Coordinate Plane: Four quadrants, ordered pairs
(x, y)
🟢 Expressions & Equations (6.EE)
Expressions: Evaluate by substituting values
for variables
Properties: Distributive: a(b + c) = ab + ac.
Combine like terms.
Equations: Solve one-step equations using
inverse operations
Inequalities: >, <, ≥, ≤ on a
number line (open vs. closed circles)
Two Variables: Independent (x) and dependent
(y) in tables and graphs
🟣 Geometry (6.G)
Area of Triangles: A = ½ × base
× height
Area of Parallelograms: A = base × height
Area of Trapezoids: A = ½(b1 + b2)
× height
Volume: V = length × width × height
(rectangular prisms)
Surface Area: Sum of all face areas of a 3D
shape
Nets: A flat pattern that folds into a 3D shape
🔴 Statistics & Probability (6.SP)
Statistical Question: A question that expects
varying answers ("How tall are 6th graders?")
Mean: Add all values, divide by count (the
average)
Median: Middle value when data is sorted
MAD: Mean Absolute Deviation — average
distance from the mean
Displays: Dot plots, histograms, box plots
Worked Examples — One Per Domain
RP: Find a Unit Rate
Problem: 12 apples cost $4.80. What is the cost
per apple?
Divide:
$4.80 ÷ 12 = $0.40 per apple
NS: Divide Fractions
Problem: Solve 3/4 ÷ 2/5
Keep-Change-Flip:
3/4 × 5/2 = 15/8 = 1 7/8
EE: Solve an Equation
Problem: Solve x + 14 = 30
Subtract 14 from both sides:
x = 30 − 14 = 16. Check: 16 + 14 = 30 ✓
G: Area of a Triangle
Problem: Find the area. Base = 10 cm, Height =
6 cm.
Use the formula:
A = ½ × 10 × 6 = 30 cm²
SP: Find the Mean
Data: Test scores: 80, 90, 70, 85, 95
Add, then divide:
(80+90+70+85+95) ÷ 5 = 420 ÷ 5 = 84
Simplified Practice — 2 Per Domain
RP
1. A recipe uses 3 cups of flour for 12 cookies. How many cups
for 20 cookies?
Find the unit rate first: cups per cookie = 3 ÷ 12.
3/12 = 0.25 cups per cookie. 0.25 × 20 = 5 cups.
RP
2. What is 30% of 80?
30% = 0.30. Multiply: 0.30 × 80.
0.30 × 80 = 24.
NS
3. Solve: 5/6 ÷ 2/3
Keep-Change-Flip: 5/6 × 3/2.
5/6 × 3/2 = 15/12 = 5/4 = 1 1/4.
NS
4. Order from least to greatest: −3, 1, −7, 0, 4
On a number line, further left = smaller. Negative numbers are
less than 0.
−7, −3, 0, 1, 4
EE
5. Solve: 7x = 63
Divide both sides by 7.
x = 9. Check: 7(9) = 63 ✓
EE
6. Evaluate 3x + 4 when x = 5.
Replace x with 5: 3(5) + 4.
3(5) + 4 = 15 + 4 = 19.
G
7. Find the area of a parallelogram: base = 8 in, height = 5 in.
Area = base × height.
A = 8 × 5 = 40 in²
G
8. Find the volume: length = 4 cm, width = 3 cm, height = 6 cm.
V = l × w × h.
V = 4 × 3 × 6 = 72 cm³
SP
9. Find the median of: 12, 5, 8, 15, 3
First sort the numbers from least to greatest, then find the
middle one.
Sorted: 3, 5, 8, 12, 15. The middle value is 8.
SP
10. Is "How old are you?" a statistical question? Why or why
not?
A statistical question expects DIFFERENT answers from different
people.
Yes, IF asked to a group — different people have different
ages. If asked to ONE person, no — there is only one
answer.
