You will learn
- Find a total from a table.
- Find a difference.
- Share equally to find an average.
- Check results.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Find a total from a table.
- Find a difference.
- Share equally to find an average.
- Check results.
Words to know
The total shared equally.
Same amount each.
All added.
How much more or less.
1. Discover: a shop week
A shop sells 24, 36, 18 and 30 loaves on four days. If the sales were the same every day, how many would that be?
2. Understand: data problems
- Total: 24 + 36 + 18 + 30 = 108.
- Tuesday minus Wednesday: 36 − 18 = 18.
- Equal share: 108 ÷ 4 = 27 loaves a day (the average).
Check: 27 × 4 = 108.
Idea 1: Total
Mon 24, Tue 36, Wed 18, Thu 30. Mon + Tue = 60. Total = 24 + 36 + 18 + 30 = 108.
Idea 2: Difference
Thu − Mon = 30 − 24 = 6. Tue − Wed = 36 − 18 = 18.
Idea 3: Average
The average is 108 ÷ 4 = 27 a day. Check: 27 × 4 = 108.
Why divide by the number of days? The average is an equal share of the total.
3. Worked examples
Example 1 (I show you): Add
Mon 24 + Tue 36
- 24 + 36.
Answer: 60
Example 2 (We do it together): Average
Total 108 over 4 days
- 108 ÷ 4.
Answer: 27
Example 3 (You try): Check
27 × 4
Show the steps and answer
- Multiply back.
Answer: 108
Did you know?
An average is what each would get if the total were shared equally.
Why this matters
Averages summarise data with one number.
4. Explore: solve
You need paper.
- Add the sales.
- Find a difference.
- Divide by 4.
- Check by multiplying.
Think about it: what did you notice?
27.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The total is ___.
- The difference is ___.
- I divide ___ by ___ to get ___.
- I check by multiplying ___ × ___.
Guided practice
Question 1. Total sales?
108.
Question 2. Tuesday minus Wednesday?
18.
Question 3. Average per day?
27.
Independent practice
Level 1: Start
- Monday + Tuesday
- Thursday − Monday
- Total of 24, 36, 18, 30
- 108 ÷ 4
- 27 × 4
Level 2: Grow
- Total of 15, 25, 35, 25
- Average of 15, 25, 35, 25
- 50 − 32
Level 3: Stretch
- Average of 12, 15, 21
- The average of 5 numbers is 30. What is their total?
- Ben says the average of 10, 20 and 30 is 60. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Total 108 loaves in 4 days. What is the average a day?
Show a sample answer
27.
Another one. A bakery sells 24, 36, 18 and 30 loaves over four days. What is the average each day?
Show a sample answer
108 ÷ 4 = 27 loaves
7. Common mistakes
Fix: Divide by the number of days.
Fix: Divide the total by the number of values.
Fix: Divide by how many values there are.
8. Lesson summary and revision card
- I can find a total from a table.
- I can find a difference.
- I can find an average.
- I can check results.
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
- Add for totals.
- Divide for averages.
- Check by multiplying.
11. Next lesson
You have finished Grade 4 Mathematics. Well done!
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.
- Mon 24, Tue 36, Wed 18, Thu 30. Find Monday + Tuesday. [2 marks]
- Find Thursday − Monday. [2 marks]
- Find the total for the four days. [2 marks]
- Find the average for the four days. [3 marks]
- Ben says the average is 108 ÷ 3 = 36. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 24 + 36 [1]; 60 [1]
- 30 − 24 [1]; 6 [1]
- 24 + 36 + 18 + 30 [1]; 108 [1]
- Total 108 [1]; divide by 4 [1]; 27 [1]
- No [1]. There are 4 days, so divide by 4 [1]. The average is 27 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Monday + Tuesday
- Thursday − Monday
- Total of 24, 36, 18, 30
- 108 ÷ 4
- 27 × 4
- Mon 24, Tue 36, Wed 18, Thu 30. The total is
- Tuesday minus Wednesday:
- The average a day:
- Monday + Tuesday:
- Thursday minus Monday:
Homework
Collect a week of data and find the average per day.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Monday + Tuesday | 60 | 2 |
| Thursday − Monday | 6 | 2 |
| Total of 24, 36, 18, 30 | 108 | 2 |
| 108 ÷ 4 | 27 | 2 |
| 27 × 4 | 108 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 60; 2 6; 3 108; 4 27; 5 108.
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): 6 108; 7 18; 8 27; 9 60; 10 6.
Independent practice answers. Level 1: 1 60; 2 6; 3 108; 4 27; 5 108. Level 2: 1 100; 2 25; 3 18. Level 3: 1 16; 2 150; 3 60 is the total. Divide by 3: 60 ÷ 3 = 20..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find a total 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 |
| O2 Find a difference | 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 Share equally to find an average | 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 Check results | 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Dividing by 3 instead of 4. Divide by the number of days.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise dividing by 4.
- 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 solves problems with totals, differences and averages. You do not need to be good at mathematics to help.
- Find your family average steps or screen time.
- Ask: what is the total? how many days?
- Check by multiplying.
- 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 a total from a table; find a difference; share equally to find an average; check results.
Prerequisite knowledge. Lessons 1 to 5.
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 is the total? How many values? What is each share?
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. Dividing by 3 instead of 4. Divide by the number of days.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Practise dividing by 4. 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.MD.B.4 and 6.SP.A.3; Cambridge Primary Mathematics Stage 5 (averages and data problems). These sources informed the lesson; no official alignment is claimed.