You will learn
- Compare two sets of numbers.
- Find which set is bigger.
- Find the difference between two totals.
- Explain a comparison in a sentence.
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
- Compare two sets of numbers.
- Find which set is bigger.
- Subtract to find the difference.
- Say the comparison in a sentence.
Words to know
Say how things are alike and different.
A group of data.
How much more or less.
Bigger.
1. Discover: two classes
Class 3A read 40 books and class 3B read 35. Which class read more? By how many?
2. Understand: comparing data
To compare two sets of data, find each total and then the difference.
- 3A: 40 books. 3B: 35 books. 3A is greater. 40 − 35 = 5 more.
- Shop A sold 30 loaves on Monday and shop B sold 45. 45 − 30 = 15 more at shop B.
Write a full sentence: “Shop B sold 15 more loaves than shop A.”
Idea 1: Difference
50 and 38 differ by 50 − 38 = 12. 42 and 42 differ by 0.
Idea 2: Which is greater
Shop A sold 25 and shop B sold 60. Shop B sold more, by 60 − 25 = 35.
Idea 3: Totals
Class A has 18 and class B has 22. Together there are 40.
Why a sentence? A sentence tells what the numbers mean.
3. Worked examples
Example 1 (I show you): Difference
50 and 38.
- 50 − 38.
Answer: 12
Example 2 (We do it together): More
Shop A 25, shop B 60. How many more at B?
- 60 − 25.
Answer: 35
Example 3 (You try): Total
Class A 18, class B 22.
Show the steps and answer
- 18 + 22.
Answer: 40
Did you know?
The difference of two equal numbers is zero.
Why this matters
Comparing data helps us make fair choices.
4. Explore: compare two groups
You need two small tables of numbers.
- Write the total for each class.
- Say which is greater.
- Subtract to find the difference.
- Write a full sentence.
Think about it: what did you notice?
The sentence names who has more and by how many.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ is greater than ___.
- The difference is ___.
- Together there are ___.
- ___ has ___ more than ___.
Guided practice
Question 1. 3A 40, 3B 35. Which is greater?
3A.
Question 2. By how many?
5.
Question 3. Shop A 30, shop B 45. Difference?
15.
Independent practice
Level 1: Start
- 50 and 38: difference
- 42 and 42: difference
- Which is greater: 67 or 76?
- Shop A 25, shop B 60: how many more at B?
- Class A 18, class B 22: total
Level 2: Grow
- 80 and 65: difference
- Which is greater: 91 or 19?
- Shop A 40, shop B 75: how many more at B?
Level 3: Stretch
- 120 and 85: difference
- Class A 36 and class B 29 together
- Ben says 56 and 48 differ by 104. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Team X scored 56 points and team Y scored 48. How many more did X score?
Show a sample answer
8 more.
Another one. Write a sentence comparing class A with 28 pupils and class B with 34 pupils.
Show a sample answer
Class B has 6 more pupils than class A.
7. Common mistakes
Fix: Subtract to find the difference.
Fix: Subtract to find the difference.
Fix: Compare the same kind of data.
8. Lesson summary and revision card
- I can compare two sets of numbers.
- I can find which set is bigger.
- I can find the difference.
- I can explain a comparison in a sentence.
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
- Compare totals.
- Subtract to find the difference.
- Write a sentence.
11. Next lesson
Next lesson: Drawing conclusions. 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.
- Find the difference between 50 and 38. [2 marks]
- Shop A sold 25 and shop B sold 60. How many more did B sell? [2 marks]
- Class A has 18 and class B has 22. How many together? [2 marks]
- Which is greater: 67 or 76? [1 mark]
- Ana says the difference between 42 and 42 is 84. Is she right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 50 − 38 [1] = 12 [1]
- 60 − 25 [1] = 35 [1]
- 18 + 22 [1] = 40 [1]
- 76 [1]
- No [1]. They are equal [1]. The difference is 0 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 50 and 38: difference
- 42 and 42: difference
- Greater: 67 or 76
- Shop A 25, shop B 60: how many more at B
- Class A 18 and class B 22: total
- 50 and 38 differ by ___.
- 42 and 42 differ by ___.
- Class A 18 and class B 22 together: ___
- Team X 56, team Y 48: X scored ___ more.
- Shop A 30, shop B 45. Which sold more?
Homework
Compare the number of pupils in two classes you know. Write a sentence.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 50 and 38: difference | 12 | 2 |
| 42 and 42: difference | 0 | 2 |
| Greater: 67 or 76 | 76 | 2 |
| Shop A 25, shop B 60: how many more at B | 35 | 2 |
| Class A 18 and class B 22: total | 40 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 12; 2 0; 3 76; 4 35; 5 40.
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 12; 7 0; 8 40; 9 8; 10 shop B.
Independent practice answers. Level 1: 1 12; 2 0; 3 76; 4 35 more; 5 40. Level 2: 1 15; 2 91; 3 35. Level 3: 1 35; 2 65; 3 He added. The difference is 56 − 48 = 8..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare two sets of numbers | 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 which set is bigger | 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 difference between two totals | 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 Explain a comparison in a sentence | 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: Adding instead of subtracting to compare. Subtract to find the difference.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise 2-digit subtraction with number lines.
- 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 compares two sets of data and explains the difference. You do not need to be good at mathematics to help.
- Compare scores or heights in your family.
- Ask: who has more? by how much?
- Use real numbers.
- 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: compare two sets of numbers; find which set is bigger; find the difference between two totals; explain a comparison in a sentence.
Prerequisite knowledge. Lessons 2 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 two small tables of numbers. 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. Which is greater? What is the difference? What is the 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. Adding instead of subtracting to compare. Subtract to find the difference.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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 2-digit subtraction with number lines. 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 3.MD.B.3 and 2.MD.D.10; Cambridge Primary Mathematics Stage 3 (comparing data). These sources informed the lesson; no official alignment is claimed.