Real-World Connections
🛒 Shopping (RP)
Comparing prices at the store uses unit rates. Which is a better
deal: 6 apples for $3 or 10 apples for $4.50? Find the price per
apple to decide.
🌡️ Temperature (NS)
Winter temperatures below zero use negative numbers. If it is
−5°F and drops 8 more degrees, the new temperature is
−13°F. The number line helps!
🏠 Home Projects (G)
Painting a room? You need area to know how much paint to buy.
Filling a fish tank? You need volume to know how much water it
holds.
⚽ Sports (SP)
A soccer player scored these goals per game: 0, 2, 1, 3, 1, 0,
2. Finding the mean (1.29) helps compare players. The median (1)
shows the typical game.
Quick Review — Domain Power Notes
🟠 RP: Ratios & Proportional Relationships
Equivalent ratios form a proportional relationship when graphed
through the origin
Unit rates can be found by dividing corresponding quantities
Percent problems use the relationship: part/whole = percent/100
Tape diagrams and double number lines are powerful
problem-solving tools
🔵 NS: The Number System
Division of fractions: multiply by the reciprocal
(Keep-Change-Flip)
Rational numbers include all integers, fractions, and
terminating/repeating decimals
On the coordinate plane, quadrants go counterclockwise: I (+,+),
II (−,+), III (−,−), IV (+,−)
GCF and LCM: GCF = largest shared factor; LCM = smallest shared
multiple
🟢 EE: Expressions & Equations
Order of Operations (PEMDAS/GEMDAS): Parentheses, Exponents,
Multiplication/Division, Addition/Subtraction
Equations: isolate the variable using inverse operations
Dependent vs. independent variables in real-world relationships
🟣 G: Geometry
Decompose irregular shapes into rectangles, triangles, and
trapezoids
Surface area = sum of all face areas (use nets to visualize)
Volume of rectangular prisms: V = lwh or V = Bh (base area
× height)
Polygons on the coordinate plane: use absolute value to find
distances
🔴 SP: Statistics & Probability
Variability measures: range, interquartile range (IQR), mean
absolute deviation (MAD)
Skewed data: use median + IQR. Symmetric data: use mean + MAD
Box plots show the five-number summary: min, Q1, median, Q3, max
Histograms show frequency distribution; dot plots show
individual values
Mixed-Standard Challenge Set
MediumRP
1. A store has a 25% off sale. A jacket originally costs $64.
After the discount, there is 6% sales tax. What is the final
price?
First find 25% of $64 and subtract. Then find 6% of the sale price
and add.
25% of 64 = $16. Sale price: $64 − $16 = $48. Tax: 6% of $48
= $2.88. Final: $48 + $2.88 = $50.88.
MediumNS
2. A submarine is at −150 feet. It rises 80 feet, then dives
45 feet. What is its final depth? How far is it from the surface?
Rising means adding (toward 0). Diving means subtracting (away
from 0).
−150 + 80 = −70. Then −70 − 45 =
−115 feet. Distance from surface: |−115| = 115 feet.
MediumEE
3. Write and simplify an equivalent expression for: 4(2x + 3)
− 2(x − 5)
Distribute each number, then combine like terms (x terms together,
constants together).
8x + 12 − 2x + 10 = 6x + 22.
HardG
4. A rectangular room is 12 ft long, 10 ft wide, and 8 ft tall.
You want to paint all 4 walls (not the ceiling or floor). One can
of paint covers 200 ft². How many cans do you need?
Find the area of each wall. Two walls are 12×8, two walls
are 10×8. Add them up.
2(12×8) + 2(10×8) = 192 + 160 = 352 ft². 352
÷ 200 = 1.76. You need 2 cans (you cannot buy 0.76 of a
can).
HardSP
5. Two classes took the same test. Class A scores: 72, 85, 90, 78,
95. Class B scores: 80, 82, 84, 81, 83. Which class did better on
average? Which class was more consistent? Use mean and MAD.
