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Slope

Ninth graders learn to measure how steep a line is using rise over run, and to read a line's direction from the sign of its slope, then match each term to its meaning.

Grade 9Slope55 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Define slope.
  • ✓Use rise over run.
  • ✓Read slope from a sign.
  • ✓Match each term.
Essential Question

A gentle ramp and a steep staircase both climb, but not at the same rate. How do we put a single number on how steep a line is?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Match It · Interactive

Match the Term

Project this and match each slope term to what it means — tap a term, then tap its meaning.

🔗 Match each term to what it meansTry it
Term
What it means
Tap a term, then tap what it means.
The Lesson · Gradual Release (I Do · We Do · You Do)

55 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Hook — Which Hill Is Steeper?

5 min

Two ramps rise the same height, but one is longer. Which is steeper, and how do you measure it?

👩‍🏫 Teacher Moves

  • Show two ramps.
  • Ask how to compare steepness.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Match the Term

12 min

Students match each slope term to its meaning.

👩‍🏫 Teacher Moves

  • Send students to Match the Term.
  • Match each pair.
  • Note the meaning.

🎒 Student Actions

  • Match.
  • Say.
  • Note it.
3

Modify — Count Rise and Run

13 min

Students find slope from a graph.

👩‍🏫 Teacher Moves

  • Pick two points on a line.
  • Count the rise and run.
  • Write the slope as a fraction.

🎒 Student Actions

  • Pick.
  • Count.
  • Write.
4

Create — Draw to a Slope

15 min

Students draw lines with target slopes.

👩‍🏫 Teacher Moves

  • Draw a line with slope 2.
  • Draw one with slope -1/2.
  • Label rise and run.

🎒 Student Actions

  • Draw.
  • Draw.
  • Label.
5

Reflect — Direction and Steepness

5 min

Students reflect on what slope tells you.

👩‍🏫 Teacher Moves

  • What does a negative slope look like?
  • What is the slope of a flat line?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School Algebra II).

CCSS
8.EE.B.5

Graph proportional relationships and interpret the unit rate as the slope of the graph.

CCSS
8.F.B.4

Construct a function to model a linear relationship; interpret the rate of change (slope).

CCSS
HSF-IF.B.6

Calculate and interpret the average rate of change of a function over an interval.

CCSS
MP.2

Reason abstractly and quantitatively.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Term + meaning cards.
  • Sentence frame: “Slope is rise over ___ .”
  • Match one pair at a time.

Support & Access

IEP / 504
  • Start with rise and run on a grid.
  • Trace lines going up vs down.
  • Match one term fully before the next.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Find slope from two coordinate points.
  • Compare zero and undefined slope.
  • Connect slope to y = mx + b.
Materials

What to gather

  • 📽️Projector / board
  • 📐Graph paper
  • 💻Match the Term
  • 📏Rulers
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

slopehow steep a line is, measured as rise over runrisethe vertical change between two pointsrunthe horizontal change between two pointspositive slopea slope whose line rises from left to rightnegative slopea slope whose line falls from left to rightzero slopethe slope of a horizontal (flat) lineundefined slopethe 'slope' of a vertical line, where run is zerorate of changehow much one quantity changes compared to another; the slope
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
How do you calculate the slope of a line?
Divide the rise (vertical change) by the run (horizontal change) between two points.
QUESTION 2
What does a negative slope look like on a graph?
A line that goes downward from left to right.
QUESTION 3
What is the slope of a horizontal line, and why?
Zero, because the rise is 0 (there is no vertical change).

Create: draw to a slope.

Have students draw one line with a slope of 2 and one with a slope of -1/2, labeling the rise and run that produce each. A printable slope worksheet is in the Mathematics library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 SlopeFlip
Card 1
Term
Tap to flip →
Meaning
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Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 SlopeQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ SlopePrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: negative slope, positive slope, rate of change, rise, run, slope, undefined slope, zero slope
  1. a slope whose line rises from left to right
  2. a slope whose line falls from left to right
  3. the 'slope' of a vertical line, where run is zero
  4. how much one quantity changes compared to another; the slope
  5. the horizontal change between two points
  6. the slope of a horizontal (flat) line
  7. how steep a line is, measured as rise over run
  8. the vertical change between two points

Part B · Show what you learned

  1. How do you calculate the slope of a line?
  2. What does a negative slope look like on a graph?
  3. What is the slope of a horizontal line, and why?
Answer key — Part A: 1) positive slope · 2) negative slope · 3) undefined slope · 4) rate of change · 5) run · 6) zero slope · 7) slope · 8) rise
Part B: 1) Divide the rise (vertical change) by the run (horizontal change) between two points. 2) A line that goes downward from left to right. 3) Zero, because the rise is 0 (there is no vertical change).