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Summative Assessment:

Written knowledge assessment.

Formative Assessment:

Engagement and participation during in-class learning and discussions.

Demonstration of understanding in individual and group activities.

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(2023). Mathematics - Year 4. Australian Curriculum V9. https://v9.australiancurriculum.edu.au/f-10-curriculum/learning-areas/mathematics/year-4?view=quick&detailed-content-descriptions=0&hide-ccp=0&hide-gc=0&side-by-side=1&strands-start-index=0

(2023). Mathematics, Year 5, Number, AC9M5N02. Australian Curriculum V9. https://v9.australiancurriculum.edu.au/f-10-curriculum/learning-areas/mathematics/year-5/content-description?subject-identifier=MATMATY5&content-description-code=AC9M5N02&load-extra-subject=MATMATY5&detailed-content-descriptions=0&hide-ccp=0&hide-gc=0&achievement-standard=a066c947-4913-4719-87a3-e193705dfe2f&side-by-side=1&strands-start-index=0&view=quick

Frey, N., & Fisher, D. (2007). Gradual Release of Responsibility Instructional Framework. ASCD: The Formative Assessment Action Plan. https://pdo.ascd.org/lmscourses/pd13oc005/media/formativeassessmentandccswithelaliteracymod_3-reading3.pdf

Pittaway, S., & Clarke, M. (2014). Marsh's Becoming a Teacher. Pearson Education Australia.

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Topic: Mathematics - Number: Multiples and Factors.

Year Level: Year Five.

Duration: Five lessons over one week.

Lesson Lengths: 50 minutes.

Learning Objective: During this unit of work, students will learn about the multiples and factors of whole numbers and understand how to identify, list and solve problems of multiples and factors.

Prior Learning: According to the Australian Curriculum V9 (2023), students will have an understanding of the following outcomes in relation to this unit:

AC9M4N05 - Students learn to 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.

AC9M4N06 - Students learn to develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder.

AC9M4A02 - Students learn to recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator.

Differentiation: The learning activities throughout the five sequenced lessons will cater for varying learning needs and abilities of all students. This includes clearly outlined higher and lower level resources, such as worksheets and online learning games. In addition, various learning tools and resources will be available for students to support their understanding and learning, including unifix blocks and scrap paper during the written knowledge assessment.

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Learning Intentions: We are learning about multiples.

Success Criteria: I can describe the term multiple. I can identify multiples of numbers.

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This Unit of Work focuses on multiples and factors for Year 5 students and stems from a focus on developing number sense and problem-solving skills. Using the Gradual Release of Responsibility Instructional Framework (Frey & Fisher, 2007), the lessons encourage scaffolding, differentiation, and hands-on learning, ensuring accessibility for all students. Following Marsh’s framework in Becoming a Teacher (2014), this unit supports active learning through structured, student-centered instruction, engaging students with practical activities and tools. Pittaway's emphasis on formative assessment guides the teacher in shaping the sequence to assess and respond to student needs, promoting a deep understanding of key mathematical concepts.

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Engage: (5 minutes). Follow the PowerPoint presentation. Introduce the topic of multiples to the students and explain the learning intentions and success criteria for the lesson. Watch the YouTube video titled 'Multiples' (King, 2019).

Teach: (10 minutes). Explain the concept of multiples by following the PowerPoint presentation slides:

What is a multiple?

How can you find a multiple?

Teacher modelling: What are the first 5 multiples of…

Model to the students how to find the first five multiples of a random whole number, demonstrating non-examples and mistakes throughout the process. Verbalise thought process and strategies out loud to students.

Ask students if they have any questions about multiples and ask them to give a thumbs up/neutral/down to show their understanding.

Practice: (15 minutes). Follow the PowerPoint presentation slides:

What are the first 5 multiples of each number?

Give the students an opportunity to practice as a group how to identify multiples of various numbers. Allow students to raise hands with ideas or answers and work collaboratively to find the multiples. Ensure to question, model and think out loud to scaffold the students understanding.

Group Activity…

Explain this activity - students will pair up with the peer next to them and will require a scrap piece of paper and a pencil. Students will select their own whole number (a number that hasn't been previously used) and will have to find as many multiples as they can in five minutes. At the end, ask each group to share how many multiples they found and if they identified any patterns.

Apply: (20 minutes). Students can apply their understandings of multiples and complete one worksheet:

Multiples Colouring in Mosaic (Higher level)

or

Multiples Odd One Out (Lower Level)

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Learning Intentions: We are learning about multiples.

