Number Navigator Anchor Chart
NUMBER NAVIGATOR
5th Grade Math Ultimate Desk Companion
HERO: ____________________
CLASS: 5TH GRADE
1. Multi-Digit Operations
Multiplication Area Model \(24 \times 13 = 312\)
×
20
4
10
200(20×10)
40(4×10)
3
60(20×3)
12(4×3)
Break numbers into place values, multiply each inner box, then add the partial products:
200 + 40 + 60 + 12 = 312
Long Division Steps
Divide
Multiply
Subtract
Bring ↓
"Does McDonald's Sell Burgers?"
032
8 ) 2 5 6
- 2 4 0
1 6
- 1 6
0
2. Fraction Factions
Fractions as Quotients
\[\frac{a}{b} = a \div b\]
Sharing Problem: 3 apples shared equally among 4 friends:
\(3 \div 4 = \frac{3}{4}\) apple each
Adding & Subtracting Fractions
You MUST find a Common Denominator first!
\(\frac{1}{2} + \frac{1}{3}\)
→
\(\frac{3}{6} + \frac{2}{6}\)
=
\(\frac{5}{6}\)
Multiplying Fractions
No common denominator needed! Multiply straight across:
\[\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\]
\(\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}\)
3. Fraction Division
The K-C-F Strategy Divide Rules
KEEP First fraction
CHANGE \(\div\) to \(\times\)
FLIP Second fraction
Whole Number ÷ Unit Fraction \(3 \div \frac{1}{3} = 9\)
1
2
3
4
5
6
7
8
9
"How many thirds are inside 3 whole units?"
Unit Fraction ÷ Whole Number \(\frac{1}{3} \div 4 = \frac{1}{12}\)
1/3 Third
1/3
1/3
1/12
Each third gets sliced into 4 slices
4. Decimal Power-Up
Decimal Place Value Patterns
Tens
Ones
.
Tenths
Hund.
Thous.
1
4
.
2
8
5
× 10 shifts digits LEFT (decimal shifts right 1 space →)
÷ 10 shifts digits RIGHT (decimal shifts left 1 space ←)
Add & Subtract Decimals "Line up the dots!"
Fill empty places with zeros and add or subtract as standard.
aligned
1 4 . 7 0
+ 0 3 . 2 5
1 7 . 9 5
Multiply Rule Multiply normally first. Then, count total decimal places in factors and slide decimal back:
\(1.2 \times 0.4 = 0.48\)
Divide Rule Multiply divisor by 10/100 to make it a whole number. Do the same to the dividend!
\(4.2 \div 0.7 \rightarrow 42 \div 7 = 6\)
5. Coordinate Graphing
How to Plot: \((x, y)\)
x-axis: Walk along hall (horizontal)
y-axis: Rise up elevator (vertical)
"Go OVER then UP!"
Origin = \((0,0)\)
(3, 2)
y
x
0
1
2
3
4
1
2
3
4
X-Axis The horizontal number line on a coordinate plane.
Y-Axis The vertical number line on a coordinate plane.
6. Finding Volume
What is Volume? 3D Space
The amount of space inside a solid 3D figure. Always measured in cubic units (\(\text{cm}^3\), \(\text{in}^3\)).
length (l) width (w) height (h)
FORMULA A:
\(V = l \times w \times h\)
FORMULA B:
\(V = B \times h\)
(B = Area of Base, \(l \times w\))
✦ DOUBLE-CHECK ALL CALCULATIONS before writing down your final answer!
MATH MAPMAKERS COMPANION SHEET • MASTER LEVEL ✦
Formula Frontiers Anchor Chart
FORMULA FRONTIERS
6th Grade Math Ultimate Desk Companion
HERO: ____________________
CLASS: 6TH GRADE
1. Intro to Ratios
What is a Ratio?
A comparison of two quantities. Order matters! Write it in 3 ways:
a : b
a to b
\(\frac{a}{b}\)
Equivalent Ratio Tables
Multiply or divide both quantities by the same number to keep them equivalent!
Apples (x)
2
4
6
8
Oranges (y)
3
6
9
12
✦ Rule: x and y change by scale factors (e.g., ×2, ×3, ×4)
2. Unit Rate & Percents
Unit Rates (Value Per 1 Unit)
A rate simplified to have a denominator of 1.
\(\frac{120 \text{ miles}}{\text{2 hours}}\)
→
\(60 \text{ miles / hour}\)
Percentages ("Out of 100")
Percentages represent a ratio with a whole of 100.
25%
50%
75%
100%
5
10
15
20
"50% of 20 is equal to 10"
Finding the Part \(\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}\)
Finding the Whole \(\text{Whole} = \text{Part} \div \frac{\text{Percent}}{100}\)
3. Fraction Division
What does Fraction Division Mean?
Measuring how many times a divisor fraction can fit into a dividend fraction!
The K-C-F Strategy
KEEP First Fraction \(\frac{3}{4}\)
CHANGE \(\div\) to \(\times\) \(\times\)
FLIP Second Fraction \(\frac{2}{3} \rightarrow \frac{3}{2}\)
\[\frac{3}{4} \div \frac{2}{3}\]
→
\[\frac{3}{4} \times \frac{3}{2}\]
=
\(\frac{9}{8} = 1\frac{1}{8}\)
4. Arithmetic in Base Ten
Decimal Operations Rules
Add & Subtract: "Line up the dots!" Fill blank spaces with zeros.
12.40 + 3.75 = 16.15
Multiply: Ignore decimals, multiply. Count total places in factors, place decimal in answer.
\(1.2 \times 0.3 \rightarrow 12 \times 3 = 0.36\)
Dividing Decimals (Base Ten Rule)
Multiply divisor by 10/100 to make it a whole number. Multiply the dividend by the same!
\(4.8 \div 0.12 \rightarrow 480 \div 12 = 40\)
