8th Grade STAAR Math Review

Step-by-Step
Concept Guide

One concept per slide. Follow along, pause anytime, and use Desmos as your superpower. 🖩

Chapter 1 of 5

📈 Finding Slope
from a Table

TEKS 8.4B & 8.4C  |  Desmos: table + regression

📈 Slope — The Endgame

This is what success looks like in Desmos.

y₁ ~ mx₁ + b
✅ y = 2x + 1
m = 2  |  b = 1
↗
straight line
appears here

m = MULTIPLIER = slope  |  b = BONUS = y-intercept. Desmos finds both automatically!

📈 Slope — Step 1

Pick ANY 2 easy points from the table.

Tacos (x)Cost (y)
1$3
⭐ 2⭐ $5
3$7
⭐ 4⭐ $9
5$11

Pro tip: pick numbers without decimals or negatives when you can. You only need 2!

📈 Slope — Step 2

Press + → Select Table in Desmos.

+ Add Item
📋 Table ← Click this!
Note
Graphing area

The Table option opens 2 columns: x₁ and y₁. Type your two points, one per row.

📈 Slope — Step 3

Type your points → click Add regression → read m & b.

x₁y₁
25
49
++
y = 2x + 1
m = 2  |  b = 1
m = MULTIPLIER
= slope
b = BONUS
= y-intercept
📈 Slope — Faded Example

A Dallas taco truck charges $2.50 per taco + $1 fee.

Fully worked ✅
Points: (1, 3.5) & (3, 8.5)
Desmos: y = 2.5x + 1
Slope = $2.50/taco
Start = $1.00
Your turn 🔶
Points: (2, 6) & (4, 11)
Desmos: y = x +
Slope = $/taco
Start = $
You've got this! ⭐
Pick your own 2 points:
( , ) &
( , )
Slope = $
Chapter 2 of 5

⚖️ Solving Equations
with Desmos

TEKS 8.5I & 8.8C  |  The Tilde (~) Method

⚖️ Equations — The Endgame

Desmos solves it instantly. Here's the finish line.

1000.75 − 10.8c ~ 800.75 − 5.8c
✅ c = 40
c = 40
The answer appears
automatically!

Type the equation using ~ (tilde) instead of = and a letter other than x. Desmos does the rest!

⚖️ Equations — Rule #1

NEVER use x in the equation.

❌ 3x + 5 = 17

WRONG — Desmos
treats x as a graphing variable!

→
✅ 3a + 5 ~ 17

Use a, b, c, d…
anything but x!

⚖️ Equations — Rule #2

Replace = with ~ (tilde).

KEYBOARD — find this key:
~
Top-left key, above Tab
(Shift + backtick)
→
15a + 30 ~ 10a + 55
✅ a = 5
⚖️ Equations — Full Process

Three steps, every time.

1

Cross out x — pick a new letter

Use a, b, c, d, t, n — literally anything but x

3a + 56 = 17a   ← from the problem
2

Replace = with ~ (tilde)

The tilde tells Desmos to solve, not graph

3a + 56 ~ 17a
3

Read the answer → substitute back to check

Plug back into BOTH sides — they should be equal!

a = 4  →  3(4)+56=68  ✅  17(4)=68
⚖️ Equations — Faded Example

Container A starts with 1000 gal, drains 10.8/min.
Container B starts with 800, drains 5.8/min. When equal?

Fully worked ✅
Letter: c (minutes)
A: 1000 − 10.8c
B: 800 − 5.8c
Desmos: 1000−10.8c ~ 800−5.8c
Answer: c = 40 minutes
Your turn 🔶
Letter:
A: 500 − 8t
B: 200 − 3t
Desmos:
Answer: t =
You've got this! ⭐
Write your own equation problem here and solve it with the tilde method.
Chapter 3 of 5

🔧 Identifying
Functions

TEKS 8.5G  |  The Golden Rule of Functions

🔧 Functions — The Rule

⭐ The Golden Rule of Functions

Every input (x) gets exactly
ONE output (y).
✅
FUNCTION
x values are all different
❌
NOT a function
same x, different y values

⚠️ STAAR TRICK: y-values CAN repeat — only x matters!

