6th Grade Anchor Charts

6th Grade Math Anchor Charts | Transform One

STUDENT ANCHOR CHARTS: Click any standard below to open its anchor page. Each anchor page includes diagrams, tips, and a button to download that specific standard as a separate HTML study guide.

Ratios & Proportions · 6.RP

Standard	Topic
6.RP.1	Ratios
6.RP.2	Unit Rate
6.RP.3a	Equivalent Ratios & Ratio Tables
6.RP.3b	Unit Rate Problems
6.RP.3c	Percents
6.RP.3d	Measurement Conversions

The Number System · 6.NS

Standard	Topic
6.NS.1	Divide Fractions by Fractions
6.NS.2	Multi-Digit Division
6.NS.3	Decimal Operations
6.NS.4	GCF & LCM
6.NS.5	Positive & Negative Numbers
6.NS.6a	Opposites on the Number Line
6.NS.6b	Rational Numbers on the Number Line
6.NS.6c	Ordered Pairs in Quadrants
6.NS.7	Compare Rational Numbers
6.NS.8	Coordinate Plane Distance

Expressions & Equations · 6.EE

Standard	Topic
6.EE.1	Write Numerical Expressions
6.EE.2a	Expressions with Variables
6.EE.2b	Identify Parts of Expressions
6.EE.2c	Evaluate Expressions
6.EE.3	Equivalent Expressions
6.EE.4	Identify Equivalent Expressions
6.EE.5	Expressions from Real World
6.EE.6	Variables to Represent Numbers
6.EE.7	Solve One-Variable Equations
6.EE.8	Write & Graph Inequalities
6.EE.9	Dependent & Independent

Geometry & Statistics · 6.G / 6.SP

Standard	Topic
6.G.1	Area of Triangles & Quadrilaterals
6.G.2	Volume of Rectangular Prisms
6.G.3	Nets & Surface Area
6.G.4	Polygons on the Coordinate Plane
6.SP.1	Statistical Questions
6.SP.2	Center, Spread & Overall Shape
6.SP.3	Summarize Numerical Data Sets
6.SP.4	Display Numerical Data
6.SP.5a	Describe Number of Observations
6.SP.5b	Describe Nature of Attribute
6.SP.5c	Give Quantitative Measures
6.SP.5d	Relate Context to Data Display

DEFINITION

A ratio is a comparison of two quantities using division. It tells you how much of one thing there is compared to another thing.

Example: 3 Stars and 2 Circles

⭐⭐⭐ 🔵🔵

The ratio of stars to circles is 3 to 2.

Colon Form

3 : 2

Read as "3 to 2"

Fraction Form

Top = first item

Word Form

3 to 2

Uses the word "to"

Part-to-Part Ratio

Comparing one part to another part.
Stars to Circles → 3 : 2

Part-to-Whole Ratio

Comparing one part to the total items.
Stars to ALL shapes → 3 : 5

🚨 WATCH OUT: Order matters! A ratio of 3:2 is completely different from 2:3. Always write the numbers in the same order as the words in the problem.

RatioComparePart-to-PartPart-to-Whole

DEFINITION

A rate compares two quantities with different units (like miles and hours). A unit rate is a rate simplified so that the denominator is exactly 1.

Rate

120 miles in 3 hours

120 miles3 hours

Different units, but not per 1.

Unit Rate

40 miles per 1 hour

40 miles1 hour

Denominator is 1.

How to find a Unit Rate: Divide the top by the bottom!

$15.005 items

→ ÷5 →

$3.001 item

The unit rate is $3.00 per item.

💡 KEY WORDS: When you see the words per, each, every, a, or one, the problem is usually asking for a unit rate!

RateUnit RateDenominator of 1Per

DEFINITION

Equivalent ratios name the same comparison. You find them by multiplying or dividing both sides of a ratio by the same number. A ratio table organizes these equivalent ratios.

Scale Up (Multiply)

2 : 3→ ×2 →4 : 6

2 : 3→ ×3 →6 : 9

Scale Down (Divide)

12 : 18→ ÷6 →2 : 3

This is also called simplifying.

Using a Ratio Table

To keep the ratio equivalent, whatever you do to the top row, you MUST do to the bottom row.

Flour (cups)	2	4	6	20
Sugar (cups)	3	6	9	?