Success Criteria: I can describe the term multiple. I can identify and list multiples of numbers.

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Learning Intentions: We are learning about factors.

Success Criteria: I can describe the term factor. I can identify factors of numbers.

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Learning Intentions: We are learning about factors.

Success Criteria: I can describe the term factor. I can identify and list factors of numbers.

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Learning Intentions: We are revising and assessing our learning and understanding about multiples and factors.

Success Criteria: I can describe the terms multiples and factors. I can identify, list and solve problems of multiples and factors.

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Engage: (5 minutes). Follow the PowerPoint presentation. Reintroduce the topic of multiples to the students and explain the learning intentions and success criteria for the lesson. Spend 3-4 minutes encouraging the students to brainstorm and write down their prior learning and knowledge of multiples.

Teach: (10 minutes). Reflect on the previous lesson by following the PowerPoint presentation slides:

Reflection... What is a multiple?

How can you find a multiple?

Teacher modelling: What are the first 5 multiples of…

Model to the students how to find the first five multiples of a random whole number, demonstrating non-examples and mistakes throughout the process. Verbalise thought process and strategies out loud to students.

Ask students if they have any questions about multiples and ask them to give a thumbs up/neutral/down to show their understanding.

Practice: (20 minutes). Follow the PowerPoint presentation slides:

What are the first 5 multiples of each number?

Give the students an opportunity to practice identifying and listing multiples of various numbers. Encourage students to raise hands with ideas or answers and work collaboratively to find the multiples, inviting students up to write their answers and demonstrate their working out on the board. Ensure to question, model and think out loud to scaffold the students understanding.

Group Activity…

Explain this activity - students will pair up and will require one Multiples Madness! worksheet, one dice and two coloured pencils between them. Students will take in turns to roll the dice and will need to shade in the box of every multiple from that number. Once all of the boxes are shaded in, the student with the most shaded boxes wins.

Apply: (15 minutes). Students can apply their understandings of multiples and play an online multiples game on laptops:

Mach 10 Multiples (Higher Level)

or

Meteor Multiplication (Lower Level)

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Engage: (5 minutes). Follow the PowerPoint presentation. Introduce the topic of factors to the students and explain the learning intentions and success criteria for the lesson. Watch the YouTube video titled 'Factors for the First Time' (Let's Do Math, 2015).

Teach: (10 minutes). Explain the concept of factors by following the PowerPoint presentation slides:

What is a factor?

How can I find factors?

How can I represent factors?

Teacher modelling: What are the factors of...

Model to the students how to find the factors of the listed whole numbers, demonstrating non-examples and mistakes throughout the process. Verbalise thought process and strategies out loud to students.

Ask students if they have any questions about factors and ask them to give a thumbs up/neutral/down to show their understanding.

Practice: (15 minutes). Follow the PowerPoint presentation slides:

Let's find some factors together...

Give the students an opportunity to practice as a group how to identify factors of various numbers. Allow students to raise hands with ideas or answers and work collaboratively to find the factors. Ensure to question, model and think out loud to scaffold the students understanding.

Group Activity…

Explain this activity - students will pair up with the peer next to them and will require a scrap piece of paper and a pencil.

Students will work together to find as many factors as they can of the following numbers: 8, 14, 26 and 50 in five minutes. At the end, ask each group to share how many factors they found.

Apply: (20 minutes). Students can apply their understandings of multiples and complete one worksheet:

Factor Flowers (Higher level)

or

Find the Factors (Lower Level)

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Engage: (5 minutes). Follow the PowerPoint presentation. Reintroduce the topic of factors to the students and explain the learning intentions and success criteria for the lesson. Spend 3-4 minutes encouraging the students to brainstorm and write down their prior learning and knowledge of factors.

Teach: (10 minutes). Reflect on the previous lesson by following the PowerPoint presentation slides:

Reflection... What is a factor?

How can I find factors?

How can I represent factors?

Introduce factor pairs to students.

Ask students if they have any questions about factors and ask them to give a thumbs up/neutral/down to show their understanding.

Practice: (20 minutes). Follow the PowerPoint presentation slides:

Let's find some factors together...

Give the students an opportunity to practice identifying and listing factors of various numbers. Encourage students to raise hands with ideas or answers and work collaboratively to find the factors, inviting students up to write their answers and demonstrate their working out on the board. Ensure to question, model and think out loud to scaffold the students understanding.

Challenge!

