Curriculum Overview
Math Direct covers foundational math skills through 150 scripted lessons organized into 7 sequential phases. Each phase builds on the one before it.
Phase 1: Foundation
The math journey begins here. Phase 1 introduces numbers 0-10, counting, one-to-one correspondence, and number recognition.
| Concept | Lesson | Type | Example |
|---|---|---|---|
| 0 | 1 | number | zero, nothing |
| 1 | 1 | number | one, single |
| 2 | 2 | number | two, pair |
| 3 | 3 | number | three |
| = | 4 | symbol | equals, is the same as |
| 4 | 5 | number | four |
| 5 | 7 | number | five |
| 6 | 9 | number | six |
| 7 | 11 | number | seven |
| 8 | 13 | number | eight |
| 9 | 15 | number | nine |
| 10 | 17 | number | ten |
| > | 18 | symbol | greater than |
| < | 18 | symbol | less than |
Skills Developed
- Recognizing and naming numbers 0-10
- Counting objects with one-to-one correspondence
- Writing numerals 0-10
- Comparing numbers (more, less, equal)
- Ordering numbers from least to greatest
Phase 2: Counting & Comparing
Phase 2 extends counting to 20, introduces number patterns, and builds fluency with number order and comparisons.
| Concept | Lesson | Type | Example |
|---|---|---|---|
| 11-15 | 21 | number range | eleven through fifteen |
| 16-20 | 26 | number range | sixteen through twenty |
| + | 31 | symbol | plus, add |
| number line | 33 | tool | 0 to 20 number line |
Skills Developed
- Counting to 20 fluently
- Counting backward from 10
- Identifying numbers 11-20
- Understanding 'one more' and 'one less'
- Introduction to the plus symbol
Phase 3: Addition
Phase 3 teaches addition facts to 10 systematically, starting with +1, +2, then building to all single-digit addition.
| Concept | Lesson | Type | Example |
|---|---|---|---|
| +1 | 41 | operation | 3 + 1 = 4 |
| +2 | 45 | operation | 5 + 2 = 7 |
| +3 | 49 | operation | 4 + 3 = 7 |
| doubles | 53 | strategy | 3 + 3 = 6 |
| +0 | 56 | operation | 5 + 0 = 5 |
| commutative | 58 | property | 2 + 3 = 3 + 2 |
| number bonds | 60 | concept | 5 = 2 + 3 |
Skills Developed
- Adding 1, 2, and 3 to any single digit
- Doubles facts (1+1 through 5+5)
- Adding zero
- Understanding the commutative property
- Number bonds to 10
- Solving addition equations with missing addends
Phase 4: Subtraction
Phase 4 introduces subtraction as 'taking away' and builds the connection between addition and subtraction.
| Concept | Lesson | Type | Example |
|---|---|---|---|
| − | 66 | symbol | minus, take away |
| −1 | 66 | operation | 5 − 1 = 4 |
| −2 | 70 | operation | 7 − 2 = 5 |
| −3 | 74 | operation | 8 − 3 = 5 |
| fact families | 78 | concept | 3+4=7, 4+3=7, 7−3=4, 7−4=3 |
| −0 | 80 | operation | 5 − 0 = 5 |
Skills Developed
- Subtracting 1, 2, and 3 from numbers to 10
- Understanding subtraction as 'taking away'
- Connecting subtraction to addition (fact families)
- Subtracting zero
- Solving subtraction equations with missing numbers
Phase 5: Place Value
Phase 5 introduces place value (tens and ones), counting to 100, and addition/subtraction within 20.
| Concept | Lesson | Type | Example |
|---|---|---|---|
| tens | 86 | place value | 10 = 1 ten, 0 ones |
| ones | 86 | place value | 13 = 1 ten, 3 ones |
| counting to 50 | 90 | number range | twenty-one through fifty |
| counting to 100 | 95 | number range | fifty-one through one hundred |
| addition to 20 | 100 | operation | 8 + 7 = 15 |
Skills Developed
- Understanding tens and ones
- Representing two-digit numbers with place value
- Counting to 100 by ones and tens
- Skip counting by 2s, 5s, and 10s
- Adding and subtracting within 20
Phase 6: Fluency
Phase 6 builds fluency with addition and subtraction facts to 20, introduces mental math strategies, and begins two-digit addition.
| Concept | Lesson | Type | Example |
|---|---|---|---|
| make 10 | 106 | strategy | 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13 |
| doubles +1 | 110 | strategy | 6 + 7 = 6 + 6 + 1 = 13 |
| two-digit + one-digit | 115 | operation | 24 + 5 = 29 |
| two-digit + tens | 120 | operation | 35 + 20 = 55 |
Skills Developed
- Rapid recall of addition/subtraction facts to 20
- Make-10 strategy
- Doubles-plus-one strategy
- Adding a one-digit number to a two-digit number
- Adding multiples of 10 to two-digit numbers
Phase 7: Mastery
Phase 7 covers two-digit addition and subtraction (with and without regrouping), word problems, and mixed practice for complete mastery.
| Concept | Lesson | Type | Example |
|---|---|---|---|
| two-digit + two-digit | 126 | operation | 34 + 25 = 59 |
| regrouping (carrying) | 130 | concept | 28 + 15 = 43 |
| two-digit − two-digit | 135 | operation | 56 − 23 = 33 |
| regrouping (borrowing) | 140 | concept | 42 − 17 = 25 |
| word problems | 145 | application | Sam has 12 apples. He gives away 5. How many are left? |
Skills Developed
- Two-digit addition without regrouping
- Two-digit addition with regrouping (carrying)
- Two-digit subtraction without regrouping
- Two-digit subtraction with regrouping (borrowing)
- Solving addition and subtraction word problems
- Mixed practice with all four types