Mode 4A

Overview

In this Phlow, learners explore the concept of mode — the most common number in a data set — using a simple, visual grid. The activity presents 30 numbers (1–4) arranged in a grid format. Students count how often each number appears, record this in a frequency table, and then identify which value occurs most frequently.

The process unfolds gradually to strengthen understanding:

Count how many 1s appear → record in the first table cell.
Repeat for 2s, 3s, and 4s.
Compare the frequencies to identify which number occurs most often.

This structured, step-by-step design supports learners in connecting raw visual data with numerical representation. It bridges early counting skills with statistical reasoning — preparing students for interpreting larger data sets, charts, and frequency tables.

Worked Example

Example grid: 30 numbers between 1 and 4

      Step 1: Count each number.
        1 → 7 times
        2 → 10 times
        3 → 6 times
        4 → 7 times

      Step 2: Complete the frequency table.

      Step 3: Identify the number with the highest frequency → 2
      Mode = 2

Sample Prompts

How many 3s can you find in the grid?
Which number appears most often?
What does “mode” mean in this context?
How does the table help you see the answer more clearly?

Why This Matters

Understanding the mode develops students’ ability to organise, summarise, and describe data — skills essential in data handling and real-life problem solving. This Phlow lays a practical foundation for working with surveys, results, and experiments where data frequency matters.

Step 1 / 5

Prerequisite Knowledge Required

Counting accuracy and comparing small whole numbers.
Understanding that “most common” means appearing most often.
Familiarity with reading and interpreting simple grids or tables.

Linked Phlows:
Data 3A – Reading Simple Tables, Mode 3B – Finding Mode from Lists, Modal 4 – Identifying Mode from Graphs.

Main Category

Statistics → Representing and Interpreting Data

Estimated Completion Time

Approx. 10–14 seconds per question.
40 questions total → Total time: 7–10 minutes.

Learner Profile	Estimated Time	Description
One Level Below	9–10 mins	May double-count or lose track while scanning. Benefits from finger-tracking or tally marks.
At Level	7–8 mins	Counts efficiently and recognises frequency patterns across rows and columns.
One Level Above	5–6 mins	Quickly estimates frequencies and visualises tallies mentally.

Cognitive Load / Step Size

Low to moderate. Each screen isolates one step — counting, recording, comparing — keeping cognitive demand manageable. Visual highlighting directs focus, and repetition reinforces the relationship between counting and frequency.

Language & Literacy Demand

Low. Instructions are concise, with minimal text and repeated phrasing. Colour-coded words (e.g., “number 2,” “how many”) support understanding, while visuals carry most of the instructional weight.

Clarity & Design

Numbers are evenly spaced in a clean grid for easy scanning.
Purple highlights indicate the current number to count.
The frequency table fills progressively, linking count to data representation.
The final step compares all values visually to identify the mode.

Curriculum Alignment (ROI Junior Cycle Mathematics)

Strand: Statistics and Probability
Strand Unit: Representing and Interpreting Data
Learning Outcomes:

Organise data into frequency tables.
Identify the mode of a small data set.
Interpret and describe frequency as a measure of occurrence.
Link visual data to numerical representation.

Engagement & Motivation

High. The grid-based task feels game-like — learners enjoy the visual puzzle of spotting and counting numbers. Immediate feedback after each count sustains attention and rewards accuracy.

Error Opportunities & Misconceptions

Skipping rows or miscounting numbers.
Confusing total count (30) with individual frequencies.
Selecting the highest number rather than the most frequent one.
Incorrectly transferring data into the frequency table.

Transferability / Real-World Anchoring

Strong. Counting and frequency recognition underpin all later data-handling and survey analysis skills. Students see how frequency connects to real-world contexts — votes, surveys, results, or experiments.

Conceptual vs Procedural Balance

Balanced. The activity combines clear procedural steps with a conceptual grasp of what “most common” means. Students learn to interpret frequency rather than memorise a rule.

Learning Objectives Addressed

Count and record frequencies from visual data.
Identify the mode as the most frequent value.
Complete and interpret a frequency table.
Connect raw visual data with summarised numerical information.

What Your Score Says About You

Less than 20: You may be skipping rows or mixing up “highest” with “most frequent.” Review your scanning technique.
21–29: You understand the process but make small counting or recording errors.
31–39: You’re accurate and confident identifying frequency patterns.
40 / 40: Excellent — you can extract, summarise, and interpret frequency data quickly and correctly.