Since 2 × 10 = 20, we do 3 × 10 = 30.

🚨 WATCH OUT: You can ONLY multiply or divide to find equivalent ratios. You can never add or subtract!

EquivalentRatio TableScale Up/DownMultiply/Divide

DEFINITION

Use a unit rate to solve real-world problems involving constant speed, pricing, and measurement. Find the rate for "1", then multiply to find the rate for any amount.

Problem: Constant Speed

A train travels 150 miles in 3 hours. How far will it travel in 5 hours at this constant speed?

Step 1: Find the Unit Rate (1 hour)

150 ÷ 3 = 50 miles per 1 hour

Step 2: Multiply by the requested amount (5 hours)

50 × 5 = 250 miles

Problem: Finding the Better Buy

Store A
12 pack of soda for $3.60
$3.60 ÷ 12 = $0.30 per soda

Store B
6 pack of soda for $2.10
$2.10 ÷ 6 = $0.35 per soda

Store A is the better buy!

💡 TIP: When finding a unit price (cost per item), money ($) ALWAYS goes inside the division house (the numerator). Cost ÷ Items = Unit Price.

Unit PriceConstant SpeedBetter Buy

DEFINITION

The word percent means "per hundred". It is a ratio that compares a number to 100. Fractions, decimals, and percents are three ways to write the same value.

The Big Three: Fraction, Decimal, Percent

25100

=0.25=25%

If you can make a fraction's denominator 100, the numerator is your percent!

80100

= 80%

Find the Part (Percent OF a Number)

What is 30% of 80?

Change % to decimal, then multiply.

0.30 × 80 = 24

Find the Whole

18 is 25% of what number?

Use a proportion: Part / Whole = % / 100

18w

25100

18 × 4 = 72

💡 DECIMAL TRICK: To change a decimal to a percent, move the decimal point 2 places to the RIGHT (0.45 → 45%). To change a percent to a decimal, move it 2 places to the LEFT (7% → 0.07).

PercentPer 100PartWholeProportion

DEFINITION

Use ratio reasoning to convert measurement units. A conversion factor is a ratio representing the relationship between two units (like 12 inches / 1 foot).

The Conversion Rule:

Multiply by a fraction where the unit you WANT is on top, and the unit you want to CANCEL is on bottom.

Convert 5 yards to feet:

5 yd1

3 ft1 yd

= 15 ft

Large to Small Units

You are making more pieces, so MULTIPLY.

4 pounds = ? ounces

4 × 16 = 64 oz

Small to Large Units

You are grouping pieces, so DIVIDE.

24 inches = ? feet

24 ÷ 12 = 2 ft

💡 TIP: Metric conversions (meters, grams, liters) just require moving the decimal point right or left by powers of 10! (King Henry Died By Drinking Chocolate Milk).

Conversion FactorCustomaryMetricCancel Units

DEFINITION

Dividing a fraction by a fraction asks: "How many of the second fraction can fit inside the first fraction?" We solve this by multiplying by the reciprocal.

Visual Model

= 3

Translation: "How many 1/4s fit inside 3/4s?" Answer: 3!

The Algorithm: K C F

KEEP
the 1st fraction exactly the same.

÷
CHANGE
division to multiplication.

FLIP
the 2nd fraction upside down (Reciprocal).

1615

= 1

115

🚨 WATCH OUT: Do NOT cross-multiply. You multiply straight across: top × top, and bottom × bottom. If you have mixed numbers, change them to improper fractions first!

ReciprocalKeep-Change-FlipQuotientImproper Fraction

DEFINITION

Use the standard long division algorithm to divide multi-digit whole numbers fluently. No calculators!

The Vocabulary of Division

Dividend ÷ Divisor = Quotient

864 ÷ 24 = 36

864 is the amount being shared (inside the house).
24 is how many groups we are making (outside).
36 is the answer.

The Steps of Long Division

Does McDonald's Sell Burgers?

Divide (How many times does divisor go into dividend?)
Multiply (Quotient digit × Divisor)
Subtract (Find the difference)
Bring Down (Bring down the next digit)
Repeat or Remainder!

💡 TIP: Keeping your numbers perfectly lined up in their place value columns will prevent 90% of division mistakes. Use graph paper if it helps!