Mean = sum/count. MAD = average distance of each value from the
mean. Lower MAD = more consistent.
Class A mean: 84, Class B mean: 82. Class A did slightly better on
average. Class A MAD: 7.2, Class B MAD: 1.2. Class B was MUCH more
consistent.
HardRPEE
6. A phone plan charges $0.05 per text message. You budgeted
$15/month for texts. Write an inequality for the number of texts
(t) you can send. If you also want to save $3 for apps, how does
the inequality change?
Cost: 0.05t. This must be ≤ your budget. If saving $3, your
text budget is $15 − $3.
0.05t ≤ 15 → t ≤ 300 texts. With $3 for apps: 0.05t
≤ 12 → t ≤ 240 texts.
ExpertRPNS
7. A recipe calls for 2 1/3 cups of sugar for 4 dozen cookies. You
want to make 10 dozen cookies for a bake sale. How much sugar do
you need? Express your answer as a mixed number.
Find the unit rate (cups per dozen), then multiply by 10. Convert
2 1/3 to an improper fraction first.
8. A garden is shaped like an L. The outer dimensions are 20 ft by
15 ft. A 10 ft by 8 ft rectangle is cut from the corner. Write an
expression for the area using subtraction. Then find the area. If
fencing costs $4.50 per foot, find the total perimeter cost.
Area = large rectangle − cut-out. For perimeter, trace the
outside of the L-shape carefully.
9. Five friends compare allowances: $10, $15, $8, $12, and one
unknown amount. The mean allowance is $12. Find the unknown
amount. If the highest allowance is removed, what is the new mean?
Mean = sum/count. If mean is 12 and count is 5, total = 60.
Subtract known values to find the unknown.
10. A scale model of a building is built at a 1:50 ratio. The real
building is 75 feet tall and has a rectangular base of 120 ft by
80 ft. Find: (a) the model's height, (b) the model's base
dimensions, (c) the volume of the real building, and (d) the
volume of the model. What is the ratio of the volumes?
Divide each real dimension by 50 for the model. For volume ratio,
think about how scaling affects all 3 dimensions.
(a) 75/50 = 1.5 ft. (b) 120/50 = 2.4 ft by 80/50 = 1.6 ft. (c)
120×80×75 = 720,000 ft³. (d)
2.4×1.6×1.5 = 5.76 ft³. Volume ratio:
720,000/5.76 = 125,000 = 50³. When length scales by 50,
volume scales by 50³!
Plan a 7-day family vacation with a $3,000 budget. Research (or
estimate) costs for: hotel per night, food per day, 3 activities,
and transportation. Create a budget using equations. If hotel
costs $120/night, write an equation for total hotel cost.
Calculate what percentage of your budget each category uses. Write
an inequality showing how much you can spend on activities after
paying for hotel and food. Present your budget with a table and
visual breakdown.
Materials: calculator, internet (optional), poster or slides for
presentation
Investigation 2: School Survey Statistician (SP + RP)
Design a statistical question and survey at least 20 people
(classmates, family, etc.). Collect the data, then: calculate
mean, median, and range. Create a dot plot AND box plot of the
data. Find the MAD. Write a paragraph analyzing your results.
Compare your data to a second group if possible. Which measure of
center best represents your data and why?
Investigation 3: Architect for a Day (G + EE + NS)
Design a tiny house with these constraints: total floor area must
be between 200 and 400 ft². Include at least 3 rooms. Draw a
floor plan with dimensions. Calculate the area of each room and
verify the total. If walls are 9 ft tall, find the volume of air
in the house. Calculate surface area for the exterior (for
painting). If paint costs $35 per gallon and covers 350 ft²,
how many gallons do you need? What is the total paint cost?
I am a number. My absolute value is 12. I am negative. When you
find 25% of me, you get an integer. When you use me as the height
of a triangle with base 10, the area is a perfect square. What
number am I?
