30‑Minute Lesson Plan — Percentages (Grade 6)

Overview

Purpose: Teach students to interpret and compute percentages of quantities using concrete → pictorial → symbolic representations so they can solve authentic problems (e.g., discounts, tax, portions). Classical structure: I-do (modeling), We-do (guided practice), You-do (independent application). Anchor on mastery threads: unit reasoning, quantity relationships, equivalence, and composition/decomposition.

Standards Alignment

• CCSS 6.RP.3 (use ratio reasoning to solve percent problems such as “What is 30% of 200?”) — applicable to typical US Grade 6 expectations for percent understanding.
• Emphasis on converting between percent, fraction, and decimal; applying to solve problems using unit reasoning and decomposition.

Materials (Low)

• 100‑grid handout or draw a 10×10 grid on whiteboard
• Paper and pencil per student
• Optional: small counters or colored pencils for grid shading
• Timer or clock

Time Allocation (30 minutes)

• 0:00–0:05 — Hook & Definitions (I-do)
• 0:05–0:12 — Annotated Worked Examples (I-do continued)
• 0:12–0:20 — Guided Practice (We-do) with Pulse Check 1
• 0:20–0:27 — Independent Practice (You-do) with Pulse Check 2
• 0:27–0:30 — Quick Quiz checkpoints and Metacognition prompts; closure

Learning Objectives (measurable)

Students will be able to:

• Define percent as “parts per 100” and represent it as fraction and decimal.
• Use unit reasoning and composition/decomposition to compute a percent of a quantity in at least 2 of 3 authentic tasks.
• Convert between percent, fraction, and decimal for common values (e.g., 50%, 25%, 10%) and use these to solve problems.

Success criteria:

• Correctly compute percent-of problems in 4 out of 5 independent tasks.
• Explain the chosen representation (grid, fraction, or decimal) and why it helps solve a real-world percent problem in a short written reflection.

Sequencing representations (concrete → pictorial → symbolic) and rationale

• Concrete: counters or shading a 100‑grid — anchors "percent = parts per 100" and supports unit reasoning (one unit = 1%).
• Pictorial: labeled 100‑grid or bar model — shows quantity relationships and equivalence (e.g., 25% = 25/100 = 1/4).
• Symbolic: fraction (25/100), decimal (0.25), and multiplication (0.25 × whole) — efficient computation and generalization to unfamiliar percentages.
  Narration: Each move preserves the unit (1% = 1/100 of the whole). Concrete makes the unit visible; pictorial maps quantity relationships; symbolic compresses the reasoning into operations for efficiency while retaining equivalence to the concrete model.

Lesson Sequence (Classical I-do / We-do / You-do)

I-do (0:00–0:12) — Direct instruction, modeled examples

1. Definition and anchor (1 minute)

   • State: “Percent means parts per 100. 1% = 1/100 of the whole.”
   • Show a 10×10 grid and shade 1 square to show 1%.

2. Annotated Worked Example A (25% of 120) (5 minutes)

   • Concrete/pictorial: Shade 25 of 100 on grid; annotate “25/100”.
   • Equivalence: Write 25/100 = 1/4 (unit reasoning: dividing both numerator and denominator by 25).
   • Composition/decomposition: 1/4 of 120 = 120 ÷ 4 = 30.
   • Symbolic alternative: 25% = 0.25 → 0.25 × 120 = 30.
   • Annotation points: show correspondence between shaded grid, fraction, and multiplication; label units (percent unit = 1/100 of the whole).
   • Explicit success statement: “We created a chain showing how a concrete 25 shaded squares equals 0.25 of the whole, so multiplying gives the answer.”

3. Annotated Worked Example B (40% of 75) (6 minutes)

   • Pictorial: Use a bar split into ten 10% chunks, label each chunk = 7.5 (since 10% of 75 = 7.5).
   • Decompose: 40% = 4 × 10% → 4 × 7.5 = 30.
   • Symbolic: 0.40 × 75 = 30.
   • Emphasize composition/decomposition (use 10% repeatedly) and quantity relationships (10% as unit increment).
   • Annotate why this approach reduces computation load and preserves equivalence.

Pulse Check 1 (during I-do → at 0:12)

• Task: Verbally explain (one sentence) how to find 25% of a number using the grid or decimal method.
• Success criteria: Student provides an explanation that includes either
  • “Shade 25/100 on the grid → reduce to fraction or multiply by 0.25,” OR
  • “Convert percent to decimal (divide by 100) and multiply by the whole.”
• Strategy for teacher: quick cold-calls or thumbs-up/thumbs-down for whole-class check; note who meets criteria.

We-do (Guided Practice 0:12–0:20)

Teacher leads two problems with students contributing steps and reasoning.

1. Problem 1 (guided): Find 15% of 200

   • Teacher prompts: “What is 10% of 200? 5%? Combine.”
   • Students compute: 10% = 20; 5% = 10; 15% = 30.
   • Annotate decomposition: show 15% = 10% + 5%.

