Courseversity

Lesson

Ordering numbers

Primary EducationGrade 1MathematicsCV-PRI-G01-MATH-NUM-U02-L0645–60 min

You will learn

  • Order numbers from smallest to greatest.
  • Order numbers from greatest to smallest.
  • Use tens and ones to order.
  • Find the number between two numbers.

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. Compare the tens first, then the ones.
  2. Smallest to greatest goes up. Greatest to smallest goes down.
  3. Ascending means smallest first. Descending means greatest first.
  4. A number between two others lies in the middle.

Words to know

order
Put in a rule.
ascending
From smallest to greatest.
descending
From greatest to smallest.
between
In the middle of two numbers.

1. Discover: a race

Four runners wear numbers 34, 12, 56 and 23. The race officials call them in order from the smallest number. Who goes first?

2. Understand: ordering numbers

To order numbers, compare them using tens and ones. For 34, 12, 56, 23: tens are 3, 1, 5, 2. Smallest is 12, then 23, then 34, then 56.

From smallest to greatest: 12, 23, 34, 56. From greatest to smallest: 56, 34, 23, 12.

A number between 23 and 34 could be 30.

Idea 1: Order using the tens

Order 52, 15 and 38. Look at the tens: 5, 1 and 3. The smallest tens is 1, so 15 is smallest. Then 3 tens is 38. Then 5 tens is 52.

Order from smallest: 15, 38, 52.

Idea 2: When the tens are equal

Order 72, 27, 70 and 17. 17 has 1 ten, 27 has 2 tens. 70 and 72 both have 7 tens, so look at the ones: 0 is less than 2.

Order from smallest: 17, 27, 70, 72.

Idea 3: A number between

A number between 40 and 50 comes after 40 and before 50. For example 43 or 47.

Remember: Order by tens first, then ones. Smallest to greatest goes up; greatest to smallest goes down.

3. Worked examples

Example 1 (I show you): Order 52, 15, 38

Put 52, 15 and 38 in order from smallest.

  1. The tens are 5, 1 and 3.
  2. The smallest tens is 1: that is 15.
  3. Next is 3 tens: 38.
  4. Last is 5 tens: 52.

Answer: 15, 38, 52

Example 2 (We do it together): Order 44, 71, 63

Put 44, 71 and 63 in order from greatest.

  1. The tens are 4, 7 and 6.
  2. The greatest tens is 7: that is 71.
  3. Next is 6 tens: 63.
  4. Last is 4 tens: 44.

Answer: 71, 63, 44

Example 3 (You try): Between 20 and 30

Name a number between 20 and 30.

Show the steps and answer
  1. It must come after 20.
  2. It must come before 30.
  3. Try 25.

Answer: 25 works. Any number from 21 to 29 is correct.

Did you know?

Dictionaries put words in order, from A to Z. Numbers also have an order, and we use tens and ones to find it.

Why this matters

Ordering helps us find a house number, rank scores and sort prices.

4. Explore: number cards

Write 6 numbers on cards: 45, 12, 78, 33, 60, 21.

  1. Mix the cards.
  2. Put them in order, smallest first.
  3. Say each number as you place it.
  4. Now order from greatest first.
Think about it: what did you notice?

Smallest first: 12, 21, 33, 45, 60, 78.

5. Practise

Say it in a sentence

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

  • Smallest to greatest: ___, ___, ___.
  • Greatest to smallest: ___, ___, ___.
  • ___ is between ___ and ___.
  • I looked at the tens first because ___.

Guided practice

Question 1. Order 25, 14, 31.

14, 25, 31.

Question 2. Greatest of 40, 29, 36?

40.

Question 3. A number between 20 and 30?

25 (any from 21 to 29).

Independent practice

Level 1: Start

  1. Order from smallest: 52, 15, 38.
  2. Order from greatest: 44, 71, 63.
  3. Which is smallest: 90, 19, 55?
  4. Write a number between 40 and 50.
  5. Explain how you ordered 52, 15, 38.

Level 2: Grow

  1. Order from smallest: 63, 36, 45.
  2. Order from greatest: 21, 12, 30.
  3. Write a number between 60 and 70.

Level 3: Stretch

  1. Order from smallest: 54, 45, 50, 40.
  2. What numbers are between 28 and 33?
  3. Ana ordered 31, 13, 33 as 13, 33, 31. What mistake did she make?

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

6. Apply: everyday mathematics

Seats are numbered 27, 8, 15. Put them in order.

Show a sample answer

8, 15, 27.

Another one. Four runners score 56, 65, 49 and 60 points. The highest score wins. Order the scores from greatest. Who wins?

Show a sample answer

65, 60, 56, 49. The runner with 65 wins.

7. Common mistakes

Mistake: Putting 9 after 15 because it looks like a bigger digit.
Fix: 9 has only ones, so it is less than 15. Compare tens first.
Another mistake: Comparing the ones first.
Fix: Look at the tens first. Only compare the ones if the tens are equal.
Another mistake: Mixing up smallest and greatest.
Fix: Smallest is the least. Greatest is the most. Say it out loud.

