Courseversity

Lesson

Mental addition strategies

Primary EducationGrade 2MathematicsCV-PRI-G02-MATH-OPS-U01-L0145–60 min

You will learn

  • Use make-ten to add.
  • Use doubles and near doubles.
  • Count on from the bigger number.
  • Add 9 by adding 10 and taking away 1.

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. Make ten to add.
  2. Use doubles and near doubles.
  3. Count on from the bigger number.
  4. To add 9, add 10 and take away 1.

Words to know

mental
Done in your head.
double
The same number added twice.
strategy
A clever way to solve a problem.
partition
Break a number into parts.

1. Discover: quick shopkeeper

A shopkeeper adds 8 + 5 in his head very fast. He thinks: 8 and 2 make 10, then 3 more. How many is that?

2. Understand: mental addition strategies

You can add in your head with clever strategies.

  • Make ten: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.
  • Doubles: 7 + 7 = 14. Near doubles: 7 + 8 = 7 + 7 + 1 = 15.
  • Count on from the bigger number: 3 + 9 is 9, 10, 11, 12.
  • Add 9: add 10 and take away 1. 46 + 9 = 46 + 10 − 1 = 55.

Idea 1: Make ten

For 8 + 5, take 2 from the 5 to make 10 with the 8. 8 + 2 = 10 and 10 + 3 = 13.

Idea 2: Doubles

A double is the same number added twice. 7 + 7 = 14. For a near double, 7 + 8 is one more than 7 + 7, so it is 15.

Idea 3: Add 9

To add 9, add 10 and take away 1. 46 + 9: 46 + 10 = 56 and 56 − 1 = 55.

Why? 9 is one less than 10.

Remember: Make ten, use doubles, count on from the bigger number, and add 9 as 10 minus 1.

3. Worked examples

Example 1 (I show you): Make ten

9 + 6 = ?

  1. 9 + 1 = 10.
  2. 6 − 1 = 5.
  3. 10 + 5 = 15.

Answer: 15

Example 2 (We do it together): Double

8 + 8 = ?

  1. Double 8 is 16.

Answer: 16

Example 3 (You try): Add 9

45 + 9 = ?

Show the steps and answer
  1. 45 + 10 = 55.
  2. 55 − 1 = 54.

Answer: 54

Did you know?

Mental maths is fast because you reuse number facts you already know, such as doubles.

Why this matters

Mental strategies help us add quickly in shops and at school without a pen.

4. Explore: strategy cards

You need paper and a pencil.

  1. Write 8 + 5 and make ten.
  2. Write 7 + 8 using a near double.
  3. Write 46 + 9 using +10 − 1.
  4. Tell a partner which strategy was fastest.
Think about it: what did you notice?

8 + 5 = 13; 7 + 8 = 15; 46 + 9 = 55.

5. Practise

Say it in a sentence

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

  • I make ten by ___.
  • The double of ___ is ___.
  • To add 9 I add ___ and take away ___.
  • The answer is ___.

Guided practice

Question 1. 8 + 5 by making ten?

8 + 2 + 3 = 13.

Question 2. 7 + 8 as a near double?

7 + 7 + 1 = 15.

Question 3. 46 + 9?

46 + 10 − 1 = 55.

Independent practice

Level 1: Start

  1. 9 + 6
  2. 8 + 8
  3. 38 + 10
  4. 45 + 9
  5. 3 + 7 + 5

Level 2: Grow

  1. 7 + 3 + 9 = ___.
  2. 9 + 9 = ___.
  3. 27 + 9 = ___.

Level 3: Stretch

  1. 26 + 19 = ___.
  2. Which strategy helps with 8 + 7? Solve it.
  3. Sade says 45 + 9 = 55 because 9 is almost 10. What is wrong?

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

6. Apply: everyday mathematics

A seller had 46 mangoes and bought 9 more. How many now?

Show a sample answer

55 mangoes.

Another one. You have 19 stickers and get 6 more. How many now? Use add 20, take away 1.

