Courseversity

Lesson

Comparing datasets

Primary EducationGrade 4MathematicsCV-PRI-G04-MATH-DAT-U01-L0545–60 min

You will learn

  • Compare totals.
  • Compare highest and lowest.
  • Compare ranges.
  • Write a comparison 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

The lesson in 60 seconds

  1. Compare the totals.
  2. Compare the highest and lowest values.
  3. Compare the ranges.
  4. Write a full sentence with numbers.

Words to know

compare
Say how alike and different.
range
Greatest minus least.
total
All added.
dataset
A group of data.

1. Discover: two weeks of reading

In week 1 a class read 8, 9, 10, 9 and 9 books on five days. In week 2 they read 10, 12, 11, 9 and 10. Which week had more?

2. Understand: comparing datasets

  • Week 1 total: 8 + 9 + 10 + 9 + 9 = 45.
  • Week 2 total: 10 + 12 + 11 + 9 + 10 = 52.
  • Difference: 52 − 45 = 7.
  • Ranges: week 1 = 10 − 8 = 2; week 2 = 12 − 9 = 3.

“Week 2 had 7 more books than week 1.”

Idea 1: Totals

Week 1: 8, 9, 10, 9, 9 totals 45. Week 2: 9, 11, 12, 10, 10 totals 52. Week 2 is greater by 52 − 45 = 7.

Idea 2: Ranges

Week 1 range: 10 − 8 = 2. Week 2 range: 12 − 9 = 3.

Idea 3: Sentence

The highest day in week 2 is 12. “Week 2 had 7 more in total than week 1 and a slightly larger range.”

Why use numbers? A comparison needs evidence.

Remember: Compare totals, highest, lowest and range.

3. Worked examples

Example 1 (I show you): Total

Week 1: 8, 9, 10, 9, 9

  1. Add them.

Answer: 45

Example 2 (We do it together): Range

Week 2: 9, 11, 12, 10, 10

  1. 12 − 9.

Answer: 3

Example 3 (You try): Compare

Totals 45 and 52

Show the steps and answer
  1. 52 − 45.

Answer: Week 2 by 7

Did you know?

A larger range means the data is more spread out.

Why this matters

Comparing datasets helps us decide which is better or bigger.

4. Explore: compare

You need paper.

  1. Add each week.
  2. Subtract.
  3. Find each range.
  4. Write a sentence.
Think about it: what did you notice?

Week 2 by 7.

5. Practise

Say it in a sentence

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

  • The total of ___ is ___.
  • The range of ___ is ___.
  • ___ is greater than ___ by ___.
  • So we can say ___.

Guided practice

Question 1. Week 1 total?

45.

Question 2. Week 2 total?

52.

Question 3. Difference?

7.

Independent practice

Level 1: Start

  1. Range of week 1
  2. Range of week 2
  3. Highest day in week 2
  4. Which total is greater?
  5. 52 − 45

Level 2: Grow

  1. Totals of 4, 6, 8 and 5, 5, 9
  2. Range of 10, 14, 20
  3. Highest of 12, 18, 15

Level 3: Stretch

  1. Class X: 12, 15, 18. Class Y: 14, 15, 16. Compare the ranges.
  2. Totals of 12, 15, 18 and 14, 15, 16
  3. Ben says a larger total always means a larger range. Give an example that shows he is wrong.

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

6. Apply: everyday mathematics

Class A read 45 books, Class B read 52. How many more did B read?

Show a sample answer

7.

Another one. Write a sentence comparing the data sets 4, 6, 8 and 5, 6, 7.

Show a sample answer

Both have a total of 18, but the first is more spread out (range 4 against 2).

7. Common mistakes

Mistake: Comparing one day only.
Fix: Compare totals and ranges.
Another mistake: Comparing only one value.
Fix: Compare totals, highest and lowest, and ranges.
Another mistake: Saying “greater” without numbers.
Fix: Use the numbers in a sentence.