DividendDivisorQuotientStandard Algorithm

DEFINITION

Fluently add, subtract, multiply, and divide multi-digit decimals using standard algorithms. The rules for the decimal point change depending on the operation!

Add & Subtract

LINE UP THE DOT!

Line up the decimal points to ensure you are adding tenths to tenths. Add zero placeholders if needed.

10.30
− 1.06
9.24

Multiply

COUNT THE JUMPS!

Ignore decimals, multiply like normal. Count total decimal places in factors, put that many in answer.

4.5 (1 jump)
×3.2 (1 jump)
14.40 (2 jumps)

Divide Decimals

MOVE THE DOT!

If the divisor (outside number) has a decimal, move it right until it is a whole number. Move the dividend (inside) decimal the EXACT same amount. Float it straight up into the quotient!

12.5 ÷ 0.5 → 125 ÷ 5 = 25

🚨 WATCH OUT: A whole number always has an invisible decimal at the end of it. ( 5 is the same as 5.0 )

Place ValueDecimal PointPlaceholder Zero

DEFINITION

GCF is the greatest number that divides evenly into two numbers. LCM is the smallest multiple that two numbers share.

Greatest Common Factor

Find the GCF of 12 and 18

Factors are numbers you multiply to GET the number. (Finite)

12: 1, 2, 3, 4, 6, 12

18: 1, 2, 3, 6, 9, 18

GCF = 6

Least Common Multiple

Find the LCM of 4 and 6

Multiples are skip-counting (like a multiplication table). (Infinite)

4: 4, 8, 12, 16, 20

6: 6, 12, 18, 24

LCM = 12

The Distributive Property with GCF

You can use the GCF to rewrite the sum of two whole numbers. Pull the GCF outside the parentheses!

36 + 8 → GCF is 4

4 (9 + 2)

💡 TIP: Use GCF when you want to simplify fractions or cut things into identical equal pieces. Use LCM when you need a common denominator or need things to happen at the same time (like buses arriving).

FactorMultipleGCFLCMDistributive Property

DEFINITION

Positive and negative numbers describe opposite quantities or directions. Zero is the neutral center point—it is neither positive nor negative.

Integers in the Real World

Context	Negative (−)	Zero (0)	Positive (+)
Money	Debt, Withdraw, Spend	Break even	Deposit, Earn, Save
Elevation	Below sea level	Sea level	Above sea level
Temperature	Below zero	Zero degrees	Above zero

Word Translation

"A diver is 45 feet below sea level."

−45

Word Translation

"You deposit $20 into your bank account."

+20

💡 TIP: When a problem asks "What does zero represent?", look at the context. In a bank, 0 means no money. In elevation, 0 means the level of the ocean.

IntegerPositiveNegativeZeroElevation

DEFINITION

Opposites are two numbers that are the exact same distance from zero on a number line, but on opposite sides.

Visualizing Opposites

-4

Distance: 4

4 and -4 are opposites because they are both exactly 4 units away from zero.

The Opposite of an Opposite

−(−5) = 5

The opposite of negative five is positive five!

🚨 WATCH OUT: Zero is its own opposite!

OppositeDistanceNumber LineSymmetry

DEFINITION

A rational number is any number that can be written as a fraction. This includes positive and negative decimals and fractions. They all have a specific spot on the number line!

Plotting Between Integers

Where do -1.5, -0.5, and 0.75 go?

-2

-1

-1.5

-1/2

0.75

Vertical Number Lines

Number lines can go up and down (like a thermometer)!

Up = Positive (Greater)

Down = Negative (Lesser)

💡 TIP: When plotting negative fractions, remember that moving LEFT means the numbers are getting smaller in value, even though the digits look bigger (e.g., -1.9 is to the left of -1.1).

Rational NumberFractionDecimalVertical

DEFINITION

An ordered pair (x, y) gives the exact location of a point on a coordinate plane. The x-axis is horizontal (left/right) and the y-axis is vertical (up/down).

The 4 Quadrants

I (+,+)

II (-,+)

III (-,-)

IV (+,-)

How to Plot ( -3, 4 )

1. Start at the Origin (0,0)

2. Look at x (-3): Move LEFT 3.

3. Look at y (4): Move UP 4.

This lands in Quadrant II.

Reflections across an axis

If you reflect (flip) a point across the x-axis, the x-coordinate stays the same, and the y-coordinate becomes its opposite.
Example: Reflecting (2, 5) across the x-axis gives (2, -5).

