Quarter 2: Day 1 of 4

Topic: What Is a Linear Equation?
Group Size: 4–6 students
Time: 20 minutes
Placement: Level C / Explicit Instruction Model
CCSS Standards:

• 8.EE.C.7: Solve linear equations in one variable
• 8.F.A.1: Understand the concept of a function as a rule
• 8.EE.B.5: Graph proportional relationships

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🎯 Learning Objective

I can identify and explain what a linear equation is, including recognizing variables and coefficients.

✅ Success Criteria

• Explain what a variable and an equation are.
• Describe how the output changes when input changes.
• Correctly solve for y when given x-values in linear equations.

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🗣 Vocabulary (Dyslexia-Friendly Font & Visuals)

Word	Meaning	Icon/Visual Aid
Equation	Math sentence with an equal sign	=
Variable	A letter that stands for a number	x
Linear	Straight-line relationship	📈
Coefficient	Number multiplied by a variable	2 in 2x

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📝 Lesson Procedures

1. Anticipatory Set – 2 minutes

Pose question aloud: “If you earn $5 every hour, how much after 1 hour? 2 hours?”
Write answers on board, showing the pattern grows by the same amount. Use color highlighting for clarity.

Ask: “What kind of rule connects hours and money?”

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2. Explicit Instruction – I DO (5 minutes)

• Define equation as a math sentence that shows balance.
• Define variable as the unknown number that can change.
• Model the equation y = 2x.
• Think aloud: “When x goes up by 1, y goes up by 2.”
• Use a visual number line or bar model to reinforce concept.

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3. Guided Practice – WE DO (5 minutes)

• Solve together: y = x + 3 for x = 1 and 2.
• Use whiteboards for immediate response; teacher circulates and models sentence stems:
  “First, substitute x with …”
• Encourage use of drawings to visualize changes.

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4. Independent Practice – YOU DO (3 minutes)

• Solve: y = x + 1 for x = 2 on individual whiteboards or paper.

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✨ Kagan Structure: Rally Coach

• Partner A solves, Partner B coaches with sentence stems:
  “First you substitute…”
  “Then you add…”
  “Finally, you get…”

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✔ Checks for Understanding

• Whiteboard responses checked visually.
• Thumbs Up / Sideways for confidence level.
• Targeted oral questions with wait time.

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Differentiation Strategies

• Use color-coded notes and graphic organizers to reduce cognitive load.
• Provide sentence frames to support language development.
• Allow oral explanations instead of writing if needed.

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Extension Activity

• Challenge: Write your own linear equation and solve it for two different x values.
• Draw a real-life situation that matches your equation.

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Function Rules & Tables

Quarter 2: Day 2 of 4

Topic: Inputs and Outputs (Functions)
Group Size: 4–6 students
Time: 20 minutes
Placement: Level C / Explicit Instruction Model
CCSS Standards:

• 8.F.A.1: Define functions and interpret input/output
• 8.F.A.2: Compare properties of functions represented in different ways

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🎯 Learning Objective

I can identify functions and complete input-output tables using linear rules.

✅ Success Criteria

• Define function, input, and output with clear examples.
• Fill in missing values in function tables accurately.
• Explain how input relates to output.

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🗣 Vocabulary (Dyslexia-Friendly Font & Visuals)

Word	Meaning	Icon/Visual Aid
Function	A rule that assigns exactly one output for each input	🔄
Input	Value you put in	In arrow →
Output	Value you get out	Out arrow →
Table	Organized data in rows and columns	📋

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📝 Lesson Procedures

1. Anticipatory Set – 2 minutes

Show picture of vending machine with money input and snack output.
Say: “The vending machine works like a function. Money goes in, snack comes out.”

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2. Explicit Instruction – I DO (5 minutes)

• Define function, input, and output.
• Model filling a function table with rule y = x + 2.
• Visualize “input” → “apply rule” → “output.”

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3. Guided Practice – WE DO (5 minutes)

• Complete partially filled table together.
• Discuss patterns and how values change.
• Highlight consistent changes with colored markers.

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4. Independent Practice – YOU DO (3 minutes)

• Fill in 1 missing output in a function table completed individually.

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✨ Kagan Structure: Think-Pair-Share

• Think: Fill one row independently.
• Pair: Compare answers with partner, discuss.
• Share: Explain reasoning aloud. Use sentence stems like:
  “I knew this because…”
  “The rule adds…”

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✔ Checks for Understanding

• Turn-and-talk observations.
• Teacher cold calling for oral answers.
• Exit slip: Circle correct output in small function sets.

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Differentiation Strategies

• Provide number lines for calculating outputs.
• Use manipulatives or counters to model function steps.
• Offer extra time for processing responses.

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Extension Activity

• Challenge students to create a new function table from an equation of their choice and explain its rule in their own words.

