Fact Tactics Reference Chart Tactical Math Guide Desk Reference
Multiplication Strategy Arsenal
Tier-2 Foundational Support
Master Difficult Facts (6s, 7s, 8s, 9s)
1
Break-Apart (5s + 2s)
Split a tough factor into friendly numbers like 5 and 2.
\( 7 \times 8 = ? \)
\( (5 \times 8) + (2 \times 8) \)
\( 40 + 16 = 56 \)
2
Double-Double (×4 & ×8)
For ×4, double twice. For ×8, double three times!
\( 4 \times 7 = ? \)
Double 7 = 14
Double 14 = 28
3
Nifty Nines (×10 - 1)
Multiply by 10, then subtract 1 equal group.
\( 9 \times 6 = ? \)
\( (10 \times 6) - 6 \)
\( 60 - 6 = 54 \)
Visual Anchors: Arrays & Area Models
Rows \(\times\) Columns = Total Area
Array Model: 4 rows of 6 \( 4 \times 6 = 24 \)
Count rows down (4), columns across (6)
Split Area Model: \( 7 \times 8 \) \( 35 + 21 = 56 \)
5 columns \( 7 \times 5 = 35 \)
3 cols \( 7 \times 3 = 21 \)
Side height is 7; width 8 is split into 5 + 3
Fact Families: The Inverse Connection
3 Numbers = 4 Facts
56
7 8
Fact Triangle
Multiplication \( 7 \times 8 = 56 \)
Commutative \( 8 \times 7 = 56 \)
Inverse Division \( 56 \div 8 = 7 \)
Inverse Division \( 56 \div 7 = 8 \)
Tough Facts Quick Key (Highlighted Square Numbers in Yellow)
Benchmark Reference
× 1 2 3 4 5 6 7 8 9 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 63 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 54 63 72 81 90 10 10 20 30 40 50 60 70 80 90 100
Fact Tactics Practice Packet FACT TACTICS INTERVENTION • UNIT 1 LEVEL: FOUNDATIONAL FLUENCY
Visual Arrays & Area Models
Part 1: Seeing Factors as Rows, Columns, and Split Areas
Name:
Date:
Concept Anchor: Total Area = Height \(\times\) Width
When solving a tough fact like \( 6 \times 7 \), picture a rectangle 6 units tall and 7 units wide. You can split 7 into \( 5 + 2 \) to make two easy rectangles: \( (6 \times 5) + (6 \times 2) = 30 + 12 = 42 \).
Section A: Array Dimensions & Products
Count the rows & columns to complete the equation
1. Array Model Rows \(\times\) Cols
____ rows \(\times\) ____ columns =
2. Array Model Rows \(\times\) Cols
____ rows \(\times\) ____ columns =
Section B: Decomposed Area Models
Calculate each sub-area, then add them together
3. Calculate \( 7 \times 8 \) Split 8 into 5 + 3
5 columns \( 7 \times 5 = \) ___
3 cols \( 7 \times 3 = \) ___
Total Area: _____ + _____ = ______
4. Calculate \( 8 \times 6 \) Split 6 into 5 + 1
5 columns \( 8 \times 5 = \) ___
1 col \( 8 \times 1 = \) ___
Total Area: _____ + _____ = ______
Section C: Design Your Area Model for \( 9 \times 7 \)
Split 7 into (5 + 2)
Draw a rectangle below. Label the height (9) and split the top width into 5 and 2. Write the two partial products inside and add them.
[ Height: 9 ] [ Split Top Width: 5 + 2 ]
\( (9 \times 5) + (9 \times 2) = \) _____ + _____ =
FACT TACTICS INTERVENTION • UNIT 1 LEVEL: FOUNDATIONAL FLUENCY
The Break-Apart Method
Part 2: Decomposing Tough Factors using Friendly 5s and 2s
Name:
Date:
The Friendly Number Rule
Multiplying by 5 is easy (skip count by 5s). Multiplying by 2 is just doubling. When you see a 7, split it into 5 + 2 . When you see an 8, split it into 5 + 3 or Double-Double-Double !