8. Lesson summary and revision card

I can…

  • I can compare totals.
  • I can compare highest and lowest.
  • I can compare ranges.
  • I can write a comparison sentence.

9. Check and master

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

1. Week 1 total:

2. Week 2 total:

3. The difference is…

4. Range of week 1:

5. Range of week 2:

6. Class A: 6, 8, 9, 7. Class B: 5, 10, 9, 8. Which total is greater?

7. Data A: 4, 6, 9. Data B: 5, 6, 7. Which has the greater range?

8. The ranges of two data sets are 5 and 2. The difference is…

9. Class A: 6, 8, 9, 7. Class B: 5, 10, 9, 8. Which has the higher highest value?

10. Two totals are 48 and 56. The difference is…

11. A larger range means the data is more…

12. Class A: 6, 8, 9, 7. Class B: 5, 10, 9, 8. Which sentence is true?

Challenge 1. Which week had the greater total?

Challenge 2. Week 1: 20, 22, 21. Week 2: 15, 25, 20. Which has the greater total and which the greater range?

Your result appears here after you answer every question.

10. Key takeaways

  • Totals.
  • Differences.
  • Ranges.

11. Next lesson

Next lesson: Solving data problems. 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. Week 1 sales: 8, 9, 10, 9, 9. Find the range. [2 marks]
  2. Week 2 sales: 9, 11, 12, 10, 10. Find the range. [2 marks]
  3. What was the highest day in week 2 (9, 11, 12, 10, 10)? [1 mark]
  4. Week 1 totals 45 and week 2 totals 52. Which is greater? Explain. [2 marks]
  5. Write a sentence comparing the two totals (45 and 52). [3 marks]

Total: 10 marks.

Marking guide and model answers
  1. Greatest 10 and least 8 [1]; 2 [1]
  2. 12 − 9 [1]; 3 [1]
  3. 12 [1]
  4. Compare 45 and 52 [1]; week 2 [1]
  5. Week 2 total 52 is greater than week 1 total 45 [1]; the difference is 7 [1]; a complete sentence [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

  1. Week 1 total
  2. Week 2 total
  3. Difference
  4. Range of week 1
  5. Range of week 2
  6. Week 1 (8, 9, 10, 9, 9) total:
  7. Week 2 (9, 11, 12, 10, 10) total:
  8. The difference is
  9. Range of week 1:
  10. Range of week 2:

Homework

Compare two weeks of your own data.

Answer key and marking scheme

Question Expected response Marks
Week 1 total 45 2
Week 2 total 52 2
Difference 7 2
Range of week 1 2 2
Range of week 2 3 2
Total 10

Practice answers: Worksheet: 1 45; 2 52; 3 7; 4 2; 5 3.

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 45; 7 52; 8 7; 9 2; 10 3.

Independent practice answers. Level 1: 1 2; 2 3; 3 read the tallest value for week 2; 4 week 2; 5 7. Level 2: 1 18 and 19, so the second is greater; 2 10; 3 18. Level 3: 1 X has range 6 and Y has range 2, so X is more spread out.; 2 45 and 45, so the difference is 0; 3 10, 10, 10 has total 30 and range 0. 5, 6, 7 has total 18 and range 2..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Compare 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
O2 Compare highest and lowest 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 Compare ranges 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 Write a comparison 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

  1. Find the misconception: Comparing one day only. Compare totals and ranges.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Compare two simple 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 compares two data sets using totals, highest and lowest values and ranges. You do not need to be good at mathematics to help.

  • Compare two weeks of weather or steps.
  • Ask: which total is bigger and by how much?
  • Use words like “more than” with 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 totals; compare highest and lowest; compare ranges; write a comparison sentence.

Prerequisite knowledge. Lessons 3 and 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. Which total is greater? Which range is greater?

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. Comparing one day only. Compare totals and ranges.

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. Compare two simple 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

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 6.SP.B.5 and 4.MD.B.4; Cambridge Primary Mathematics Stage 5 (comparing data). These sources informed the lesson; no official alignment is claimed.

Scroll to Top