Math Toolbelt Reference Insert
MATH TOOLBELT
Page 1: Numbers & Operations
NAME:
1
Place Value Explorer
Whole Numbers to 100,000s
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
100,000
10,000
1,000
100
10
1
3
5
2
8
1
4
Move Left: Each place is 10x larger (\times 10) Move Right: Each place is 10x smaller (\div 10)
Standard Form
352,814
Expanded Form
300,000 + 50,000 + 2,000 + 800 + 10 + 4
Word Form
Three hundred fifty-two thousand, eight hundred fourteen.
2
Rounding Runway
Slide Back 0, 1, 2, 3, 4
Roll Forward 5, 6, 7, 8, 9
Peak (5)
1
Underline the place you are rounding to.
Round 4,382 to hundreds
2
Look next door (to the right) and circle it.
Look at the 8 → 4,3(8)2
3
Apply the rule: 8 is 5 or more!
Raise the score → 3 becomes 4
4
All digits to the right turn into zeros!
Result: 4,400
The Rounding Chant
"5 or more, raise the score! 🚀
4 or less, let it rest! 💤"
3
Fact Family Houses
Numbers share addition/subtraction or multiplication/division relationships!
12 7 5
7 + 5 = 12
5 + 7 = 12
12 - 7 = 5
12 - 5 = 7
ADD / SUB
24 3 8
3 \times 8 = 24
8 \times 3 = 24
24 \div 3 = 8
24 \div 8 = 3
MULT / DIV
Operation Clues
Addition (+) Sum, total, in all, altogether, join.
Subtraction (-) Difference, fewer, left, how many more.
Mult (\times) Product, times, each, equal groups.
Division (\div) Quotient, share equally, split, cut.
Remember: Addition/Mult can go in any order! 🔄
Math Toolbelt Reference Guide
Keep in your Math Folder!
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MATH TOOLBELT
Page 2: Fractions, Shapes & Measurement
GRADE: 3RD / 4TH
4
Fraction & Decimal Playground
Visual Fractions & Equivalent Parts
Fraction Bars (Comparing Parts)
1 Whole
1/2
1/2
1/3
1/3
1/3
1/4
1/4
1/4
1/4
1/6
1/6
1/6
1/6
1/6
1/6
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
Notice: 1/2 = 2/4 = 3/6 = 4/8! They cover the same space!
Fraction Anatomy
3
4
← Numerator: Parts we have
← Denominator: Total parts
Decimals & Fractions
0.1 = 1/10 "One Tenth" (Dime)
0.01 = 1/100 "One Hundredth" (Penny)
5
Geometry Station
Angle Types
Acute Angle < 90° ("So cute!")
Right Angle = 90° ("Square corner")
Obtuse Angle Larger than 90° (> 90°)
Line Relationships
Parallel Lines Never touch or cross.
Perpendicular Cross at 90° corner.
Tri: 3 Quad: 4 Pent: 5 Hex: 6 Oct: 8
6
Measurement & Formulas
Area & Perimeter (Rectangles)
L = 6 cm Rectangle W = 4 cm
Perimeter (Fence Around)
P = s + s + s + s
6+4+6+4 = 20 cm
Area (Tiles Inside)
A = L \times W
6 \times 4 = 24 sq cm
Customary
- 1 ft = 12 in
- 1 yd = 3 ft
- 1 lb = 16 oz
- 1 gal = 4 qt
Metric
- 1 m = 100 cm
- 1 km = 1000 m
- 1 kg = 1000 g
- 1 L = 1000 mL
Gallon Castle:
1 Gal (G) → 4 Qt (Q) → 8 Pt (P) → 16 C (C)
Tip: Metric prefixes stay standard! (Kilo = 1000 | Centi = 1/100 | Milli = 1/1000)
Math Toolbelt Reference Guide
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