Ratios and Models

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Grade Level

6th Grade

Duration

71 minutes

Class Size

20 Students

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Standards Alignment

Common Core State Standards - Mathematics

• CCSS.MATH.CONTENT.6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
• CCSS.MATH.CONTENT.6.RP.A.3.A: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane.
• CCSS.MATH.PRACTICE.MP4: Model with mathematics.
• CCSS.MATH.PRACTICE.MP7: Look for and make use of structure.

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Learning Objectives

By the end of this lesson, students will be able to:

1. Model ratios using tape diagrams to visualize part-to-part relationships.
2. Solve ratio problems using tape diagrams and apply their understanding to word problems.
3. Create and complete ratio tables to find equivalent ratios and missing values.
4. Use movement and problem solving in a scavenger hunt format to actively engage with ratio tables.
5. Demonstrate understanding of ratio concepts by constructing their own equivalent ratio tables in an exit ticket.

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Materials Needed

• Tape diagram templates (printed sheets or whiteboards)
• Ratio table handouts with one missing value each (10–12 cards)
• Word problem and tape diagram matching cards (sets for pairs)
• Markers, pencils, erasers
• Chart paper or projector for examples
• Exit ticket slips

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Lesson Procedure

1. Warm-Up: Tape Diagram Introduction (8 minutes)

Objective: Introduce modeling ratios visually to build conceptual understanding.

• Begin by writing the ratio 3:2 on the board and explaining it represents 3 blue marbles for every 2 red marbles.
• Ask students: “How can we show this visually?”
• Have students draw a tape diagram with 3 equal parts for blue and 2 equal parts for red on their papers or mini whiteboards.
• Then pose the problem: “If there are 15 blue marbles, how many red marbles are there? What is the total number of marbles?”
• Guide students to find that each part in the tape diagram represents 5 marbles (15 ÷ 3 = 5), so they can calculate red marbles (2 × 5 = 10) and total marbles (15 + 10 = 25).
• Quickly review and discuss answers as a class, emphasizing how tape diagrams help solve ratio problems.

2. Activity 1: Ratio Table Scavenger Hunt (20 minutes)

Objective: Deepen ratio understanding by finding missing values in ratio tables.

• Explain the task: Around the room, 10–12 paper “Ratio Table” cards are posted at different spots, each containing a two-column ratio table with a missing value.
• Students will move freely around the room in pairs to find a card, work together to solve for the missing value, then record their answer on a provided answer sheet.
• Each ratio table correlates to real-world scenarios (e.g., cups of juice to glasses, miles to hours).
• Example card:
  | Cups of Juice | Glasses |
  | 3 | ? |
  | 6 | 4 |
• They identify the pattern and solve for the missing value.
• Once solved, they walk to find the next card, trying to solve as many as time allows.
• Circulate to support struggling pairs and encourage explanation of reasoning aloud between partners.

3. Activity 2: Tape Diagram Matching (15 minutes)

Objective: Connect word problems and visual models.

• Distribute sets of matching cards: one card describes a ratio word problem; the other shows various tape diagrams.
• In pairs, students read the word problem and discuss which tape diagram best models it, then physically match the cards.
• Examples include scenarios like "The recipe calls for 4 parts flour to 1 part sugar" or "There are 5 goldfish for every 3 guppies in a fish tank."
• After matching, pairs explain their reasoning to another pair or to the teacher.
• Teacher clarifies any misconceptions and reinforces tape diagram features.

4. Wrap-Up & Exit Ticket (8 minutes)

Objective: Check individual understanding of equivalent ratios and ratio tables.

• Present a new ratio verbally— for example, 2:5 (sharks to dolphins).
• Instruct students to create an equivalent ratio table with at least three pairs (showing multiplication or division to scale the ratio).
• Example table structure:

  Sharks	Dolphins
  2	5
  4	10
  6	15

• Collect exit tickets as students leave.

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Differentiation and Extensions

• For students who need support: Partner with a peer for activities, use color-coded tape diagrams, or provide step-by-step ratio table templates.
• Extension: Challenge advanced students to create their own ratio word problems and corresponding ratio tables/tape diagrams for classmates to solve.
• Use a digital tool (if available) to have students create tape diagrams or ratio tables interactively.

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Assessment

• Informal assessment through observation during activities and class discussions.
• Accuracy and completeness of answers in the scavenger hunt recorded on answer sheets.
• Quality of explanations during matching activity.
• Exit ticket serves as a formal formative assessment of individual understanding of equivalent ratios.

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Teacher Reflection Questions

• Did the tape diagram visuals help all students grasp ratio relationships?
• How effectively did the scavenger hunt engage active learning and movement?
• Were students able to make connections between word problems and their visual models meaningfully?
• Did the exit ticket reveal any common misconceptions to address in future lessons?

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This lesson leverages visual models, kinesthetic learning, peer collaboration, and real-world contexts — all while tightly aligned to Common Core standards — to deepen 6th graders’ conceptual understanding of ratios using tape diagrams and ratio tables.