT.5  7 x 18 = ?  
22.2  Division with Remainders  4.NBT.6  25 ÷ 8 = ? R ?  
22.3  1Digit x 3Digits  4.NBT.5  8 x 106 = ?  
22.4  Division Missing Factor and Divisor  4.NBT.6  102 ÷ 17 = ?  
22.5  2Digits x 2Digits  4.NBT.5  26 x 21 = ?  
23  Multiplying Fractions and Whole Numbers  5  1/4 x 32 = ?  
23.1  Whole Numbers x Unit Fractions  5.NF.4  1/4 x 32 = ?  
23.2  Whole Numbers x NonUnit Fractions  5.NF.4  5 x 3/5 = ?  
23.3  Fractions x Whole Numbers: Missing Part  5.NF.4  2/3 x ? = 18  
24  Magnitude and Place Value  5  7.01 x 100 = ?  
24.1  Multiply by 10, 100, and 1000  5.NBT.1  7.01 x 100 = ?  
24.2  Multiply by 1/10 and 1/100  5.NBT.1  392 x 1/100= ?  
24.3  Divide by 10 and 100  5.NBT.1  35.6 ÷ 10= ?  
25  Decimals to Thousandths  5 


25.1  Decimal Notation  5.NBT.3  2×100 + 3×1 + 5x(1/10)  
25.2  Add and Subtract Decimals  5.NBT.7  4.09 + 3.4 = ?  
25.3  Decimal Comparison  5.NBT.3  3.56 ? 3.5  
26  Expanded Mode *÷ with Decimals  5  7 x 0.5 = ?  
26.1  1Digit x Decimals  5.NBT.5  7 x 0.5 = ?  
26.2  3Digit x Decimals  5.NBT.6  134 x 0.8 = ?  
26.3  Division with Decimals  5.NBT.5  18 ÷ 0.9 = ?  
26.4  Decimal x Decimal  5.NBT.6  2.6 x 4.5 = ? 