Construct and use back to back stem and leaf diagrams

• Maths
• Upper Secondary (Key Stage 4)
• Lower Secondary (Key Stage 3)
• GCSE

Construct and use back to back stem and leaf diagrams

Today’s Learning Goals

Title: Constructing and Using Back-to-Back Stem-and-Leaf Diagrams

Learning Goals:

“Understand how to construct a back-to-back stem-and-leaf diagram.”

“Use the diagram to effectively compare two data sets.”

Get Started

Purpose: Engage students with a warm-up or review activity.

Slide Heading: “Get Started” or “Kick-Off Activity”

Example: Display a quick review question on data representation

Key Concepts

Purpose: Introduce new vocabulary and core concepts for the lesson.

Slide Heading: “Key Concepts” or “What You Need to Know”

Example: Define terms like “stem,” “leaf,” and “back-to-back comparison.”

To Know

Key Concepts:

Stem: The common “backbone” of the diagram, where the middle digits are placed.

Leaf: The individual values for each data set, listed on opposite sides of the stem.

Visual Example: Show a sample back-to-back stem-and-leaf diagram to illustrate the format.

Teacher Demonstration (I Do)

Modeling:

Demonstrate the construction of a back-to-back stem-and-leaf diagram step-by-step.

Explain each step: identifying the stem, placing leaves in ascending order, and organizing each data set on separate sides of the stem.

Example: Use a data set (e.g., ages) to build the diagram in real-time.

Checking for Understanding (CFU)

Quick Check:

Show a partially completed back-to-back stem-and-leaf diagram with intentional errors.

Ask students to identify and correct the mistakes (e.g., leaves out of order, incorrect stems).

Method: Use mini whiteboards or quick questions to assess if students understand the construction process.

Guided Practice (We Do)

Activity: Lead the class in constructing a back-to-back stem-and-leaf diagram with new data.

Prompt: “Arrange each data set on either side of the stem and ensure leaves are in ascending order.”

Discussion: “What patterns do you notice? How does this representation help with comparing the two groups?”

Independent Practice (You Do)

Task: Students create their own back-to-back stem-and-leaf diagram with two new data sets (e.g., scores from two teams).

Instructions: “Arrange the leaves in ascending order for each side. Label each data set clearly.”

Monitoring: Walk around to provide feedback and support as needed.

Exit Ticket

Questions:

“What does each side of a back-to-back stem-and-leaf diagram represent?”

“How do you make sure data is correctly ordered?”

“How can this type of diagram help in data comparison?”

Purpose: Assess understanding and confirm that students achieved the learning goals.

Retrieval of Knowledge

Review: Summarize the steps in constructing a back-to-back stem-and-leaf diagram.

Questions: “Why is the order of leaves important? What does the stem represent?”

Activity: Have students explain how they would use this type of diagram in a different context.

Stamp It

Key Takeaway:

“Back-to-back stem-and-leaf diagrams make it easy to compare two data sets by aligning them around a shared stem.”

Wrap-Up Activity: Ask students to write one sentence summarizing how this diagram helps in data comparison.