🔧 Functions — Method 1

Ordered Pairs & Tables — x-Ray Vision

Step 1: Find all x-values
{ (1, 5), (2, 7), (3, 9), (2, 11) }
⚠️ x = 2 appears TWICE → ❌
Step 2: Check the table
xy
13
2 ⚠️7
311
2 ⚠️15
NOT a function ❌
🔧 Functions — Method 2

Mapping Diagrams — The Arrow Rule

✅ FUNCTION
1
2
3
→ → →
5
9
13
ONE arrow leaves each x
❌ NOT a Function
1
2
→ → →
5
9
13
TWO arrows from same x ⚠️
🔧 Functions — Method 3

Graphs — The Pencil (Vertical Line) Test

Slide a vertical line left → right
touches ONCE ✅
✅ FUNCTION
Slide a vertical line left → right
touches TWICE ❌
❌ NOT a Function

If your pencil crosses the line in 2+ spots at the same time → NOT a function.

🔧 Functions — Faded Example

Is it a function? Find the x-values!

Fully worked ✅
{(1,3),(2,5),(3,7),(4,9)}
x-values: 1, 2, 3, 4
Any repeats? No
Function? YES ✅
Your turn 🔶
{(2,4),(3,6),(2,8),(5,10)}
x-values:
Repeats?
Function?
You've got this! ⭐
xy
15
25
35
45
Function?
Chapter 4 of 5

🔢 Ordering
Real Numbers

TEKS 8.2D  |  The x = Method in Desmos

🔢 Ordering — The Endgame

Vertical lines appear on the number line — left to right = least to greatest.

1.5
7/4
√4
π
1.5 < 7/4 < √4 < π

The lines show up automatically — you just read them left to right!

🔢 Ordering — The Steps

Order:   ½   √16   75%   −3   2

x = 0.5  (½)
x = 4  (√16)
x = 0.75  (75%)
x = −3
x = 2
Conversion Hints
½ → type 1/2
√16 → type sqrt(16)
75% → type 75/100
π → type pi
2³ → type 2^3

Read the vertical lines left → right: −3, ½, 75%, 2, √16

🔢 Ordering — Faded Example

Order least to greatest:   √50   7.1   22/3   7¼

Fully worked ✅
x = sqrt(50) → 7.07
x = 7.1
x = 22/3 → 7.33
x = 7.25 (7¼)
Order: √50, 7.1, 7¼, 22/3
Your turn 🔶
Order: 3.5, √10, π, 11/3
x =
x =
x =
Order:
You've got this! ⭐
Order GREATEST to least:
2³, √60, 7.8, 23/3

Order:
⚠️ Read RIGHT → LEFT!
Chapter 5 of 5

📦 Volume
with Desmos

TEKS 8.7A  |  Cylinder · Cone · Sphere

📦 Volume — The Three Shapes

Know your shape, know your formula.

r h

Cylinder

V = πr²h
Desmos: V ~ π·r²·h
r h

Cone

V = ⅓πr²h
Desmos: V ~ (1/3)·π·r²·h
r

Sphere

V = 4/3·πr³
Desmos: V ~ (4/3)·π·r³
📦 Volume — In Desmos

Type formula with ~, define known values, leave V blank.

Cylinder
V ~ π · r² · h
r = 6
h = 10
✅ V ≈ 1130.97
Cone
V ~ (1/3) · π · r² · h
r = 4
h = 12
✅ V ≈ 201.06
Sphere
V ~ (4/3) · π · r³
r = 4.7
✅ V ≈ 435.05
📦 Volume — Faded Example

Fair Park water tank: cylinder, r = 6 ft, h = 10 ft.

Fully worked ✅
Shape: Cylinder
Desmos Line 1: V ~ π·r²·h
Desmos Line 2: r = 6
Desmos Line 3: h = 10
V ≈ 1,130.97 ft³
Your turn 🔶
Raspa cone: r = 4 cm, h = 12 cm
Shape:
Line 1: V ~
r =   h =
V ≈ cm³
You've got this! ⭐
Mavericks basketball: r = 4.7 in

Shape:
Desmos formula:
V ≈ in³
🎉

You reviewed all 5 concepts!

📈 Slope ✅ ⚖️ Equations ✅ 🔧 Functions ✅ 🔢 Ordering ✅ 📦 Volume ✅

You have the tools. You have the strategies. Go show that STAAR test what you've got! 💪

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