You will learn
- Build a frequency table.
- Find cumulative frequency.
- Find the mode.
- Answer questions from a table.
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
- A frequency table counts how often each value appears.
- Cumulative frequency is a running total.
- The mode has the highest frequency.
- The last cumulative value equals the total.
Words to know
How many times.
Running total.
Most frequent.
Organised data.
1. Discover: shoe sizes
Seven pupils have shoe sizes 2, 3, 3, 4, 4, 4, 5. How can a table show this?
2. Understand: frequency tables
| Size | Frequency | Cumulative |
|---|---|---|
| 2 | 1 | 1 |
| 3 | 2 | 3 |
| 4 | 3 | 6 |
| 5 | 1 | 7 |
- Total pupils: 7. Mode: 4.
- Pupils with size 3 or less: cumulative 3.
Idea 1: Table
Sizes 2, 3, 3, 4, 4, 4, 5. Frequencies: size 2 → 1, size 3 → 2, size 4 → 3, size 5 → 1.
Idea 2: Cumulative
Running totals: 1, 3, 6, 7. Total pupils 7. Pupils with size 4 or less: 6. Mode: 4.
Idea 3: Largest
The largest size is 5.
Why cumulative? It answers “how many up to here?” quickly.
3. Worked examples
Example 1 (I show you): Frequency
Size 3 in 2, 3, 3, 4, 4, 4, 5
- Count the 3s.
Answer: 2
Example 2 (We do it together): Cumulative
Size 4 or less
- 1 + 2 + 3.
Answer: 6
Example 3 (You try): Mode
Highest frequency
Show the steps and answer
- Size 4 appears 3 times.
Answer: 4
Did you know?
The mode is the value with the highest frequency.
Why this matters
Frequency tables turn long lists into clear summaries.
4. Explore: table
You need paper.
- List values.
- Tally.
- Add a cumulative column.
- Check last cumulative.
Think about it: what did you notice?
7.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The frequency of ___ is ___.
- The mode is ___ because ___.
- Cumulative at ___ is ___.
- The last cumulative equals the ___.
Guided practice
Question 1. Frequency of 4?
3.
Question 2. Total?
7.
Question 3. Cumulative at 3?
3.
Independent practice
Level 1: Start
- Frequency of size 3
- Mode
- Total pupils
- Pupils with size 4 or less
- Largest size
Level 2: Grow
- Books read by 9 pupils: 1, 2, 2, 3, 3, 3, 3, 4, 5. Frequency of 3
- Same data: mode
- Same data: total pupils
Level 3: Stretch
- Same data: pupils who read 2 or fewer
- Same data: pupils who read more than 3
- Ben says the cumulative at size 4 is 3. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Seven pupils: sizes 2,3,3,4,4,4,5. How many wear size 4 or less?
Show a sample answer
6.
Another one. Make a frequency table for 10 numbers you choose. Check the last cumulative equals 10.
Show a sample answer
The last cumulative is 10
7. Common mistakes
Fix: Last cumulative = total.
Fix: Cumulative is a running total.
Fix: Last cumulative equals the total.
8. Lesson summary and revision card
- I can build a frequency table.
- I can find cumulative frequency.
- I can find the mode.
- I can answer questions from a table.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Frequency counts.
- Cumulative is a running total.
- Check against total.
11. Next lesson
Next lesson: Dot plots. 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.
- Seven pupils have shoe sizes 2, 3, 3, 4, 4, 4, 5. Find the frequency of size 3. [2 marks]
- Same data. Find the mode. [2 marks]
- Same data. How many pupils in total? [2 marks]
- Same data. How many pupils wear size 4 or less? [2 marks]
- Ali says 3 pupils wear size 4 or less because the frequency of size 4 is 3. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Count the 3s [1]; 2 [1]
- The most frequent size [1]; 4 [1]
- 1 + 2 + 3 + 1 [1]; 7 [1]
- Add frequencies for 2, 3 and 4: 1 + 2 + 3 [1]; 6 [1]
- No [1]. 3 is the frequency of size 4 only [1]. Cumulative adds the running total: 6 [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
- Frequency of 3
- Mode
- Total pupils
- Size 4 or less
- Largest size
- Frequency of 3 (sizes 2, 3, 3, 4, 4, 4, 5)
- Mode
- Total pupils
- Size 4 or less
- Largest size
Homework
Make a frequency table of ten values.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Frequency of 3 | 2 | 2 |
| Mode | 4 | 2 |
| Total pupils | 7 | 2 |
| Size 4 or less | 6 | 2 |
| Largest size | 5 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2; 2 4; 3 7; 4 6; 5 5.
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 2; 7 4; 8 7; 9 6; 10 5.
Independent practice answers. Level 1: 1 2; 2 4; 3 7; 4 6; 5 5. Level 2: 1 4; 2 3; 3 9. Level 3: 1 3; 2 2; 3 3 is the frequency of 4. Cumulative adds: 1 + 2 + 3 = 6..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Build a frequency table | 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 cumulative frequency | 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 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 |
| O4 Answer questions from a table | 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
- Find the misconception: Cumulative not ending at the total. Last cumulative = total.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Tally.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child builds frequency tables. You do not need to be good at mathematics to help.
- Make a table for the shoe sizes in your family.
- Ask: how many times does each appear?
- Check the total.
- 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: build a frequency table; find cumulative frequency; find the mode; answer questions from a table.
Prerequisite knowledge. Lesson 3.
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. How many times? What is the running total?
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. Cumulative not ending at the total. Last cumulative = total.
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. Tally. 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.B.5; Cambridge Primary Mathematics Stage 6 (frequency tables). These sources informed the lesson.