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TN-MATH-GR3-11880 · v3.-7

Tangent Ratio

Grade 3 · Math · Trigonometry · Cambridge (CAIE)

Grade

Grade 3

Subject

Math

Topic

Trigonometry

Subtopic

Tangent Ratio

Curriculum

Cambridge (CAIE)

Difficulty

Core

Time

30 minutes

Total marks

Student name

Teacher name

Date

Learning objectives

Recognise tangent ratio accurately in math contexts.
Explain the underlying rule of tangent ratio in the student's own words.
Apply tangent ratio to multi-step and unfamiliar problems.
Justify a chosen method and identify errors in another student's work.

Skills assessed

Fluency and recall
Method and setting out
Reasoning and justification
Problem solving in context
Self-assessment

Instructions

Write your name, your teacher's name and the date in the header.
Answer every question in the space provided. Continue on the back if needed.
Show all working — method marks are awarded even when the final answer is wrong.
Aim to finish in about 30 minutes.
Complete the reflection box at the end before you hand the sheet in.

Warm-up

Bloom: Remember · 4 marks

Answer quickly. These check you are ready for the topic.

1.State one fact you already know about tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
2.Write down one fact you already know about tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
3.Circle one fact you already know about tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
4.Name one fact you already know about tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.

Recall

Bloom: Remember · 4 marks

Complete from memory. No calculator, no notes.

1.Complete the key term used in tangent ratio described here: item 1.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
2.Label the key term used in tangent ratio described here: item 2.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
3.Label the key term used in tangent ratio described here: item 3.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
4.Define the key term used in tangent ratio described here: item 4.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.

FreeMathWorksheet · Grade 3 Math

Tangent Ratio

Basic Practice

Bloom: Understand · 5 marks

Work through each item. Show the step you used.

1.Identify part 1 using the rule for tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
2.Match part 2 using the rule for tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
3.Match part 3 using the rule for tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
4.Match part 4 using the rule for tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
5.Work out part 5 using the rule for tangent ratio.
[1]
AnswerAccept any correct response that applies the tangent ratio rule accurately.

Guided Practice

Bloom: Understand · 8 marks

The first step is given. Finish the reasoning.

1.Continue the working for part 1. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
2.Continue the working for part 2. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
3.Continue the working for part 3. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
4.Using the first step given, finish part 4. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.

FreeMathWorksheet · Grade 3 Math

Tangent Ratio

Independent Practice

Bloom: Apply · 10 marks

No scaffolding. Set out your full method.

1.Work out fully part 1 on tangent ratio without help.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
2.Solve part 2 on tangent ratio without help.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
3.Work out fully part 3 on tangent ratio without help.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
4.Calculate part 4 on tangent ratio without help.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
5.Solve part 5 on tangent ratio without help.
[2]
AnswerAccept any correct response that applies the tangent ratio rule accurately.

Challenge Questions

Bloom: Analyse · 9 marks

Harder items. Attempt every one, even partially.

1.Prove the statement in part 1 about tangent ratio.
[3]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
2.Deduce the statement in part 2 about tangent ratio.
[3]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
3.Find and justify the statement in part 3 about tangent ratio.
[3]
AnswerAccept any correct response that applies the tangent ratio rule accurately.

FreeMathWorksheet · Grade 3 Math

Tangent Ratio

Real-life Application

Bloom: Apply · 6 marks

Use the skill in context. State units in your answer.

1.Apply a real math situation that depends on tangent ratio.
[3]
AnswerAccept any correct response that applies the tangent ratio rule accurately.
2.Use the information to decide a real math situation that depends on tangent ratio.
[3]
AnswerAccept any correct response that applies the tangent ratio rule accurately.

Reflection

Bloom: Create · 0 marks

Not marked. Answer honestly — this guides your next worksheet.

1.Reflect on how confident you feel with tangent ratio and what you will practise next.
[—]
AnswerStudent response — not marked.
2.Record how confident you feel with tangent ratio and what you will practise next.
[—]
AnswerStudent response — not marked.

FreeMathWorksheet

Answer key · Tangent Ratio

Warm-up

1.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Recall

1.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Basic Practice

1.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
5.Accept any correct response that applies the tangent ratio rule accurately.[1]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Guided Practice

1.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Independent Practice

1.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
5.Accept any correct response that applies the tangent ratio rule accurately.[2]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Challenge Questions

1.Accept any correct response that applies the tangent ratio rule accurately.[3]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the tangent ratio rule accurately.[3]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the tangent ratio rule accurately.[3]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Real-life Application

1.Accept any correct response that applies the tangent ratio rule accurately.[3]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the tangent ratio rule accurately.[3]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Reflection

1.Student response — not marked.[0]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Student response — not marked.[0]
1. Recall the definition that underpins tangent ratio.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

FreeMathWorksheet

Teacher pack · Tangent Ratio

Marking scheme

Band	Marks	Descriptor
Mastered	39–46	Applies tangent ratio fluently, including in unfamiliar contexts, with clear justification.
Secure	30–38	Reliable in routine questions; reasoning is mostly complete.
Developing	18–29	Secure in scaffolded items, inconsistent once support is removed.
Emerging	0–17	Needs re-teaching of the core rule before progressing.

Teacher notes

Set the warm-up as a five-minute starter; it diagnoses readiness for tangent ratio before you teach.
Guided practice is the pivot point — circulate here rather than during independent practice.
Mark the reasoning questions with the marking scheme bands, not raw totals, so progress is comparable across variants.
Students who band Emerging should repeat the Easy variant of this same subtopic before moving on within Trigonometry.

Common student mistakes

Confusing tangent ratio with a neighbouring idea in trigonometry.

Teaching tips

Model one worked example of tangent ratio under a visualiser before handing the sheet out.
Ask students to predict which question they will find hardest, then check the prediction afterwards.
Pair Developing students with Secure students for the guided practice block only.
Use the answer key as a self-marking station rather than collecting the sheets in.

Extension activities

Challenge worksheet on tangent ratio with justification-only questions.
Design your own tangent ratio question and write the mark scheme for it.
Link tangent ratio to the next subtopic in Trigonometry and explain the connection.
Ten-minute timed practice to convert accuracy into fluency.