You will learn
- Add by drawing pictures.
- Use circles or tally marks to show groups.
- Find the total from a picture.
- Write the number sentence from a picture.
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
- Draw circles or dots to stand for things.
- A tally mark is a line, one for each thing.
- Count all the circles or marks to find the total.
- Write the number sentence from the picture.
Words to know
A drawing that shows something.
A line we draw for each thing we count.
Make a picture with a pencil.
How many in all.
1. Discover: draw it
You do not always have objects to count. You can draw a picture instead. Draw 3 flowers and then 4 more flowers. How many flowers did you draw?
2. Understand: adding with pictures
We can draw circles, dots or tally marks to stand for things. To add 3 + 4, draw 3 circles, then 4 more circles. Count all the circles: 7.
We write 3 + 4 = 7.
Tally marks are quick lines: ||| for 3 and |||| for 4. Draw them together and count.
Idea 1: Draw circles
3 circles and 5 circles: ●●● ●●●●●. Count all the circles: 8.
Why draw? When you have no real objects, a quick drawing shows the problem.
Idea 2: Tally marks
A tally mark is a line, one line for each thing. |||| is 4. We can count tally marks the same way as objects.
Tally marks are quick to draw and easy to count.
Idea 3: From a picture to a sentence
Picture: ●●●● ●●. There are 4 and 2. The sentence is 4 + 2 = 6.
3. Worked examples
Example 1 (I show you): 3 + 5 with circles
Draw 3 circles and 5 circles: ●●● ●●●●●
- Count the first group: 3.
- Count on the second group: 4, 5, 6, 7, 8.
Answer: 3 + 5 = 8
Example 2 (We do it together): Tally marks
Tally marks ||| and ||||. What is the total?
- Count the first group: 3.
- Count on the second group: 4, 5, 6, 7.
Answer: The total is 7.
Example 3 (You try): Write the sentence
Picture: ★★ ★★★★. Write the number sentence.
Show the steps and answer
- The first group has 2.
- The second group has 4.
- Join them: 6.
Answer: 2 + 4 = 6
Did you know?
Tally marks are very old. People made marks on bones, wood and walls to count. We still use them today to count votes or goals.
Why this matters
Drawing helps when there are no objects. A quick sketch shows the problem and the answer.
4. Explore: draw and add
You need paper and a pencil.
- Draw 5 circles. Next to them, draw 2 circles.
- Count all the circles.
- Write the number sentence.
- Draw your own pictures for 4 + 4.
Think about it: what did you notice?
5 circles and 2 circles make 7 circles. 5 + 2 = 7.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I drew ___ and ___.
- The total is ___.
- My picture shows ___ + ___ = ___.
- Tally marks help me ___.
Guided practice
Question 1. Draw 2 and 3 circles. Total?
5.
Question 2. ||||| and || . How many tally marks?
5 + 2 = 7.
Question 3. What sentence matches 4 dots and 4 dots?
4 + 4 = 8.
Independent practice
Level 1: Start
- Draw 3 circles and 5 circles. How many altogether?
- Draw 6 dots and 2 dots. Write the sentence.
- 5 + 4 = __ (draw to check)
- Make tally marks for 4 and 3. Total?
- Draw a picture for 2 + 6.
Level 2: Grow
- Draw 4 circles and 2 circles. How many altogether?
- ||| and |||||. What is the total?
- Write the sentence for ●●●● and ●●●●●.
Level 3: Stretch
- Draw a picture for 7 + 2. Write the total.
- Tara draws 6 circles and 3 circles and says the total is 8. Is she right?
- Draw two groups that make 10 altogether.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A farmer sees 6 goats and 3 sheep. Draw them and say how many animals.
Show a sample answer
6 + 3 = 9 animals.
Another one. There are 4 goats and 5 goats in a field. Draw a quick picture and find the total.
Show a sample answer
Draw 4 circles and 5 circles. Count all: 9 goats.
7. Common mistakes
Fix: Leave a space between groups, and count each circle once.
Fix: Draw small circles of the same size in tidy rows.
Fix: Draw the two groups with a gap. Count the first, then count on.
8. Lesson summary and revision card
- I can add by drawing pictures.
- I can use circles or tally marks to show groups.
- I can find the total from a picture.
- I can write the number sentence from a picture.
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
- Draw circles or tally marks to add.
- Count all to find the total.
- Write the number sentence.
11. Next lesson
Next lesson: Number bonds to 10. 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.
- Draw 4 circles and 3 circles. How many circles altogether? [2 marks]
- Tally marks: ||| and |||||. What is the total? [1 mark]
- Write the number sentence for ●●●●●● and ●●. [2 marks]
- There are 5 hens and 4 chicks. Draw a picture to find how many animals. [2 marks]
- Ali draws 7 dots and 2 dots. He says the total is 10. Is he right? Explain. [2 marks]
Total: 9 marks.
Marking guide and model answers
- Picture with 4 and 3 [1]; 7 [1]
- 8 [1]
- 6 + 2 [1] = 8 [1]
- Picture [1]; 9 [1]
- No [1]. 7 and 2 make 9 when counted [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
- 2 + 5 = __
- 4 + 4 = __
- 3 + 6 = __
- 6 + 2 = __
- Draw circles for 3 + 3. Total?
- Draw 2 circles and 5 circles. What is the total?
- ||| and ||. What is the total?
- Write the sentence for ●●●●●● and ●●●.
- 6 + 4 = __ (draw to check)
- What can you draw for each thing when you add?
Homework
Draw pictures for three addition problems at home (for example 2 + 4, 5 + 3, 6 + 2). Write the total beside each one.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 + 5 = __ | 7 | 2 |
| 4 + 4 = __ | 8 | 2 |
| 3 + 6 = __ | 9 | 2 |
| 6 + 2 = __ | 8 | 2 |
| Draw circles for 3 + 3. Total? | 6 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 7; 2 8; 3 9; 4 8; 5 6.
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 7; 7 5; 8 6 + 3 = 9; 9 10; 10 A circle, dot or tally mark.
Independent practice answers. Level 1: 1 8; 2 6 + 2 = 8; 3 9; 4 7; 5 two groups of 2 and 6 circles, joined, total 8. Level 2: 1 6; 2 8; 3 4 + 5 = 9. Level 3: 1 9; 2 No. 6 and 3 make 9.; 3 For example 5 circles and 5 circles.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Add by drawing pictures | 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 circles or tally marks to show groups | 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 total from a picture | 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 the number sentence from a picture | 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: Drawing groups too close together so they cannot be counted. Leave a space between groups, and count each circle once.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Go back to counters, then draw the same groups slowly.
- 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 adds by drawing circles or tally marks. You do not need to be good at mathematics to help.
- Draw dots in sand or on paper to solve small sums.
- Make tally marks to count goals or shared sweets.
- Ask your child to explain their drawing.
- 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: add by drawing pictures; use circles or tally marks to show groups; find the total from a picture; write the number sentence from a picture.
Prerequisite knowledge. Lesson 3: adding with objects.
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 did you draw for each thing? How do you find the total? What is the sentence for your picture?
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. Drawing groups too close together so they cannot be counted. Leave a space between groups, and count each circle once.
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. Go back to counters, then draw the same groups slowly. 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 K.OA.A.1 (drawings to represent addition); Cambridge Primary Mathematics Stage 1. These sources informed the lesson; no official alignment is claimed.