🚨 WATCH OUT: Always run before you jump! The x-coordinate (left/right) always comes first.

Ordered Pair (x,y)QuadrantOriginReflection

DEFINITION

Compare numbers using inequality symbols (<, >, =). Absolute Value |x| is a number's distance from zero, which is always positive!

Comparing Negatives

−10 < −5

Even though 10 looks bigger, losing $10 is worse than losing $5. -10 is further left on the number line.

Absolute Value | |

|−8| = 8

|8| = 8

Both represent a distance of 8 units from zero.

Interpreting Comparisons in the Real World

Statement	Meaning
-3°C > -7°C	-3 degrees is warmer than -7 degrees.
-$20 < -$10	A debt of $20 is worse than a debt of $10.
\|-15\| > \|-5\|	A distance of 15 feet is farther than 5 feet.

💡 TIP: The alligator mouth always eats the bigger value. Any positive number is greater than any negative number.

Inequality < >Absolute ValueMagnitudeDistance

DEFINITION

Find the distance between two points that share either the same x-coordinate (vertical line) or the same y-coordinate (horizontal line) by counting grid units or using absolute value.

Method 1: Using Absolute Value

Find the distance between A(2, 4) and B(2, -3).

1. Cross out the matching coordinates: (2, 4) and (2, -3).

2. Look at the remaining coordinates: 4 and -3.

3. Since they are in different quadrants (one positive, one negative), ADD their absolute values.

|4| + |-3| = 4 + 3 = 7 units

Same Quadrant Rule

SUBTRACT absolute values.

Distance from (5, 8) to (5, 2)

|8| - |2| = 6 units

Different Quadrant Rule

ADD absolute values.

Distance from (-4, 3) to (5, 3)

|-4| + |5| = 9 units

💡 TIP: In 6th grade, you will only ever find straight horizontal or straight vertical distances. Never diagonal!

DistanceAbsolute ValueHorizontalVertical

DEFINITION

An exponent tells you how many times to multiply the base by itself. An expression with an exponent is called a power.

Parts of a Power

5 3

Base (5): The big number being multiplied.

Exponent (3): The tiny number telling you how many times to write the base.

5³ = 5 × 5 × 5 = 125

Squared

An exponent of 2.

7² = 7 × 7 = 49

Cubed

An exponent of 3.

2³ = 2 × 2 × 2 = 8

🚨 WATCH OUT: 5³ is NOT 5 × 3 = 15. It is 5 × 5 × 5 = 125! Never multiply the base and the exponent together!

BaseExponentPowerSquaredCubed

DEFINITION

Write algebraic expressions to translate words into math. A variable is a letter used to represent an unknown number.

Translation Dictionary

Addition (+)	Sum, more than, increased by, added to, total
Subtraction (−)	Difference, less than, decreased by, subtracted from
Multiplication (×)	Product, times, twice (2x), doubled, groups of
Division (÷)	Quotient, divided by, half (÷2), ratio of

Tricky Translations ("Turnaround Words")

The words "than" and "from" mean you must reverse the order of the numbers!

"5 less than x" is written as x − 5 (NOT 5 - x)
"Subtract 10 from y" is written as y − 10

💡 TIP: We don't use "x" for multiplication anymore because it looks like a variable. Write "4 times n" as 4n or 4(n) or 4·n.

VariableAlgebraic ExpressionTranslate

DEFINITION

Use precise mathematical vocabulary to identify the different parts of an algebraic expression.

Deconstructing an Expression

4x + 7 + y

Terms	Parts separated by + or - signs. $4x$ , $7$ , and $y$ are the 3 terms here.
Coefficient	The number touching (multiplying) the variable. The coefficient of x is 4. The invisible coefficient of y is 1.
Constant	A number standing all by itself (it constantly stays the same). The constant is 7.
Variable	The letter representing an unknown value. The variables are x and y.

🚨 WATCH OUT: A variable without a number in front of it actually has an invisible "1". So, the coefficient of m is 1 (because 1m is just m).

TermCoefficientConstantVariable

DEFINITION

To evaluate means to find the final numerical value of an expression. You do this by substituting (plugging in) a number for the variable and using the Order of Operations.