I am −12. |−12| = 12. 25% of −12 = −3
(integer). Area = ½(10)(−12) — wait, height
should be positive, so using 12: ½(10)(12) = 60. Is 60 a
perfect square? No! The teaser is tricky — re-read:
"use me as the height" uses the absolute value 12. A =
60. Actually, 60 is NOT a perfect square. The clue about
"perfect square" was a red herring to test careful
checking! Always verify your answer against ALL conditions.
Teaser 2: The Number Detective
Using the digits 1, 2, 3, 4, 5 exactly once each, create a
fraction division problem where the answer is a whole number.
Example format: AB/C ÷ D/E = whole number. How many
solutions can you find?
One solution: 15/4 ÷ 3/2 = 15/4 × 2/3 = 30/12 = 5/2.
Not whole! Try: 12/3 ÷ 4/5 = 12/3 × 5/4 = 60/12 = 5.
That uses 1,2,3,4,5 once each and equals 5!
Teaser 3: The Geometry Riddle
I am a 3D shape. My volume is 60 cm³. My base is a triangle
with area 12 cm². What is my height? What type of prism am I?
If each triangular face has a base of 6 cm and height of 4 cm,
what is my total surface area?
V = Bh, so 60 = 12h, h = 5 cm. I am a triangular prism. Surface
area: 2 triangles (2 × 12 = 24) + 3 rectangles. Need the
triangle sides — if base 6, height 4, the two sides are each
5 (3-4-5 right triangle). Rectangles: 6×5 = 30, 5×5 =
25, 5×5 = 25. SA = 24 + 30 + 25 + 25 = 104 cm².
Teaser 4: The Statistics Stump
Create a data set of exactly 7 numbers where: the mean is 10, the
median is 8, and the range is 15. Can you do it? Is there more
than one answer?
Mean = 10, so total = 70. Median = 8, so the 4th number (when
sorted) is 8. Range = 15, so max − min = 15. One solution:
{3, 5, 6, 8, 12, 18, 18}. Sum = 70, median = 8, range = 18 −
3 = 15. Yes, many solutions exist!
Where All This Math Leads — The Big Connections
Ratios → Proportional Relationships → Linear Functions
Your work with ratios and rates becomes proportional relationships
in 7th grade (y = kx), which becomes slope and linear functions (y
= mx + b) in 8th grade, and eventually leads to algebra and
calculus.
Number System → Real Numbers → Complex Numbers
Integers lead to rational numbers in 7th grade, irrational numbers
(like π and √2) in 8th grade, and eventually to complex
numbers in high school algebra.
Expressions & Equations → Algebra → Advanced Math
One-step equations grow into multi-step equations, then systems of
equations, then quadratics, then polynomials. Every equation you
solve now builds the foundation for high school and college math.
Area and volume grow into transformations (slides, flips, turns)
in 7th–8th grade, geometric proofs in high school, and
eventually trigonometry and 3D calculus.
Statistics → Data Science → Machine Learning
Mean, median, and data displays evolve into probability in 7th
grade, two-variable statistics in high school, and ultimately data
science and machine learning — some of the most in-demand
skills in today's workforce.
End-of-Year Self-Assessment
Rate your confidence in each domain. Click to check off areas you
feel strong in:
RP I can find unit
rates and solve proportion problems
RP I can convert
between fractions, decimals, and percents
NS I can divide
fractions and mixed numbers
NS I can compute with
decimals and understand integers/absolute value
EE I can evaluate and
simplify expressions using properties
EE I can solve
one-step equations and inequalities
EE I can represent
two-variable relationships in tables, equations, and graphs
G I can find area of
triangles, parallelograms, and trapezoids
G I can find volume and
surface area of rectangular prisms
SP I can calculate
mean, median, and MAD
SP I can create and
interpret dot plots, histograms, and box plots
I feel confident and prepared for the MCAP assessment