You will learn
- Build a ratio table.
- Find missing entries.
- Find the unit value.
- Read a table to solve.
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
- A ratio table lists equivalent ratios.
- Multiply across a row by the same number.
- The unit value is the amount for one.
- Use the table to scale up or down.
Words to know
Table of equivalent ratios.
Value for one.
Multiply across.
Horizontal line.
1. Discover: pens and price
3 pens cost 6. What do 5 pens cost?
2. Understand: ratio tables
| Pens | 1 | 3 | 5 | 10 |
|---|---|---|---|---|
| Cost | 2 | 6 | 10 | 20 |
- 3 pens cost 6, so 1 pen costs 6 ÷ 3 = 2.
- 5 pens cost 5 × 2 = 10.
- 10 pens cost 20.
- Every column keeps the same ratio 1 : 2.
Idea 1: Unit value
If 1 pen costs 2, then 4 pens cost 4 × 2 = 8 and 7 pens cost 14.
Idea 2: Table
Pens 1, 4, 7, 20. Cost 2, 8, 14, 40. Each cost is 2 × pens.
Idea 3: Backward
Cost 14 means 14 ÷ 2 = 7 pens.
Why a table? It lays out the pattern so missing values are easy to spot.
3. Worked examples
Example 1 (I show you): Cost
4 pens at 2 each
- 4 × 2.
Answer: 8
Example 2 (We do it together): Pens
Cost 14 at 2 each
- 14 ÷ 2.
Answer: 7 pens
Example 3 (You try): Cost
20 pens
Show the steps and answer
- 20 × 2.
Answer: 40
Did you know?
The unit value is the constant that links the two rows.
Why this matters
Ratio tables solve shopping, cooking and speed problems quickly.
4. Explore: table
You need paper.
- Find cost of 1.
- Multiply for any number.
- Fill the table.
- Check the ratio.
Think about it: what did you notice?
10.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- One ___ costs ___.
- I multiply / divide by ___.
- The missing value is ___.
- The pattern is ___.
Guided practice
Question 1. Cost of 1 pen?
2.
Question 2. Cost of 5 pens?
10.
Question 3. Cost of 10 pens?
20.
Independent practice
Level 1: Start
- Cost of 4 pens
- Pens for 14
- Cost of 7 pens
- Cost of 20 pens
- Cost of 1 pen
Level 2: Grow
- 2 books cost 6. Cost of 1 book
- Cost of 5 books at 3 each
- Books for 12
Level 3: Stretch
- 4 kg cost 12. Kg for 21
- 3 : 5 = 9 : ?
- Ben says if 3 pens cost 6 then 5 pens cost 8 (5 + 3). What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
3 pens cost 6. What do 5 pens cost?
Show a sample answer
10.
Another one. 5 pens cost 10. What do 8 pens cost?
Show a sample answer
16
7. Common mistakes
Fix: Multiply each row by the same number.
Fix: Multiply or divide by the same number.
Fix: Label each row.
8. Lesson summary and revision card
- I can build a ratio table.
- I can find missing entries.
- I can find the unit value.
- I can read a table to solve.
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
- Find the unit value.
- Multiply across.
- Same ratio in every column.
11. Next lesson
Next lesson: Unit rates. 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.
- A table shows 1 pen costs 2. Find the cost of 4 pens. [2 marks]
- A table shows 1 pen costs 2. How many pens cost 14? [2 marks]
- A table shows 1 pen costs 2. Find the cost of 7 pens. [2 marks]
- A table shows 1 pen costs 2. Find the cost of 20 pens. [2 marks]
- Ali says if 3 pens cost 6 then 5 pens cost 8 because 5 + 3 = 8. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 4 × 2 [1]; 8 [1]
- 14 ÷ 2 [1]; 7 pens [1]
- 7 × 2 [1]; 14 [1]
- 20 × 2 [1]; 40 [1]
- No [1]. The unit cost is 6 ÷ 3 = 2 [1]. 5 pens cost 5 × 2 = 10 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Cost of 4 pens
- Pens for 14
- Cost of 7 pens
- Cost of 20 pens
- Cost of 1 pen
- Cost of 4 pens (2 each)
- Pens for 14
- Cost of 7 pens
- Cost of 20 pens
- Cost of 1 pen
Homework
Make a ratio table for apples at 3 for 9.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Cost of 4 pens | 8 | 2 |
| Pens for 14 | 7 | 2 |
| Cost of 7 pens | 14 | 2 |
| Cost of 20 pens | 40 | 2 |
| Cost of 1 pen | 2 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 8; 2 7; 3 14; 4 40; 5 2.
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 8; 7 7; 8 14; 9 40; 10 2.
Independent practice answers. Level 1: 1 8; 2 7 pens; 3 14; 4 40; 5 2. Level 2: 1 3; 2 15; 3 4. Level 3: 1 7 kg; 2 15; 3 Use the unit cost 2: 5 × 2 = 10..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Build a ratio table | 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 missing entries | 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 unit value | 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 Read a table to solve | 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
- Find the misconception: Adding instead of multiplying across. Multiply each row by the same number.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Times tables.
- 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 uses ratio tables. You do not need to be good at mathematics to help.
- Make a price table for fruit.
- Ask: what is the cost of one?
- Check each row.
- 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: build a ratio table; find missing entries; find the unit value; read a table to solve.
Prerequisite knowledge. Lesson 3.
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. What is the unit value? What do I multiply by?
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 instead of multiplying across. Multiply each row by the same number.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Times 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
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 6 » The Number System. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 6.RP.A.3a; Cambridge Primary Mathematics Stage 6 (ratio tables). These sources informed the lesson.