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Graphing Linear Lines

Quarter 2: Day 3 of 4

Topic: Graphing Linear Functions
Group Size: 4–6 students
Time: 20 minutes
Placement: Level C / Explicit Instruction Model
CCSS Standards:

• 8.F.A.3: Interpret equations as linear functions with slope and intercept
• 8.EE.C.7: Graph proportional relationships and find slope

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🎯 Learning Objective

I can plot points and graph linear equations on coordinate planes.

✅ Success Criteria

• Correctly label x- and y-axes.
• Plot points given by linear equations.
• Draw a straight line connecting points.

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🗣 Vocabulary (Dyslexia-Friendly Font & Visuals)

Word	Meaning	Icon/Visual Aid
Graph	Picture showing the relationship between numbers	📉
Slope	Rate of change or steepness	↗️
Y-intercept	Point where line crosses y-axis	⚫
Coordinate	Pair of numbers (x, y)	➕

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📝 Lesson Procedures

1. Anticipatory Set – 2 minutes

Ask: “Have you ever tracked your steps on a phone graph?”
Explain: “Graphs tell stories with points and lines.”

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2. Explicit Instruction – I DO (5 minutes)

• Introduce coordinate plane: x-axis(horizontal), y-axis(vertical).
• Model plotting points for y = x on graph paper or grid mat.
• Show slope (rise/run) and y-intercept concepts simply and visually.

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3. Guided Practice – WE DO (5 minutes)

• Together, graph y = x + 1 on a classroom grid.
• Use colored markers or sticky dots for points.
• Describe each step explicitly.

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4. Independent Practice – YOU DO (3 minutes)

• Plot one point from an equation independently on graph paper.

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✨ Kagan Structure: Quiz-Quiz-Trade

• Students have cards with graphs, tables, or equations.
• Quiz partner, trade cards, and repeat to reinforce connections.

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✔ Checks for Understanding

• Monitor point placement accuracy
• Ask quick explanations to clarify thinking
• Visual thumbs up/down after graph completion

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Differentiation Strategies

• Use tactile graphing mats for kinesthetic learners.
• Provide graph paper with grid lines highlighted for dyslexia-friendly access.
• Scaffold tasks with partially filled graph templates.

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Extension Activity

• Explore changes in slope and y-intercept by graphing equations like y = 2x + 1 or y = -x + 3 and predict graph behavior.

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Match & Connect

Quarter 2: Day 4 of 4

Topic: Matching Functions (Review & Apply)
Group Size: 4–6 students
Time: 20 minutes
Placement: Level C / Explicit Instruction Model
CCSS Standards:

• 8.F.A.1–3: Understanding functions and representations
• 8.EE.C.7: Solve and graph linear functions

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🎯 Learning Objective

I can match equations, tables, and graphs that represent the same linear function.

✅ Success Criteria

• Correctly link an equation to its matching table and graph.
• Explain in my own words how the matches show the same relationship.

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🗣 Vocabulary (Dyslexia-Friendly Font & Visuals)

Word	Meaning	Icon/Visual Aid
Match	Pair items that belong together	🔗
Representation	Different ways to show the same idea	🖼️
Review	Go over what we learned	🔄

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📝 Lesson Procedures

1. Anticipatory Set – 2 minutes

Ask: “Can different math representations show the SAME idea?”
Show quick examples in mixed form (graph, equation, table).

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2. Explicit Instruction – I DO (4 minutes)

• Model matching an equation to its table, then to its graph.
• Describe key features in each that connect (pattern, points, rule).

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3. Guided Practice – WE DO (5 minutes)

• Group matches 3 sets of cards (equation, table, graph) laid out.
• Discuss reasoning as a group with teacher support and visual aids.

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4. Independent Practice – YOU DO (4 minutes)

• Each student independently matches 2 or 3 sets of cards at their table.

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✨ Kagan Structure: Round Robin

• Each student explains one match using sentence frames:
  “This equation matches the table because…”
  “The graph shows the same pattern as…”

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✔ Checks for Understanding

• Accuracy in matches
• Oral justifications observed by teacher
• Checklist completed by teacher during activity

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Differentiation Strategies

• Provide visual cue cards with symbols for slope, y-intercept to aid matching.
• Allow students to work with assistive technology (e.g., reading cards aloud).
• Use peer modeling for support during Round Robin.

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Extension Activity

• Create “mystery” cards where students write their own equation, table, or graph and challenge classmates to match them.

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Summary

This 4-day mini-unit utilizes explicit instruction, Kagan cooperative learning strategies, and frequent formative checks to build skills aligned tightly to Common Core math standards centered on linear functions, equations, and representations. Dyslexia-friendly options, multi-sensory activities, and differentiation ensure accessibility for all learners in small-level C groups.

Teachers are encouraged to use the formative data collected each day to tailor next steps and support. This plan balances rigor with engagement and social interaction to empower struggling learners to master these foundational concepts in middle school math.