Show a sample answer

19 + 6: 20 + 6 = 26, then 26 − 1 = 25

7. Common mistakes

Mistake: Taking away 10 instead of 1 when adding 9.
Fix: Add 10 first, then take away 1.
Another mistake: Forgetting to take away 1 after adding 10 for +9.
Fix: Add 10, then take away 1.
Another mistake: Counting on from the smaller number.
Fix: Start from the bigger number and count on.

8. Lesson summary and revision card

I can…

  • I can make ten to add.
  • I can use doubles and near doubles.
  • I can count on from the bigger number.
  • I can add 9 mentally.

9. Check and master

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

1. 8 + 5 =

2. 7 + 7 =

3. 7 + 8 =

4. 46 + 9 =

5. 6 + 4 + 7 =

6. 9 + 6 =

7. 8 + 8 =

8. 38 + 10 =

9. 45 + 9 =

10. 3 + 7 + 5 =

11. 6 + 7 =

12. 30 + 19 =

Challenge 1. 25 + 19 =

Challenge 2. 29 + 29 =

Your result appears here after you answer every question.

10. Key takeaways

  • Make ten.
  • Use doubles.
  • Add 9 as +10 − 1.

11. Next lesson

Next lesson: Addition within 100. 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. Work out 7 + 5 using make ten. [2 marks]
  2. What is the double of 9? [1 mark]
  3. Work out 36 + 9. [2 marks]
  4. Work out 6 + 4 + 8. [1 mark]
  5. Ben says 7 + 8 = 14 because 7 + 7 = 14. Is he right? Explain. [3 marks]

Total: 9 marks.

Marking guide and model answers
  1. 7 + 3 = 10 [1]; 10 + 2 = 12 [1]
  2. 18 [1]
  3. 36 + 10 = 46 [1]; 45 [1]
  4. 18 [1]
  5. No [1]. 8 is one more than 7 [1]. 7 + 8 = 15 [1].

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. 9 + 6
  2. 8 + 8
  3. 38 + 10
  4. 45 + 9
  5. 3 + 7 + 5
  6. 8 + 6 = ___.
  7. Double 6 = ___.
  8. 23 + 9 = ___.
  9. 5 + 5 + 7 = ___.
  10. 74 + 10 = ___.

Homework

Pick five addition facts. Solve each with a different strategy and tell a family member how.

Answer key and marking scheme

Question Expected response Marks
9 + 6 15 2
8 + 8 16 2
38 + 10 48 2
45 + 9 54 2
3 + 7 + 5 15 2
Total 10

Practice answers: Worksheet: 1 15; 2 16; 3 48; 4 54; 5 15.

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 14; 7 12; 8 32; 9 17; 10 84.

Independent practice answers. Level 1: 1 15; 2 16; 3 48; 4 54; 5 15. Level 2: 1 19; 2 18; 3 36. Level 3: 1 45; 2 Near double: 7 + 7 + 1 = 15; 3 You must take 1 away after adding 10. 45 + 9 = 54..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Use make-ten to add 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 Use doubles and near doubles 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 Count on from the bigger number 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 Add 9 by adding 10 and taking away 1 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: Taking away 10 instead of 1 when adding 9. Add 10 first, then take away 1.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Use counters to make a ten before adding the rest.
  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 learns quick mental ways to add. You do not need to be good at mathematics to help.

  • Practise doubles from 1 to 10.
  • Ask quick sums, such as 9 + 4, and ask how they found the answer.
  • Use a ten frame or fingers to make ten.
  • 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: use make-ten to add; use doubles and near doubles; count on from the bigger number; add 9 by adding 10 and taking away 1.

Prerequisite knowledge. Grade 1 addition within 20.

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. Which strategy did you use? Can you make ten? Is it a double?

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. Taking away 10 instead of 1 when adding 9. Add 10 first, then take away 1.

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. Use counters to make a ten before adding the rest. 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 » Operations & Algebraic Thinking; 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.OA.B.2 (fluently add within 20) and 2.NBT.B.5; Cambridge Primary Mathematics Stage 2. These sources informed the lesson.

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