Guided Decompositions (Fill in the blanks)
Problem 1: Solve \( 7 \times 7 \) Break first 7 into (5 + 2)
Step 1: Friendly 5s \( 5 \times 7 = \) _____
Step 2: Friendly 2s \( 2 \times 7 = \) _____
Step 3: Combine ____ + ____ = ____
Problem 2: Solve \( 6 \times 8 \) Break 6 into (5 + 1)
Step 1: Friendly 5s \( 5 \times 8 = \) _____
Step 2: Add 1 Group \( 1 \times 8 = \) _____
Step 3: Combine ____ + ____ = ____
Fact Strategy Flashcards Tactical Strategy Flashcards
Sheet 1 of 2 • Cut along dashed lines. Fold or use double-sided.
Print & Cut (6 Cards)
Card 01 Friendly 5s + 2s
\( 7 \times 8 \)
= 56
Split: \( (5 \times 8) + (2 \times 8) \)
\( = 40 + 16 = \mathbf{56} \)
Inverse: \( 56 \div 8 = 7 \) • \( 56 \div 7 = 8 \)
Card 02 Friendly 5s + 1
\( 6 \times 7 \)
= 42
Split: \( (5 \times 7) + (1 \times 7) \)
\( = 35 + 7 = \mathbf{42} \)
Inverse: \( 42 \div 7 = 6 \) • \( 42 \div 6 = 7 \)
Card 03 Double-Double-Double
\( 8 \times 6 \)
= 48
Double: \( 6 \to 12 \to 24 \to \mathbf{48} \)
Or: \( (5 \times 6) + (3 \times 6) = 30 + 18 = \mathbf{48} \)
Inverse: \( 48 \div 8 = 6 \) • \( 48 \div 6 = 8 \)
Card 04 Nifty Nines (×10 - 1)
\( 9 \times 7 \)
= 63
Split: \( (10 \times 7) - 7 \)
\( = 70 - 7 = \mathbf{63} \)
Inverse: \( 63 \div 9 = 7 \) • \( 63 \div 7 = 9 \)
Card 05 Square Fact (5s + 3s)
\( 8 \times 8 \)
= 64
Split: \( (5 \times 8) + (3 \times 8) \)
\( = 40 + 24 = \mathbf{64} \)
Inverse: \( 64 \div 8 = 8 \) (Square Root)
Card 06 Nifty Nines (×10 - 1)
\( 9 \times 6 \)
= 54
Split: \( (10 \times 6) - 6 \)
\( = 60 - 6 = \mathbf{54} \)
Inverse: \( 54 \div 9 = 6 \) • \( 54 \div 6 = 9 \)
Tactical Strategy Flashcards
Sheet 2 of 2 • Cut along dashed lines. Fold or use double-sided.
Print & Cut (6 Cards)
Card 07 Square Fact (5s + 2s)
\( 7 \times 7 \)
= 49
Split: \( (5 \times 7) + (2 \times 7) \)
\( = 35 + 14 = \mathbf{49} \)
Inverse: \( 49 \div 7 = 7 \) (Square Root)
Card 08 Nifty Nines (×10 - 1)
\( 9 \times 8 \)
= 72
Split: \( (10 \times 8) - 8 \)
\( = 80 - 8 = \mathbf{72} \)
Inverse: \( 72 \div 9 = 8 \) • \( 72 \div 8 = 9 \)
Card 09 Square Fact (5s + 1)
\( 6 \times 6 \)
= 36
Split: \( (5 \times 6) + (1 \times 6) \)
\( = 30 + 6 = \mathbf{36} \)
Inverse: \( 36 \div 6 = 6 \) (Square Root)
Card 10 Square Fact (×10 - 1)
