Year 6 Maths Questions 2024: 50 Practice Problems With Answers

Maths can be a challenging subject for many Year 6 students, especially as they prepare for secondary school. In Australia, Year 6 maths students are expected to master key concepts such as fractions, decimals, and geometry. 

According to a recent report from the Australian Curriculum, Assessment and Reporting Authority (ACARA), only 74% of students met the minimum numeracy standard in 2023. This highlights the need for targeted practice and support to help students excel.

To aid in this, we’ve compiled 50 practice problems specifically tailored for Year 6 students, complete with answers. These questions cover a range of topics that are crucial for success in Year 6 maths. 

Whether your child needs extra practice or you’re looking for a way to reinforce their learning, these questions will provide valuable support. You may also review the Year 6 Maths Curriculum to better understand your child’s Maths journey. 

What Are the Top Year 6 Maths Questions for 2024?

Here are 50 carefully selected Year 6 maths questions for 2024. These problems are designed to challenge and enhance your child’s understanding of key mathematical concepts:

Numbers & Place Value

Place Value

1. What is the value of the digit 7 in the number 47,583?
a) 7
b) 700
c) 7000
d) 7,000

2. Write the number 3,205,678 in words.
a) Three million, two hundred five thousand, six hundred seventy-eight.
b) Thirteen million, two hundred five thousand, six hundred seventy-eight.
c) Thirty million, two hundred five thousand, six hundred seventy-eight.
d) Three hundred million, two hundred five thousand, six hundred seventy-eight.

3. What is the value of the digit 4 in the number 3.482?
a) 4
b) 40
c) 0.4
d) 0.04

4. In the number 5,239, which digit is in the hundreds place?
a) 9
b) 3
c) 2
d) 5

5. If you add 10 to the digit in the tens place of 5,948, what is the new number?
a) 6948
b) 5948
c) 5998
d) 5958

Word form to Standard form

1. Write “Four hundred seventy-three thousand, eight hundred ninety-one” in standard form.
a) 473,891
b) 473,881
c) 4,473,891
d) 473,891.1

2. Convert “Two million, fifty thousand, three hundred twelve” to standard form.
a) 2,250,312
b) 2,050,313
c) 2,050,312
d) 2,051,312

3. How do you write “Seven hundred sixty-four thousand, two hundred nine” in standard form?
a) 764,109
b) 764,209
c) 763,209
d) 764,409

4. Write “Five million, one hundred forty-six thousand, three hundred” in standard form.
a) 5,116,300
b) 5,146,300
c) 5,136,300
d) 5,126,300

5. Convert “Nine thousand, two hundred eighty-four” to standard form.
a) 9,299
b) 9,289
c) 9,284.9
d) 9,284

Standard form to Expanded form

1. Write the number 4,572 in expanded form.
a) 40,000 + 500 + 70 + 2
b) 400,000 + 500 + 70 + 2
c) 4,000 + 500 + 70 + 2
d) 4,400 + 500 + 70 + 2

2. Express 83,209 in expanded form.
a) 80,000 + 3,000 + 200 + 0 + 9
b) 800,000 + 3,000 + 200 + 0 + 9
c) 80,800 + 3,000 + 200 + 0 + 9
d) 80,880 + 3,000 + 200 + 0 + 9

3. Convert 6,431 to expanded form.
a) 6,000 + 400 + 30 + 11
b) 6,000 + 400 + 31 + 1
c) 6,000 + 401 + 30 + 1
d) 6,000 + 400 + 30 + 1

4. Write 52,048 in expanded form.
a) 50,000 + 2,000 + 0 + 40 + 8
b) 50,000 + 3,000 + 0 + 40 + 8
c) 50,000 + 4,000 + 0 + 40 + 8
d) 50,000 + 8,000 + 0 + 40 + 8

5. Express 109,305 in expanded form.
a) 100,000 + 1 + 9,000 + 300 + 0 + 5
b) 100,000 + 0 + 9,000 + 300 + 0 + 5
c) 100,000 + 2 + 9,000 + 300 + 0 + 5
d) 100,000 + 8 + 9,000 + 300 + 0 + 5