Order of Operations

GEMDAS / PEMDAS

1. Grouping symbols ( )

2. Exponents x²

3. Multiply/Divide (Left to Right)

4. Add/Subtract (Left to Right)

Example Problem

Evaluate 3x² + 4 when x = 5

1. Substitute 5 for x:

3(5)² + 4

2. Exponents first:

3(25) + 4

3. Multiply next:

75 + 4 = 79

Formulas in Real Life

Find the volume of a cube with side length (s) = 4 inches.
Formula: V = s³

V = (4)³
V = 4 × 4 × 4 = 64 cubic inches.

💡 TIP: Whenever you substitute a number for a variable, put parentheses around it! This prevents mistakes, especially with multiplication (e.g. 5x becomes 5(2), not 52).

EvaluateSubstituteOrder of Operations

DEFINITION

Apply properties of operations (like the Distributive Property) to create expressions that look different but are mathematically equal.

The Distributive Property

Multiply the outside term by EVERY term inside the parentheses!

4(x + 3)

(4 × x)+(4 × 3)

4x + 12

Combining Like Terms

You can only add or subtract terms that have the exact same variable.

3y + 2y = 5y

7x + 2 + x = 8x + 2

*(Remember, plain x is the same as 1x)*

💡 TIP: Factoring is the opposite of Distributing! To factor 6x + 15, find the GCF (3) and pull it out: 3(2x + 5).

Distributive PropertyLike TermsFactor

DEFINITION

Expressions are equivalent if they result in the exact same number, no matter what value you plug in for the variable.

Are these equivalent? 3(x + 2) and 3x + 6

Method 1: Use Properties
Distribute the 3: 3(x) + 3(2) = 3x + 6. Yes!

Method 2: Plug in a Number (Substitution Test)
Let's pretend x = 4.

3(4 + 2)
3(6)
18

3(4) + 6
12 + 6
18

Since both equal 18, they are equivalent!

🚨 WATCH OUT: A common mistake is thinking x³ is equivalent to 3x. Let's test x=2. (2)³ = 8, but 3(2) = 6. They are NOT equivalent!

EquivalentSubstitution TestProve Equality

DEFINITION

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?

The Substitution Test

Is x = 4 a solution to the equation 3x + 2 = 14?

3(4) + 2 = 14

12 + 2 = 14

14 = 14 ✅

Yes, it makes the statement TRUE!

Testing an Inequality

Which of these values {2, 4, 6} make the inequality y + 3 > 8 true?

Test 2	2 + 3 > 8	5 > 8	❌ False
Test 4	4 + 3 > 8	7 > 8	❌ False
Test 6	6 + 3 > 8	9 > 8	✅ True

REMEMBER: A "solution" is just a number that makes the math sentence a true statement when you plug it in.

Solution SetEquationInequalityTrue/False

DEFINITION

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or any number in a specified set.

Defining the Variable

Before you write an expression, you must state what the letter stands for!

Let m = the number of movie tickets bought.

Building the Expression

Context: A movie theater charges $12 per ticket, plus a one-time online convenience fee of $5. Write an expression for the total cost.

$12 per ticket

Multiply 12 by the number of tickets (m). → 12m

Plus $5 fee

Add 5 at the very end. → + 5

12m + 5

💡 TIP: Look for "rate" words (per, each, every) to know which number multiplies the variable, and "flat fee" words (starting fee, one-time cost) for the constant that gets added or subtracted.

Define VariableWrite ExpressionReal World Context

DEFINITION

Solve real-world problems by writing and solving 1-step equations of the form x + p = q and px = q. Use inverse (opposite) operations to isolate the variable.

Addition/Subtraction Eq.

Sarah had some money. She spent $14 and has $20 left.

x − 14 = 20

Inverse op: Add 14 to both sides.

x = 34

Multiplication/Division Eq.

3 identical shirts cost $45 total.

3y = 45

Inverse op: Divide both sides by 3.

y = 15

The Balance Scale Rule

An equation is like a perfectly balanced scale. Whatever operation you do to one side of the equals sign, you MUST do to the exact same thing to the other side to keep it balanced!

🚨 WATCH OUT: Don't try to just guess the answer in your head. Practice writing down the inverse operation step on paper. This builds the habit for when equations get much harder next year!

