Courseversity

Lesson

Real-world applications

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-NUM-U02-L0835–45 min

You will learn

  • Scale a recipe.
  • Use a map scale.
  • Solve speed problems.
  • Convert money.

Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.

Student lesson

Words to know

scale
Ratio on a map or plan.
recipe
Ingredient instructions.
exchange rate
Money for money.
speed
Distance per time.

1. Discover: real life

A rice recipe uses 2 cups of rice to 3 cups of water. How much water for 6 cups of rice?

2. Understand: real-world ratios

  • 6 ÷ 2 = 3, so water is 3 × 3 = 9 cups.
  • Map scale 1 cm to 5 km: 4 cm is 20 km.
  • Speed 60 km/h for 2.5 h: 60 × 2.5 = 150 km.
  • Exchange 1 to 12: 5 units gives 60.
Remember: Find the multiplier and apply it.

3. Explore: apply

You need paper.

  1. Find the multiplier.
  2. Apply it to the other term.
  3. Write units.
  4. Check sense.
Think about it: what did you notice?

9 cups.

4. Practise

Guided practice

Question 1. Water for 6 cups rice?

9.

Question 2. 4 cm on a 1 cm = 5 km map?

20 km.

Question 3. 60 km/h for 2.5 h?

150 km.

Independent practice

  1. Water for 4 cups rice (2 : 3)
  2. 8 cm on a 1 cm = 5 km map
  3. 60 km/h for 3 h
  4. 5 units at 1 to 12
  5. 2 cm on a 1 cm = 5 km map

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

5. Apply: everyday mathematics

Rice and water are 2 : 3. How much water for 6 cups of rice?

Show a sample answer

9 cups.

6. Common mistake

Mistake: Forgetting to scale both terms.
Fix: Use the same multiplier.

7. Check and master

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

1. Water for 4 cups rice:

2. 8 cm on a 1 cm = 5 km map:

3. 60 km/h for 3 h:

4. 5 units at 1 to 12:

5. 2 cm on the same map:

Challenge. 60 km/h for 2.5 h gives:

Your result appears here after you answer every question.

8. Key takeaways

  • Find the multiplier.
  • Scale both terms.
  • Write units.

9. Next lesson

Next lesson: Percentages as ratios per hundred. Keep going with the next idea in this course.

Printable worksheet

  1. Water for 4 cups rice
  2. 8 cm on 1 cm = 5 km
  3. 60 km/h for 3 h
  4. 5 units at 1 to 12
  5. 2 cm on 1 cm = 5 km

Homework

Scale a recipe of yours for twice as many people.

Answer key and marking scheme

Question Expected response Marks
Water for 4 cups rice 6 2
8 cm on 1 cm = 5 km 40 km 2
60 km/h for 3 h 180 km 2
5 units at 1 to 12 60 2
2 cm on 1 cm = 5 km 10 km 2
Total 10

Practice answers: Worksheet: 1 6; 2 40 km; 3 180 km; 4 60; 5 10 km.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Scale a recipe 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 a map scale 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 Solve speed problems 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 Convert money 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 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.

If a learner struggles

  1. Find the misconception: Forgetting to scale both terms. Use the same multiplier.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Scaling.
  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.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: scale a recipe; use a map scale; solve speed problems; convert money.

Prerequisite knowledge. Lessons 3–7.

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. 35–45 minutes.

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.

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. Forgetting to scale both terms. Use the same multiplier.

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

Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Scaling. 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.

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