Courseversity

Lesson

Number sequences

Primary EducationGrade 2MathematicsCV-PRI-G02-MATH-NUM-U01-L0845–60 min

You will learn

  • Skip-count in 2s, 5s, 10s and 100s.
  • Find the rule of a sequence.
  • Fill missing numbers.
  • Continue a sequence.

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. A sequence follows a rule.
  2. Skip count in 2s, 5s, 10s and 100s.
  3. Find the rule by looking at the jumps.
  4. Fill missing numbers and continue.

Words to know

sequence
Numbers in an order that follows a rule.
rule
What changes each time.
skip count
Count in jumps of the same size.
missing
Not there yet.

1. Discover: steps on a path

Stones on a path are numbered 105, 110, 115, 120. What is the next stone? What did you add each time?

2. Understand: number sequences

A sequence follows a rule. For 105, 110, 115, 120 the rule is “add 5”. The next number is 125.

Look at what changes. If only the tens digit changes by 1, the rule is add 10: 230, 240, 250. If only the hundreds change, the rule is add 100: 300, 400, 500.

Sequences can go down too: 500, 450, 400 has the rule “subtract 50”.

Idea 1: The rule

A sequence is a list of numbers that follows a rule. In 230, 240, 250 the rule is add 10.

Idea 2: Skip counting

To skip count is to jump by the same amount. 105, 110, 115, 120 jumps by 5. 98, 100, 102 jumps by 2.

Idea 3: Missing numbers

In 200, __, 400 the jump is 100, so the missing number is 300.

Why the rule? The rule lets us find any number in the sequence.

Remember: Find how much changes each time. That is the rule.

3. Worked examples

Example 1 (I show you): Add 5

105, 110, 115, 120, __. What is next?

  1. The jump is 5.
  2. 120 + 5 = 125.

Answer: 125

Example 2 (We do it together): Take away 100

700, 600, 500, __.

  1. The rule is take away 100.

Answer: 400

Example 3 (You try): Fill the gap

Fill the gap: 200, __, 400.

Show the steps and answer
  1. The jump from 200 to 400 is 200, in two steps of 100.

Answer: 300

Did you know?

The numbers on a hundred square make sequences. Going down a column adds 10 each time.

Why this matters

Sequences help us count quickly and spot patterns in numbers.

4. Explore: find the rule

You need paper and a pencil.

  1. Write 105, 110, 115, 120, __.
  2. Find the rule.
  3. Write 700, 600, 500, __.
  4. Make a sequence of your own and ask a partner for the rule.
Think about it: what did you notice?

The first rule is add 5, the second subtract 100.

5. Practise

Say it in a sentence

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

  • The rule is ___.
  • The jump is ___.
  • The next number is ___.
  • The missing number is ___.

Guided practice

Question 1. 105, 110, 115, 120, __

125.

Question 2. Rule for 230, 240, 250?

add 10.

Question 3. 700, 600, 500, __

400.

Independent practice

Level 1: Start

  1. Next: 310, 320, 330, __
  2. Next: 450, 455, 460, __
  3. Rule for 800, 700, 600?
  4. Fill the gap: 200, __, 400
  5. Next: 98, 100, 102, __

Level 2: Grow

  1. Next: 25, 30, 35, __.
  2. Rule for 400, 300, 200?
  3. Fill the gap: 150, __, 250.

Level 3: Stretch

  1. After 84, add 2 each time. Write the next three numbers.
  2. Find the mistake: 100, 200, 300, 350, 500.
  3. Ama says the rule for 20, 40, 60 is add 10. What is wrong?

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

6. Apply: everyday mathematics

A bus fare rises by 50 each year: 300, 350, 400. What will it be next?

Show a sample answer

450.

Another one. Ben saves 50 each week. Write his savings after weeks 1 to 5.

Show a sample answer

50, 100, 150, 200, 250

7. Common mistakes

Mistake: Adding the wrong amount because only the first jump was checked.
Fix: Check the jump between every pair.
Another mistake: Using the wrong jump.
Fix: Check the jump between two numbers.
Another mistake: Forgetting to check every step.
Fix: The rule must work for each step.