Isolate VariableInverse OperationBalance

DEFINITION

An inequality represents a constraint or limit that has infinitely many solutions. We write inequalities using <, >, ≤, ≥ and graph them on a number line.

Translating Inequalities

Symbol	Meaning	Circle Type
<	Less than, fewer than	⭕ Open
>	Greater than, more than	⭕ Open
≤	Less than or equal to, maximum, at most	⚫ Closed
≥	Greater than or equal to, minimum, at least	⚫ Closed

Graphing on a Number Line

"You must be at least 54 inches to ride the rollercoaster." ➔ h ≥ 54

💡 TRICK: If the variable is on the LEFT side (like x > 5), the inequality symbol looks like an arrowhead pointing in the direction you should shade! (> points right ➔)

InequalityConstraintOpen/Closed CircleInfinite Solutions

DEFINITION

Variables can show a relationship between two quantities. The independent variable is the input (what you choose/control). The dependent variable is the output (the result that depends on the input).

Real World Example

You earn $15 per hour at a part-time job. Let h = hours worked, and m = total money earned.

Equation: m = 15h

Independent (Input)	h (Hours) - You control how many hours you work. Usually the x-axis.
Dependent (Output)	m (Money) - Your total money depends on the hours. Usually the y-axis.

Table Representation

Hours (x)	Money (y)
1	$15
2	$30
3	$45

Graph Representation

The graph plots the relationship as a straight line.

💡 TIP: Try saying a sentence out loud: "The [Dependent] depends on the [Independent]." (e.g. "My test score depends on my hours studied." It makes sense!)

Independent (x)Dependent (y)TableGraph

DEFINITION

Find the area of polygons by composing into rectangles or decomposing into triangles and other shapes. Area is the 2D space inside a shape, measured in square units.

Area of a Rectangle / Parallelogram

A = b × h

Base and height MUST form a right angle (90°).

Area of a Triangle

A = ½(b × h)

A triangle is always exactly half of a rectangle.

Decomposing Irregular Polygons

To find the area of a weird shape, cut it up into rectangles and triangles you know how to solve! Find the area of each piece, then add them all together.

Area 1

Area 2

Total Area = Area 1 + Area 2

🚨 WATCH OUT: When finding height, look for the dotted line with the tiny square (right angle symbol). Never use the slanted side length of a triangle or parallelogram as the height!

AreaBaseHeightDecomposeSquare Units

DEFINITION

Volume measures the 3D space inside a solid figure. For a right rectangular prism (a box), multiply the length, width, and height. In 6th grade, these lengths can be fractions!

Volume Formula 1

V = l × w × h

Length times width times height.

Volume Formula 2

V = B × h

"B" means the Area of the Base (which is l × w).

Example with Fractions

Find the volume of a cereal box measuring 4 ½ in, 2 in, and 6 in.

V = 4 ½ × 2 × 6

V =

1082

= 54 in³

💡 TIP: Volume is always measured in cubic units (like cm³, in³, ft³) because you are multiplying 3 dimensions together! Think of how many little 1x1x1 cubes fit inside the box.

Volume3D SpaceCubic UnitsFractional Edges

DEFINITION

A net is a 2D drawing of all the faces of a 3D figure laid out flat. Surface Area is the total area of all the outer faces added together. Think of wrapping paper!

Net of a Rectangular Prism

A box has 6 rectangular faces (Top/Bottom, Front/Back, Left/Right).

Top

Left

Front

Right

Back

Bottom

How to Find Surface Area

1. Unfold the 3D shape into a 2D net.
2. Find the area of EACH individual face (rectangle or triangle).
3. Add all the areas together.

Surface Area = Sum of ALL faces.

🚨 WATCH OUT: Don't confuse Surface Area with Volume! Volume is the space inside (cubic units), Surface Area is wrapping the outside (square units).

Surface AreaNetFacesSquare Units

DEFINITION

You can draw polygons in the coordinate plane by plotting their vertices (corners). Use the coordinates to find the lengths of horizontal or vertical sides to calculate area or perimeter.

Plotting a Rectangle

Finding Dimensions

Width (horizontal):
From x=1 to x=3 is 2 units.

Length (vertical):
From y=2 down to y=-1 is 3 units.