Decimals

1. What is 0.7 + 0.5?
a) 1.7
b) 1.5
c) 1.3
d) 1.2

2. Subtract 4.6 from 9.3. What is the result?
a) 4.7
b) 4.3
c) 4.6
d) 4.9

3. Multiply 3.2 by 0.5. What is the product?
a) 1.2
b) 1.6
c) 1.5
d) 1.0

4. Divide 8.4 by 2. What is the quotient?
a) 4.8
b) 4.4
c) 4.2
d) 4.0

5. What is the value of 7.65 rounded to the nearest whole number?
a) 7
b) 6
c) 8
d) 5

Arithmetic

Adding and subtracting whole numbers by transformation

1. If you start with 65 and add 47, what is the result?
a) 113
b) 115
c) 122
d) 112

2. Subtract 123 from 250 using the transformation method.
a) 127
b) 123
c) 125
d) 120

3. Start with 84 and add 29. Use transformation to find the sum.
a) 118
b) 113
c) 128
d) 123

4. Subtract 48 from 200 using transformation techniques.
a) 122
b) 132
c) 142
d) 152

5. Add 58 and 36. Use a transformation to find the sum.
a) 94
b) 93
c) 90
d) 99

Division Using Area Models

1. Divide 24 by 4 using an area model.
a) 6
b) 66
c) 5
d) 16

2. Use an area model to divide 36 by 6.
a) 16
b) 6
c) 66
d) 166

3. Divide 56 by 8 using an area model.
a) 1
b) 6
c) 7
d) 2

4. Use an area model to divide 45 by 5.
a) 9
b) 6
c) 3
d) 5

5. Divide 72 by 9 using an area model.
a) 2
b) 8
c) 4
d) 6

Order of Operations

1. What is the result of 8+2×58+2×5?
a) 18
b) 19
c) 20
d) 21

2. Calculate (6+4)×3.
a) 20
b) 30
c) 40
d) 50

3. What is the value of 12÷4+7?
a) 11
b) 20
c) 31
d) 10

4. Solve 15−(3+2)×4.
a) 55
b) 50
c) 15
d) 5

5. Find the result of 9+6×(5−3).
a) 31
b) 11
c) 21
d) 41

Multiplication

Multiplying using square models

1. Multiply 4 by 5 using a square model.
a) 10
b) 30
c) 20
d) 40

2. Use a square model to find the product of 6 and 7.
a) 22
b) 42
c) 32
d) 52

3. What is the result of multiplying 8 by 3 using a square model?
a) 12
b) 32
c) 24
d) 56

4. Find the product of 9 and 4 using a square model.
a) 56
b) 36
c) 12
d) 33

5. Multiply 5 by 6 using a square model.
a) 10
b) 20
c) 30
d) 40

Multiplying fractions and whole numbers using expanded form

1. Multiply 3/4 by 6 using the expanded form.
a) 9/2 or 4.5
b) 9/2 or 4.9
c) 19/2 or 4.5
d) 7/2 or 4.5

2. Calculate 5/8 × 4 using expanded form.
a) 20/1 or 2.5
b) 20/8 or 2.5
c) 20/9 or 2.5
d) 20/1 or 2.1

3. Multiply 2/3 by 9 using the expanded form.
a) 7
b) 6
c) 6/3
d) 18/3

4. What is 7/10 × 5 using expanded form?
a) 35/10 or 3.5
b) 35/11 or 3.5
c) 25/10 or 3.5
d) 35/10 or 4.5

5. Find the product of 4/5 and 8 using the expanded form.
a) 32/5 or 6.4
b) 33/5 or 6.4
c) 32/5 or 6.0
d) 32/3 or 6.4

Multiplying fractions using a number line

1. Multiply 2/3 by 3/4 using a number line.
1. 3/4
2. 1/3
3. 1/2
4. 1/4

2. Calculate 3/5 multiplied by 2/3 using a number line.
1. 1/5
2. 1/9
3. 1/3
4. 1/4

3. Find 4/7 multiplied by 1/2 using a number line.
1. 2/7
2. 3/7
3. 2/7
4. 5/7

4. What is 5/8 multiplied by 3/4 using a number line?
1. 15/32
2. 5/4
3. 11/8
4. 8/4

5. Multiply 7/10 by 2/5 using a number line.
1. 10/5
2. 7/5
3. 2/10
4. 7/25

Answer Key

Here are the answer keys for Year 6 Maths Questions 2024: 50 Practice Problems 

Numbers & Place Value

Place Value

1. a) 7,000 (The digit 7 is in the thousands place.)
2. a) Three million, two hundred five thousand, six hundred seventy-eight.
3. c) 0.4 (The digit 4 is in the tenth place.)
4. c) 2 (The digit 2 is in the hundreds place.)
5. d) 5,958 (The digit 4 in the tens place increases by 10, changing it to 5.)

