Ten Times 10

A Bounded Differentiated Problem Exploring Multiplication by 10

Years 1 to 4

What really happens when we multiply by 10?

Ten Times 10 helps teachers develop students’ conceptual understanding of multiplication by 10 through mathematical investigation, reasoning, representation and proof.

Rather than simply applying familiar rules such as “add a zero” or “move the decimal point”, students investigate mathematical claims, test examples, represent their thinking, and justify whether a rule is always true.

Ten Times 10 is a hands-on bounded differentiated investigation that invites students to explore the structure and patterns of multiplication by 10 through purposeful investigation. A bounded differentiated investigation is a worthwhile mathematical experience with intentional supports, constraints and extensions that reveal student thinking. Rather than creating multiple tasks for different learners, all students engage with the same rich mathematical investigation while accessing it at an appropriate level of challenge.

Using concrete materials, drawings, arrays, place-value representations, equations and mathematical language, learners investigate what happens when a number is multiplied by 10. Students explore the relationship between multiplication by 10 and place value, investigate one tenth and 10 × one tenth, and test whether common rules about multiplying by 10 are always true. As the learning progresses, students move beyond identifying patterns to proving mathematical ideas, justifying their reasoning and making generalisations across ×10, ×100, ×1,000 and ×10,000.

Rather than providing another worksheet to practise multiplication by 10, this resource encourages students to think like mathematicians. Learners investigate whether mathematical rules are always true, communicate their reasoning, use evidence to support their conclusions, and deepen their conceptual understanding through purposeful discussion and problem-solving. The built-in supports, constraints and extensions allow every learner to access the same worthwhile mathematical investigation while making their thinking visible for assessment and responsive teaching.

Curriculum Connection

Australian Curriculum v9 — Year 4 Mathematics

AC9M4NO5: solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits

The investigation provides opportunities for students to develop place-value understanding while reasoning, representing, testing mathematical claims and justifying conclusions.

This resource includes:

• Editable PowerPoint lesson presentation
• Learning intention and success criteria
• Bounded differentiated investigation for Years 1–4
• Let’s Go, Strive for Success and Mathematician prompts
• Printable task cards
• Reflection and discussion prompts
• Student self-assessment tool
• Teacher notes
• Responsive teaching ideas, extension opportunities and common misconceptions
• Australian Curriculum Version 9 aligned materials

Students will:

• Investigate whether mathematical rules about multiplying by 10 are always true.
• Explore what happens when a number is multiplied by 10.
• Represent multiplication by 10 using concrete materials, drawings, arrays, place-value representations and equations.
• Explore what one tenth means and represent 10 × one tenth in different ways.
• Test mathematical ideas using multiple examples and evidence.
• Identify when a mathematical claim is sometimes true and when it is always true.
• Use examples and counterexamples to investigate mathematical rules.
• Extend their thinking to multiplication by 10, 100, 1,000 and 10,000.
• Identify and explain common place-value patterns.
• Prove and justify their mathematical thinking.
• Develop reasoning, generalisation and mathematical communication through investigation.

Perfect for:

• Years 1 to 4 classrooms
• Multiplication and place-value units
• Rich mathematical investigations
• Differentiated mathematics instruction
• Bounded problem-solving experiences
• Formative assessment opportunities
• Small-group support and extension
• Developing mathematical reasoning, problem-solving and communication

This resource promotes conceptual understanding, reasoning, problem-solving and mathematical communication through purposeful investigation of what multiplication by powers of 10 really means, helping students move beyond rules and shortcuts towards understanding the place-value structure that makes the mathematics work.