8. Lesson summary and revision card

I can…

  • I can order numbers from smallest to greatest.
  • I can order numbers from greatest to smallest.
  • I can use tens and ones to order.
  • I can find a number between two numbers.

9. Check and master

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

1. Which is in order from smallest to greatest?

2. Which is the greatest: 40, 29, 36?

3. Which is the smallest: 90, 19, 55?

4. Which list is greatest to smallest?

5. Which number is between 20 and 30?

6. Which list is in order from smallest to greatest?

7. Which is the greatest: 38, 83 or 33?

8. Which is the smallest: 71, 17 or 47?

9. Which list is in order from greatest to smallest?

10. Which number is between 40 and 45?

11. Order 31, 13 and 33 from smallest to greatest.

12. Which number comes just after 59?

Challenge 1. Order 72, 27, 70, 17 from smallest to greatest.

Challenge 2. Order 64, 46, 60 and 40 from greatest to smallest.

Your result appears here after you answer every question.

10. Key takeaways

  • Order by tens first, then ones.
  • Smallest to greatest and greatest to smallest.
  • Find numbers between two numbers.

11. Next lesson

Next lesson: Circles. 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. Order from smallest: 52, 15, 38. [2 marks]
  2. Order from greatest: 44, 71, 63. [2 marks]
  3. Write a number between 40 and 50. [1 mark]
  4. Which is the smallest: 90, 19 or 55? Explain. [2 marks]
  5. Order from smallest: 72, 27, 70, 17. [2 marks]

Total: 9 marks.

Marking guide and model answers
  1. 15, 38, 52 [2]. Give 1 mark if one number is out of place.
  2. 71, 63, 44 [2]. Give 1 mark if one number is out of place.
  3. Any number from 41 to 49 [1]
  4. 19 [1]; it has only 1 ten [1]
  5. 17, 27, 70, 72 [2]. Give 1 mark if one number is out of place.

Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.

Printable worksheet

  1. Order from smallest: 34, 12, 56.
  2. Order from greatest: 21, 45, 33.
  3. Smallest of 60, 16, 41?
  4. Greatest of 88, 78, 98?
  5. A number between 50 and 60?
  6. Order from smallest: 23, 32, 22.
  7. Which is the greatest: 45, 54 or 50?
  8. What number is between 19 and 21?
  9. Order from greatest: 15, 51, 11.
  10. Write a number between 70 and 75.

Homework

Choose 5 two-digit numbers. Write them in order from smallest to greatest, then greatest to smallest. Show a family member.

Answer key and marking scheme

Question Expected response Marks
Order from smallest: 34, 12, 56. 12, 34, 56 2
Order from greatest: 21, 45, 33. 45, 33, 21 2
Smallest of 60, 16, 41? 16 2
Greatest of 88, 78, 98? 98 2
A number between 50 and 60? Any from 51 to 59 2
Total 10

Practice answers: Worksheet: 1 12, 34, 56; 2 45, 33, 21; 3 16; 4 98; 5 Any from 51 to 59.

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 22, 23, 32; 7 54; 8 20; 9 51, 15, 11; 10 71, 72, 73 or 74.

Independent practice answers. Level 1: 1 15, 38, 52; 2 71, 63, 44; 3 19; 4 any number from 41 to 49; 5 compare the tens: 15 has 1 ten, 38 has 3 tens and 52 has 5 tens. Level 2: 1 36, 45, 63; 2 30, 21, 12; 3 Any number from 61 to 69. Level 3: 1 40, 45, 50, 54; 2 29, 30, 31, 32; 3 33 is greater than 31. The right order is 13, 31, 33..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Order numbers from smallest to greatest 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 Order numbers from greatest to smallest 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 Use tens and ones to order 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 Find the number between two 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

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: Putting 9 after 15 because it looks like a bigger digit. 9 has only ones, so it is less than 15. Compare tens first.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Order three numbers with different tens, then add numbers with equal tens.
  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 puts two-digit numbers in order. You do not need to be good at mathematics to help.

  • Write 5 two-digit numbers on paper. Ask your child to put them in order.
  • Ask: which digit do we look at first?
  • Use house numbers or bus numbers to practise ordering.
  • 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: order numbers from smallest to greatest; order numbers from greatest to smallest; use tens and ones to order; find the number between two numbers.

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). Write 6 numbers on cards: 45, 12, 78, 33, 60, 21. 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 digit do you look at first? What if the tens are equal? What is between 40 and 50?

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. Putting 9 after 15 because it looks like a bigger digit. 9 has only ones, so it is less than 15. Compare tens first.

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

Use the quiz and worksheet on this page. The 9-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. Order three numbers with different tens, then add numbers with equal tens. 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 1 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.

Research used to shape this lesson. Common Core 1.NBT.B.3 and 2.NBT.A.4 (comparing and ordering numbers); Cambridge Primary Mathematics Stage 1. These sources informed the lesson.

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