Word form to Standard form

1. a) 473,891
2. c) 2,050,312
3. b) 764,209
4. b) 5,146,300
5. d) 9,284

Standard form to Expanded form

1. c) 4,000 + 500 + 70 + 2
2. a) 80,000 + 3,000 + 200 + 0 + 9
3. d) 6,000 + 400 + 30 + 1
4. a) 50,000 + 2,000 + 0 + 40 + 8
5. b) 100,000 + 0 + 9,000 + 300 + 0 + 5

Decimals

1. d) 1.2
2. a) 4.7
3. b) 1.6
4. c) 4.2
5. c) 8

Arithmetic

Adding and subtracting whole numbers by transformation

1. d) 112
Transformation: Adding 60 (65 + 60 = 125) and then subtracting 13 (125 – 13 = 112).

2. a) 127
Transformation: Add 100 to 123 (123 + 100 = 223) and then subtract 223 from 250 (250 – 223 = 27).

3. b) 113
Transformation: Add 30 to 84 (84 + 30 = 114) and then subtract 1 (114 – 1 = 113).

4. d) 152
Transformation: Subtract 50 from 200 (200 – 50 = 150) and then add 2 (150 + 2 = 152).

5. a) 94
Transformation: Add 60 to 58 (58 + 60 = 118) and then subtract 24 (118 – 24 = 94).

Division Using Area Models

1. a) 6
Area Model: Draw a rectangle divided into 4 equal parts, with a total area of 24 square units. Each part has an area of 6 square units (24 ÷ 4 = 6).

2. b) 6
Area Model: Draw a rectangle with a total area of 36 square units and divide it into 6 equal parts. Each part has an area of 6 square units (36 ÷ 6 = 6).

3. c) 7
Area Model: Draw a rectangle with a total area of 56 square units and divide it into 8 equal parts. Each part has an area of 7 square units (56 ÷ 8 = 7).

4. a) 9
Area Model: Draw a rectangle with a total area of 45 square units and divide it into 5 equal parts. Each part has an area of 9 square units (45 ÷ 5 = 9).

5. b) 8
Area Model: Draw a rectangle with a total area of 72 square units and divide it into 9 equal parts. Each part has an area of 8 square units (72 ÷ 9 = 8).

Order of Operations

1. a) 18
Explanation: According to the order of operations, you should perform multiplication before addition. So, 2×5=102×5=10, then 8+10=188+10=18.

2. b) 30
Explanation: Operate the parentheses first: 6+4=106+4=10. Then multiply by 3: 10×3=3010×3=30.

3. d) 10
Explanation: Perform the division before addition. So, 12÷4=312÷4=3, then 3+7=103+7=10.

4. d) 5
Explanation: First, perform the operations inside the parentheses: 3+2=53+2=5. Then multiply by 4: 5×4=205×4=20. Finally, subtract from 15: 15−20=−515−20=−5.

5. c) 21
Explanation: Start by solving inside the parentheses: 5−3=25−3=2. Then multiply by 6: 6×2=126×2=12. Finally, add 9: 9+12=219+12=21.

Multiplication

Multiplying using square models

1. c) 20
Explanation: Draw a square model with 4 rows and 5 columns. Count the total number of squares: 4×5=204×5=20.

2. b) 42
Explanation: Draw a square model with 6 rows and 7 columns. Count the total number of squares: 6×7=426×7=42.

3. c) 24
Explanation: Draw a square model with 8 rows and 3 columns. Count the total number of squares: 8×3=248×3=24.

4. b) 36
Explanation: Draw a square model with 9 rows and 4 columns. Count the total number of squares: 9×4=369×4=36.

5. c) 30
Explanation: Draw a square model with 5 rows and 6 columns. Count the total number of squares: 5×6=305×6=30.