Area = 2 × 3 = 6 sq units

Perimeter = 2+3+2+3 = 10 units

💡 TIP: To find a side length without graphing, use absolute value! Between (3, 2) and (3, -1), the x-coordinates are the same. Find the distance between the y-coordinates: |2| + |-1| = 3.

Vertex/VerticesSide LengthArea & Perimeter

DEFINITION

A statistical question is a question that anticipates variability (differences) in the data. You expect to get many different answers, not just one single fact.

Identifying Statistical Questions

Question	Type	Why?
"How many siblings do 6th graders have?"	Statistical	You will get many different answers (0, 1, 3, etc.)
"How many siblings does Bob have?"	NOT Statistical	There is only one exact factual answer.
"What are the heights of the trees in the park?"	Statistical	Every tree is a different height.

💡 TIP: If you can answer a question by looking up one specific fact or asking just one person, it is NOT statistical. You need to survey a group or collect a dataset!

Statistical QuestionVariabilityData Collection

DEFINITION

A set of data forms a distribution that can be described by its center, its spread, and its overall shape. We describe the group as a whole.

Center

Where is the middle of the data?

Mean or Median

Spread (Variability)

How clustered or stretched out is the data?

Range or MAD/IQR

Shape

What does the graph look like?

Symmetrical or Skewed

Common Data Shapes

Symmetrical

Bell-shaped; left matches right.

Skewed Right

Tail stretches to the right side.

Skewed Left

Tail stretches to the left side.

REMEMBER: When describing data, you aren't talking about one individual student or item, you are summarizing the behavior of the whole group!

DistributionCenterSpreadSymmetricalSkewed

DEFINITION

We use a single number to summarize a data set. A Measure of Center tells us the "typical" value. A Measure of Variability tells us how much the data varies or changes.

Measures of Center (Typical Value)

Mean (Average)	Add all the numbers, then divide by how many numbers there are.
Median (Middle)	Put numbers in order from least to greatest. Find the exact middle number. (If there are two middle numbers, average them).
Mode (Most)	The number that appears the most often. You can have no mode, or multiple modes.

Measures of Variability (Spread)

Range

The difference between the highest value and the lowest value. (Maximum − Minimum).

Interquartile Range (IQR) & Mean Absolute Deviation (MAD)

These measure how far data points are from the center. (Detailed heavily in 7th grade).

💡 TRICK: "Mean" is the "meanest" one to calculate because it requires the most math (adding and dividing).

MeanMedianModeRange

DEFINITION

We create visual plots to easily see the shape, center, and spread of numerical data.

Dot Plot

Places a dot over a number line for every value. Great for small datasets to see exact numbers.

Histogram

Groups data into equal "bins" or ranges (e.g. 0-9, 10-19). Bars touch each other. Loses exact values.

Box Plot (Box and Whisker)

Displays data based on its "Five-Number Summary": Minimum, Quartile 1, Median, Quartile 3, and Maximum. It breaks the data into 4 sections, each containing 25% of the data.

Min

Median

Max

🚨 WATCH OUT: A histogram is NOT a bar graph! Bar graphs are for categorical data (favorite color). Histograms are for numerical data grouped in ranges.

Dot PlotHistogramBox PlotFive-Number Summary

DEFINITION

Summarize numerical data sets in relation to their context by reporting observations, attributes, quantitative measures, and relating the shape to the measures of center.

Real World Dataset: Student Jump Heights (inches)

12, 14, 14, 15, 16, 19, 35

5a: Observations & 5b: Attribute

Number of Observations (n): 7 total jumps recorded.

Attribute: Vertical jump height.

Units: Measured in inches.

5c: Quantitative Measures

Mean: 125 ÷ 7 ≈ 17.8

Median: 15 (the exact middle)

Mode: 14

Range: 35 − 12 = 23

5d: Relating Context to the Display

Choosing the Best Measure of Center

Look at the data: 12, 14, 14, 15, 16, 19, 35. The value 35 is an outlier (a striking deviation that is much higher than the rest).

Because of the outlier 35, the mean (17.8) is pulled artificially high. Only one student actually jumped higher than 16! Therefore, the median (15) is the BEST description of a "typical" jump height for this group.

💡 TIP: If data is perfectly symmetrical, Mean = Median. If data is skewed by an outlier, the Median is a better measure of center!

ContextOutlierBest Measure of Center

6th Grade Anchor Charts

Transform One Consulting Agency