Explain this activity - Students will pair up and will have 10 minutes to find all the factors listed on the slide. At the end, ask each group to share how many factors they found and to share what strategies they used to find the factors.

Apply: (15 minutes). Students can apply their understandings of multiples and play an online multiples game on laptops:

Maths Lines Multiplication (Higher Level)

or

Factor Pair Up (Lower Level)

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Engage: (10 minutes). Follow the PowerPoint presentation. Explain the learning intentions and success criteria for the lesson. Tune in with a YouTube video titled 'Multiples and Factors Song' (Adam Up Maths, 2022). Reflect and brainstorm prior learning of multiples and factors.

Teach/Practice: (10 minutes). Introduce word problems in relation to multiples and factors by follow the PowerPoint presentation:

Let's practice a word problem...

Model to the students how to answer the word problem question, demonstrating non-examples and mistakes throughout the process. Verbalise thought process and strategies out loud to students.

Ask students if they have any questions about multiples and ask them to give a thumbs up/neutral/down to show their understanding.

Apply: (30 minutes). Explain to students the expectations, tools and criteria of the assessment, for example:

•You will now be completing an assessment on multiples and factors.

•You will have the remainder of the lesson to complete your assessment.

•This is an individual and silent task at your desks.

•Unifix blocks are available at the front if you require.

•When you are finished, please bring your assessment to Miss Jemma and you can log onto maths prodigy.

Students may commence their assessment task.

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Multiples Lesson One PowerPoint

Multiples Colouring in Mosaics worksheet

Multiples Odd One Out worksheet

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Multiples Lesson Two Powerpoint

Multiples Madness! worksheet

Student laptops

Online multiples game links: Mach 10 Multiples (Higher level) https://www.mathplayground.com/mach_10_multiples.html or Meteor Multiplication (Lower level) https://www.mathplayground.com/ASB_MeteorMultiplication.html

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Australian Curriculum V9 (2023) Connections:

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Australian Curriculum V9 (2023) Connections:

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Content Descriptors: AC9M5N02 - Students learn to express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another.

General Capabilities: Numeracy: Number sense and algebra - Multiplicative strategies.

Cross Curriculum Priorities: N/A.

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Factors Lesson One Powerpoint

Factor Flowers worksheet

Find the Factors worksheet

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Factors Lesson Two PowerPoint

Student laptops

Online factors game links: Maths Lines Multiplication (Higher Level) https://www.mathplayground.com/math_lines_multiplication.html

or Factor Pair Up (Lower Level) https://www.mathplayground.com/factor_pair_up.html

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[Brian King]. (2019, November 14). Multiples eLearning Video Math Lesson for Kids [Video]. YouTube. https://www.youtube.com/watch?v=W0rnv6MeoTo

Smith, J. (2024). Multiples Colouring in Mosaic. [Unpublished Assessment Submitted for EPE211].

Smith, J. (2024). Multiples Odd One Out. [Unpublished Assessment Submitted for EPE211].

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(2024). Math Games. Math Playground. https://www.mathplayground.com/

Smith, J. (2024). Multiples Madness. [Unpublished Assessment Submitted for EPE211].

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[Let's Do Math]. (2015, September 23). Factors for the First Time [Video]. YouTube. https://www.youtube.com/watch?v=yJ-T8z2-Zg4

Smith, J. (2024). Factor Flowers. [Unpublished Assessment Submitted for EPE211].

Smith, J. (2024). Find the Factors. [Unpublished Assessment Submitted for EPE211].

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(2024). Math Games. Math Playground. https://www.mathplayground.com/

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[Adam Up Maths]. (2022, September 27). Multiples and Factors Song [Video]. YouTube. https://www.youtube.com/watch?v=JSHqhzpM-As

Smith, J. (2024). Multiples and Factors Assessment. [Unpublished Assessment Submitted for EPE211].

Smith, J. (2024). Assessment Task - Rubric. [Unpublished Assessment Submitted for EPE211].

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Smith, J. (2024). Assessment Task - Rubric. [Unpublished Assessment Submitted for EPE211].

Smith, J. (2024). Multiples and Factors Assessment. [Unpublished Assessment Submitted for EPE211].

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Multiples & Factors (Revision & Assessment) PowerPoint

Multiples & Factors Written Knowledge Assessment

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Multiples and Factors (Revision and Assessment) PowerPoint

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Multiples and Factors (Revision and Assessment) PowerPoint

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Multiples & Factors Written Knowledge Assessment

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Multiples & Factors Written Knowledge Assessment