BEDMAS
Order of Operations
B
Brackets first: do whatever's inside ( ) before anything else.
E
Exponents next: powers like 2³ or square roots.
D
Division and
M
Multiplication: left to right, whichever comes first.
A
Addition and
S
Subtraction: left to right, whichever comes first.
Evaluate 3 + 2 × (4 + 1)²:
Brackets: (4 + 1) = 5
Exponent: 5² = 25
Multiplication: 2 × 25 = 50
Addition: 3 + 50 = 53
Integer Rules
Adding, Subtracting, Multiplying, Dividing
Adding integers
- Same signs: add the numbers, keep the sign. (+3) + (+5) = +8. (−3) + (−5) = −8.
- Different signs: subtract smaller from larger, keep the sign of the bigger number. (+7) + (−3) = +4. (−7) + (+3) = −4.
Subtracting integers
"Keep, change, change": keep the first number, change subtraction to addition, change the sign of the second number. Then add.
5 − (−3) → 5 + (+3) = 8.
(−4) − 7 → (−4) + (−7) = −11.
Multiplying and dividing
- Same signs → positive result. (+) × (+) = +. (−) × (−) = +.
- Different signs → negative result. (+) × (−) = −. (−) × (+) = −.
Prime and Composite Numbers
Numbers from 1 to 50
Prime: exactly 2 factors (1 and itself). Composite: more than 2 factors.
1 is neither prime nor composite.
Test if 23 is prime: try dividing by 2 (no), 3 (no), 4 (no, but 4=2x2 already done), 5 (no). √23 ≈ 4.8, so we stop. 23 is prime.
Polygon Family Tree
Classify 2D shapes by sides and angles
Triangles (3 sides)
- By sides: equilateral (3 equal), isosceles (2 equal), scalene (none equal)
- By angles: acute (all < 90°), right (one = 90°), obtuse (one > 90°)
Quadrilaterals (4 sides)
- Trapezoid: exactly one pair of parallel sides
- Parallelogram: both pairs of opposite sides parallel
- Rectangle: all angles 90°
- Rhombus: all sides equal
- Square: all sides equal AND all angles 90° (both!)
More sides
- 5 sides = pentagon, 6 = hexagon, 7 = heptagon, 8 = octagon
- 9 = nonagon, 10 = decagon, 12 = dodecagon
- Regular = all sides equal AND all angles equal
Measurement Benchmarks
If you forget the unit, remember these
Length
1 cm
width of a fingernail
Mass
Capacity
1 mL
a drop from a dropper
Math Mindset
What to say when math is hard
instead of
"I can't do this."
try
"I can't do this YET."
instead of
"I'm bad at math."
try
"I'm growing my math skills."
instead of
"This is wrong, I give up."
try
"Mistakes help my brain grow."
try
"Have I checked my work?"
Math Talk Moves
How to talk about math with classmates
Explain your thinking
- "I started by..."
- "First I noticed that..."
- "I picked this strategy because..."
Ask for clarification
- "Can you say more about...?"
- "What did you do after...?"
- "Why does that work?"
Agree or build on
- "I agree with ___ because..."
- "I have a different way to..."
- "That makes me think of..."
Politely disagree
- "I see it a different way."
- "I don't think that's quite right because..."
- "What if we tried..."
Geometry Vocabulary
Words you need for shapes and space
Point
A single location, no size. Shown as a dot.
Line
Goes on forever in both directions.
Line segment
Part of a line between two endpoints.
Ray
Starts at one point, goes on forever in one direction.
Angle
Two rays meeting at a vertex (corner).
Parallel
Two lines that never meet, like train tracks.
Perpendicular
Two lines that meet at exactly 90°.
Vertex
A corner where edges or sides meet.
Face
A flat surface on a 3D shape.
Edge
Where two faces of a 3D shape meet.
Symmetry
A shape that looks the same on both sides of a line.
Congruent
Exactly the same shape and same size.