Courseversity

Mode

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-DAT-U01-L0945–60 min

You will learn

  • Find the mode.
  • Find data with two modes.
  • Find data with no mode.
  • Choose when to use mode.

Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.

Student lesson

The lesson in 60 seconds

  1. The mode is the most frequent value.
  2. A data set can have two modes or none.
  3. The mode works for categories too.
  4. Use the mode for the most common choice.

Words to know

mode
Most frequent.
bimodal
Two modes.
no mode
All values once.
category
Non-numerical group.

1. Discover: popular shoe size

A shoe shop wants to order the most popular size. Which measure helps?

2. Understand: mode

  • Mode of 2, 3, 3, 5 is 3.
  • 1, 1, 2, 2, 3 has two modes: 1 and 2.
  • 1, 2, 3, 4 has no mode.
  • The mode works for categories: favourite colour.

Idea 1: One mode

Mode of 2, 3, 3, 5: 3 appears twice, so 3. Mode of red, blue, red, green is red.

Idea 2: Two or none

1, 1, 2, 2, 3 has two modes: 1 and 2. 1, 2, 3, 4 has no mode.

Idea 3: Use

For shoe orders, the best measure is the mode.

Why mode? A shop needs the most common size, not an average size.

Remember: The value that appears most.

3. Worked examples

Example 1 (I show you): Mode

2, 3, 3, 5

  1. 3 appears twice.

Answer: 3

Example 2 (We do it together): Two modes

1, 1, 2, 2, 3

  1. 1 and 2 both twice.

Answer: 1 and 2

Example 3 (You try): None

1, 2, 3, 4

Show the steps and answer
  1. All once.

Answer: no mode

Did you know?

The mode is the only average that works for words and categories.

Why this matters

The mode answers “what is most common?”

4. Explore: mode

You need paper.

  1. Count each value.
  2. Find the most.
  3. Check ties.
  4. State the mode.
Think about it: what did you notice?

3.

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

  • ___ appears ___ times.
  • The mode is ___.
  • There are two modes: ___ and ___.
  • There is no mode because ___.

Guided practice

Question 1. Mode of 2, 3, 3, 5?

3.

Question 2. Modes of 1, 1, 2, 2, 3?

1 and 2.

Question 3. Mode of 1, 2, 3, 4?

none.

Independent practice

Level 1: Start

  1. Mode of 2, 3, 3, 5
  2. Mode of 1, 1, 2, 2, 3
  3. Mode of 1, 2, 3, 4
  4. Mode of red, blue, red, green
  5. Best measure for shoe orders

Level 2: Grow

  1. Mode of 4, 5, 5, 6, 7
  2. Mode of 5, 6, 7, 8
  3. Mode of cat, dog, dog, cat, dog

Level 3: Stretch

  1. Mode of 3, 3, 4, 4, 5, 5
  2. Mode of 9, 9, 9, 3, 4
  3. Ben says the mean is better than the mode for shoe orders. What is wrong?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

A shop sells sizes 2,3,3,5. Which size should it stock most?

Show a sample answer

3.

Another one. A shop sells T-shirts in sizes S, M, L. Which measure tells which size to order most?

Show a sample answer

The mode

7. Common mistakes

Mistake: Giving the frequency as the mode.
Fix: Give the value.
Another mistake: Thinking every data set has one mode.
Fix: There can be two or none.
Another mistake: Using the mean for categories.
Fix: Categories have no mean.

8. Lesson summary and revision card

I can…

  • I can find the mode.
  • I can find data with two modes.
  • I can find data with no mode.
  • I can choose when to use the mode.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. Mode of 2, 3, 3, 5:

2. Mode of 1, 1, 2, 2, 3:

3. Mode of 1, 2, 3, 4:

4. Mode of red, blue, red, green:

5. Best measure for shoe orders:

6. Mode of 4, 5, 5, 6, 7

7. Mode of 2, 2, 3, 3, 4

8. Mode of 5, 6, 7, 8

9. Mode of cat, dog, dog, cat, dog

10. Mode of 9, 9, 9, 3, 4

11. The best measure for the most common T-shirt size to order

12. A data set with no repeated value has

Challenge 1. Two values tie for most frequent:

Challenge 2. Mode of 3, 3, 4, 4, 5, 5

Your result appears here after you answer every question.

10. Key takeaways

  • Mode is most frequent.
  • May have two or none.
  • Works for categories.

11. Next lesson

Next lesson: Range. Keep going with the next idea in this course.

Exam practice

These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.

  1. Find the mode of 2, 3, 3, 5. [2 marks]
  2. Find the mode of 1, 1, 2, 2, 3. [2 marks]
  3. Find the mode of 1, 2, 3, 4. [2 marks]
  4. Find the mode of red, blue, red, green. [2 marks]
  5. Ali says the mean is better than the mode for ordering shoes. Is he right? Explain. [3 marks]

Total: 11 marks.

Marking guide and model answers
  1. 3 appears twice [1]; 3 [1]
  2. 1 and 2 both appear twice [1]; two modes: 1 and 2 [1]
  3. Every value appears once [1]; no mode [1]
  4. Red appears twice [1]; red [1]
  5. No [1]. Shoe orders need the most common size [1]. The mean may be a size nobody wears, so use the mode [1].

Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.

Printable worksheet

  1. Mode of 2,3,3,5
  2. Mode of 1,1,2,2,3
  3. Mode of 1,2,3,4
  4. Mode of red, blue, red, green
  5. Best for shoe orders
  6. Mode of 2, 3, 3, 5
  7. Mode of 1, 1, 2, 2, 3
  8. Mode of 1, 2, 3, 4
  9. Mode of red, blue, red, green
  10. Best measure for shoe orders

Homework

Find the mode of the vowels in your name.

Answer key and marking scheme

Question Expected response Marks
Mode of 2,3,3,5 3 2
Mode of 1,1,2,2,3 1 and 2 2
Mode of 1,2,3,4 none 2
Mode of red, blue, red, green red 2
Best for shoe orders mode 2
Total 10

Practice answers: Worksheet: 1 3; 2 1 and 2; 3 none; 4 red; 5 mode.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.

Extra worksheet answers (items 6 onward): 6 3; 7 1 and 2; 8 none; 9 red; 10 mode.

Independent practice answers. Level 1: 1 3; 2 1 and 2; 3 none; 4 red; 5 mode. Level 2: 1 5; 2 none; 3 dog. Level 3: 1 3, 4 and 5; 2 9; 3 Shops need the most common size: the mode..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Find the mode Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O2 Find data with two modes Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O3 Find data with no mode Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O4 Choose when to use mode Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation

Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.

If a learner struggles

  1. Find the misconception: Giving the frequency as the mode. Give the value.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Frequency tables.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child finds the mode, including ties and no mode. You do not need to be good at mathematics to help.

  • Find the most common colour in a bag of sweets.
  • Ask: what appears most?
  • Notice ties.
  • Ask “how do you know?” after each answer, and listen.
  • Praise effort, not only right answers. Mistakes are how we learn.
  • Ten to fifteen minutes a day is better than one long session.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: find the mode; find data with two modes; find data with no mode; choose when to use mode.

Prerequisite knowledge. Lesson 4.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 45–60 minutes. It can be split into two shorter sessions.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Key questions. What appears most? Is there a tie?

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Giving the frequency as the mode. Give the value.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 11-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Frequency tables. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.

Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 6 » Statistics & Probability. These pages list the standards that cover this topic area; read them alongside the lesson.

Research used to shape this lesson. Common Core 6.SP.A.3 (centre); Cambridge Primary Mathematics Stage 6 (mode). These sources informed the lesson.

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