Multiplying fractions and whole numbers using expanded form

1. a) 9/2 or 4.5
Explanation: Expand 3/4 × 6 as 3 × 6/4. Multiply the numerator: 3 × 6 = 18, then divide by 4: 18/4 = 4.5.

2. b) 20/8 or 2.5
Explanation: Expand 5/8 × 4 as 5 × 4/8. Multiply the numerator: 5 × 4 = 20, then divide by 8: 20/8 = 2.5.

3. b) 6
Explanation: Expand 2/3 × 9 as 2 × 9/3. Multiply the numerator: 2 × 9 = 18, then divide by 3: 18/3 = 6.

4. a) 35/10 or 3.5
Explanation: Expand 7/10 × 5 as 7 × 5/10. Multiply the numerator: 7 × 5 = 35, then divide by 10: 35/10 = 3.5.

5. a) 32/5 or 6.4
Explanation: Expand 4/5 × 8 as 4 × 8/5. Multiply the numerator: 4 × 8 = 32, then divide by 5: 32/5 = 6.4.

Multiplying fractions using a number line

1. c) 1/2
Explanation: On a number line, mark 2/3 and divide it into 4 equal parts to represent 3/4 of 2/3. The result is 1/2.

2. a) 1/5
Explanation: Mark 3/5 on a number line and divide it into 3 equal parts to represent 2/3 of 3/5. The result is 1/5.

3. c) 2/7
Explanation: On a number line, mark 4/7 and divide it into 2 equal parts to represent 1/2 of 4/7. The result is 2/7.

4. a) 15/32
Explanation: Mark 5/8 on a number line and divide it into 4 equal parts to represent 3/4 of 5/8. The result is 15/32.

5. d) 7/25
Explanation: Mark 7/10 on a number line and divide it into 5 equal parts to represent 2/5 of 7/10. The result is 7/25.

Need Extra Help? Boost Your Child’s Confidence with Expert Tutoring Services

At Dr. Study Tutoring, we understand that Year 6 maths can be challenging, but we’re here to help your child succeed. Our personalised maths tutoring services are designed to make a significant difference in your child’s understanding of maths.

Our services focus on key areas to ensure your child’s success:

• Customised Tutoring Sessions: Our experienced tutors provide one-on-one support, focusing on areas where your child needs the most help, whether it’s mastering fractions or acing algebra.
  
• Personalised Learning Plans: Each student receives a personalised learning plan that targets their specific needs, ensuring they gain the skills and confidence required to succeed.
  
• Flexible Scheduling: We offer flexible scheduling options to fit your family’s routine, making it easier for your child to get the help they need without disrupting their other activities.
  
• Comprehensive Support: Our maths tutoring covers a wide range of maths topics, ensuring your child builds a strong foundation and stays ahead in their studies.
  
• Interactive Environment: We use engaging and interactive methods to keep your child motivated and make learning maths a positive experience.

By choosing Dr. Study Tutoring, you can be confident that your child will not only overcome their challenges in Year 6 maths but will also be well-prepared for future academic success.

Frequently Asked Questions (FAQs)

Let’s go over some frequently asked questions by parents on Year 6 Maths Questions:

Conclusion

Year 6 is a crucial stage in a child’s educational journey, marking the transition from primary to secondary school. During this pivotal year, students build on foundational maths skills and are introduced to more complex concepts that will be essential for their future studies. 

By practising these 50 Year 6 maths questions, your child has the opportunity to reinforce their understanding and gain confidence in their abilities. This consistent practice helps solidify their knowledge, ensuring they are well-prepared for the more challenging mathematics they will encounter in secondary school.

Ready to give your child the support they need to excel in Year 2 maths? 

Book a free online assessment with Dr. Study Tutoring today and discover how our expert tutors can help your child achieve their full potential.

Author

Dr. Olga Abeysekera

Dr Olga Abeysekera, founder of Dr Study Tutoring and the Dr Progress Group Pty Ltd, is passionate about transforming education through innovative and personalised tutoring. With a PhD in Management from Monash University and a background in both academic research and private tutoring, she has a deep commitment to helping students excel.
Her holistic approach at Dr Study Tutoring emphasises not only academic success but also the development of lifelong skills, ensuring that each student receives the best education and support possible. Dr Olga’s dedication to continuous improvement drives her mission to inspire a love for learning that lasts a lifetime.

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