8. Lesson summary and revision card

I can…

  • I can skip count in 2s, 5s, 10s and 100s.
  • I can find the rule.
  • I can fill missing numbers.
  • I can continue a sequence.

9. Check and master

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

1. 105, 110, 115, 120, __

2. Rule for 230, 240, 250?

3. 700, 600, 500, __

4. Fill the gap: 200, __, 400

5. Next: 98, 100, 102, __

6. 210, 220, 230, __

7. 90, 80, 70, __

8. The rule for 100, 200, 300, 400 is…

9. Fill the gap: 5, 10, __, 20.

10. 600, 500, __, 300

11. Next two: 20, 22, 24, __, __

12. The rule for 95, 90, 85 is…

Challenge 1. Next two numbers: 465, 475, 485, __, __

Challenge 2. A sequence starts at 12 and adds 5 each time. What is the 5th number?

Your result appears here after you answer every question.

10. Key takeaways

  • A sequence follows a rule.
  • Check all jumps.
  • Count on and back.

11. Next lesson

Next lesson: Odd and even numbers. 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. Next: 330, 340, 350, __. [1 mark]
  2. What is the rule for 800, 700, 600? [1 mark]
  3. Fill the gap: 120, __, 140. [1 mark]
  4. Write the next two numbers: 65, 70, 75, __, __. [2 marks]
  5. Ali says the rule for 5, 10, 15 is add 10. Is he right? Explain. [3 marks]

Total: 8 marks.

Marking guide and model answers
  1. 360 [1]
  2. Take away 100 [1]
  3. 130 [1]
  4. 80 [1]; 85 [1]
  5. No [1]. 10 − 5 = 5 [1]. The rule is add 5 [1].

Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.

Printable worksheet

  1. Next: 310, 320, 330, __
  2. Next: 450, 455, 460, __
  3. Rule: 800, 700, 600?
  4. Fill: 200, __, 400
  5. Next: 98, 100, 102, __
  6. Next: 10, 20, 30, __.
  7. Rule for 90, 80, 70?
  8. Fill: 300, __, 500.
  9. Next: 46, 48, 50, __.
  10. Rule for 5, 10, 15?

Homework

Make a sequence of five numbers with a rule. Ask a family member for the rule.

Answer key and marking scheme

Question Expected response Marks
Next: 310, 320, 330, __ 340 2
Next: 450, 455, 460, __ 465 2
Rule: 800, 700, 600? subtract 100 2
Fill: 200, __, 400 300 2
Next: 98, 100, 102, __ 104 2
Total 10

Practice answers: Worksheet: 1 340; 2 465; 3 subtract 100; 4 300; 5 104.

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 40; 7 Take away 10; 8 400; 9 52; 10 Add 5.

Independent practice answers. Level 1: 1 340; 2 465; 3 take away 100; 4 300; 5 104. Level 2: 1 40; 2 Take away 100; 3 200. Level 3: 1 86, 88, 90; 2 350 should be 400; 3 The jump is 20, so the rule is add 20..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Skip-count in 2s, 5s, 10s and 100s 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 the rule of a sequence 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 Fill missing 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
O4 Continue a sequence 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: Adding the wrong amount because only the first jump was checked. Check the jump between every pair.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Use a number line to 200 and jump by 10.
  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 skip counts and finds the rule of number sequences. You do not need to be good at mathematics to help.

  • Count in 2s, 5s, 10s and 100s together.
  • Ask: what is the rule? What comes next?
  • Skip count on the stairs.
  • 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: skip-count in 2s, 5s, 10s and 100s; find the rule of a sequence; fill missing numbers; continue a sequence.

Prerequisite knowledge. Lessons 1 to 7.

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 and a pencil. 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 jump? What is the rule? What is missing?

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 the wrong amount because only the first jump was checked. Check the jump between every pair.

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

Use the quiz and worksheet on this page. The 8-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. Use a number line to 200 and jump by 10. 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 2 » 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 2.NBT.A.2 (skip counting); Cambridge Primary Mathematics Stage 2 (sequences). These sources informed the lesson.

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