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Worksheet with Answers

TN-MATH-GR3-57976 · v1.-5

Cosine Ratio

Grade 3 · Math · Trigonometry · Common Core

Grade

Grade 3

Subject

Math

Topic

Trigonometry

Subtopic

Cosine Ratio

Curriculum

Common Core

Difficulty

Core

Time

30 minutes

Total marks

Student name

Teacher name

Date

Learning objectives

Recognise cosine ratio accurately in math contexts.
Explain the underlying rule of cosine ratio in the student's own words.
Apply cosine 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.Write down one fact you already know about cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
2.State one fact you already know about cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
3.Circle one fact you already know about cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
4.Circle one fact you already know about cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.

Recall

Bloom: Remember · 4 marks

Complete from memory. No calculator, no notes.

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

FreeMathWorksheet · Grade 3 Math

Cosine Ratio

Basic Practice

Bloom: Understand · 5 marks

Work through each item. Show the step you used.

1.Match part 1 using the rule for cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
2.Work out part 2 using the rule for cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
3.Match part 3 using the rule for cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
4.Identify part 4 using the rule for cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
5.Match part 5 using the rule for cosine ratio.
[1]
AnswerAccept any correct response that applies the cosine 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 cosine ratio rule accurately.
2.Using the first step given, finish part 2. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the cosine ratio rule accurately.
3.Complete the method for part 3. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the cosine 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 cosine ratio rule accurately.

FreeMathWorksheet · Grade 3 Math

Cosine Ratio

Independent Practice

Bloom: Apply · 10 marks

No scaffolding. Set out your full method.

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

Challenge Questions

Bloom: Analyse · 9 marks

Harder items. Attempt every one, even partially.

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

FreeMathWorksheet · Grade 3 Math

Cosine Ratio

Real-life Application

Bloom: Apply · 6 marks

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

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

Reflection

Bloom: Create · 0 marks

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

1.Describe how confident you feel with cosine ratio and what you will practise next.
[—]
AnswerStudent response — not marked.
2.Describe how confident you feel with cosine ratio and what you will practise next.
[—]
AnswerStudent response — not marked.

FreeMathWorksheet

Answer key · Cosine Ratio

Warm-up

1.Accept any correct response that applies the cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[1]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[2]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[3]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[3]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[3]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[3]
1. Recall the definition that underpins cosine 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 cosine ratio rule accurately.[3]
1. Recall the definition that underpins cosine 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 cosine 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 cosine 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 · Cosine Ratio

Marking scheme

Band	Marks	Descriptor
Mastered	39–46	Applies cosine 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 cosine 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 cosine ratio with a neighbouring idea in trigonometry.

Teaching tips

Model one worked example of cosine 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 cosine ratio with justification-only questions.
Design your own cosine ratio question and write the mark scheme for it.
Link cosine ratio to the next subtopic in Trigonometry and explain the connection.
Ten-minute timed practice to convert accuracy into fluency.