2. Problem 2 (guided): Find 12.5% of 64

   • Teacher models fraction equivalence: 12.5% = 12.5/100 = 1/8.
   • Use unit reasoning: 1/8 of 64 = 8.
   • Student contribution: identify fractional equivalence and compute.

Pulse Check 2 (We-do midpoint)

• Task: Solve one of the two guided problems independently on paper and hold up answer.
• Success criteria: Correct numeric answer shown and a one-line justification (e.g., “15% = 10%+5%, so 20+10=30”).
• Teacher records how many students meet criteria; goal: at least 70% of class success to proceed.

You-do (Independent Practice 0:20–0:27) — Individual application

Students complete 5 short percent-of problems on paper. Success criteria for this block:

• Individual success goal: correctly solve at least 4 out of 5 problems and annotate which representation used (grid, fraction, decimal, or decomposition).

Independent problems (choose low-material approach):

1. 25% of 80
2. 30% of 50
3. 10% of 230
4. 18% of 200 (hint: find 10% and 1%)
5. 5% of 120

Teacher circulates, notes misconceptions, quick corrective mini-demonstrations if >30% struggle.

Pulse Check 3 (during You-do, quick exit check at 0:26)

• Task: On the exit slip, write the answer to problem #3 and one sentence: “Which representation I used and why.”
• Success criteria: Correct answer to problem #3 and a sentence that names a representation (e.g., “I used decimal because it was faster: 0.10×230=23”) that matches method.

Quick Quiz-style Checkpoints (10 items with success criteria)

Use these as instant checks, exit tickets, or a short paper quiz. For each item, success criteria = correct numeric answer (tolerate common decimal formatting) and short justification for two select items (see notes).

1. What is 50% of 60?

   • Success: 30.

2. What is 25% of 120?

   • Success: 30 (justification optional: “¼ of 120”).

3. Convert 0.4 to a percent.

   • Success: 40%.

4. Convert 75% to a decimal and fraction in simplest form.

   • Success: 0.75 and 3/4.

5. Find 10% of 450.

   • Success: 45.

6. Find 40% of 75 (use decomposition or decimal).

   • Success: 30.

7. A $80 jacket is on sale for 25% off. What is the sale price?

   • Success: Discount = $20; sale price = $60. (Student must show subtraction).

8. What percent is 15 out of 60? (express as percent)

   • Success: 25%.

9. Find 12.5% of 56 (best if student shows method).

   • Success: 7 (show 12.5% = 1/8, 56 ÷ 8 = 7).

10. If 30% of a class of 40 students brought lunch from home, how many students is that?

    • Success: 12 (show 0.30 × 40 = 12 or 30/100 × 40).

Use scoring rubric: 1 point each. Mastery benchmark for lesson: >= 8/10 indicates secure performance today.

Metacognition Prompts (embedded)

• After independent practice: “Describe in 2–3 sentences when you would use a grid, fraction, or decimal to find a percent in real life (for example, shopping discounts, recipes, or sports statistics).”
• Exit reflection: “Which method made the problem easiest for you today? Give one real-world example where you would use that method.”
• Short writing success criteria: Student names a context and connects it explicitly to the representation (e.g., “I use decimals for money because prices are dollars and cents”).

Differentiation (brief)

• Support: Provide 100‑grid copies, allow students to shade or use counters; offer decomposition prompts (start with 10% then adjust).
• Challenge: Offer problems with non-standard percentages (e.g., 17.5% of 120) and ask students to explain conversion to decimal and compute.

Assessment & Feedback

• Formative checks: Pulse Checks 1–3 and teacher observation during We-do and You-do.
• Summative mini-assessment: 10 quick quiz-style checkpoints; score 8/10 for mastery on this lesson’s objectives.
• Feedback focus: correctness and clarity of representation choice and justification; correct unit reasoning and equivalence steps.

Teacher Notes — Common misconceptions and quick corrections

• Mistake: Interpreting percent as whole number rather than per 100. Correction: Always relate to a 100-grid or “per 100” phrasing and show 1% as one unit.
• Mistake: Multiplying percent value directly instead of converting (e.g., 25 × 120). Correction: Model conversion to decimal/fraction and show equivalence to grid.
• Mistake: Confusion between percent of vs percent increase/decrease. Correction: Explicitly label tasks as “percent of” for this lesson; reserve increase/decrease for a later lesson.

Closing (0:27–0:30)

• Collect exit slips (Pulse Check 3 responses).
• Announce mastery expectations: students who met success criteria (4/5 independent tasks or 8/10 quiz score) demonstrated expected proficiency in percent-of computations today.
• Metacognitive final prompt (written on board to take home): “Name a real-world situation this skill helps you solve and write one sentence connecting the method you chose to that situation.”