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Lesson 1: Embedding Multiples of 7 and 9

Learning Objective (LO)

• To recognise and identify multiples of 7 and 9 in everyday contexts.
  (National Curriculum ref: Number - Multiples, factors and primes – KS3 Maths Programme of Study)

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Personalisation

Start by asking:

• “Can you think of anything in your day that comes in sevens or nines? For example, days of the week or items in groups?”
  Connect answers to familiar experiences, e.g., "There are 7 days in one week, so that’s a multiple of 7!"

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Recap

• Review what a multiple is:
  “A multiple of a number is what you get when you multiply that number by a whole number.”
• Use examples from previous lessons (multiples of 2, 3, and 5).
• Write multiples of 7 and 9 up to 63 and 81 on the board.
• Ask students to touch their heads when they hear a multiple of 7, and tap their desks when they hear a multiple of 9 (auditory and kinaesthetic engagement).

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Introduce

• Introduce multiples of 7 and 9 with simple, clear visuals:
  Show a number line highlighting multiples of 7 (7, 14, 21...) and 9 (9, 18, 27...)
• Explain: “Today, we will look for multiples of 7 and 9 in everyday situations.”

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Model

• Demonstrate with functional life examples:
  • Counting 7 apples in a pack, how many apples in 3 packs? (7 x 3 = 21)
  • Seats arranged in rows of 9 in a cinema, how many seats in 4 rows? (9 x 4 = 36)
• Model writing and reading these calculations aloud.
• Use number cards to build multiples together visually.

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Practice

• In pairs with TA support, students work on functional problems:

  1. “A box has 7 chocolates. How many chocolates in 5 boxes?”
  2. “There are 9 pencils in a pack. If you have 2 packs, how many pencils do you have?”
     Use counters or pictures if needed.

• TA guides students to read the questions and helps with recording answers with simple sentence starters:
  “7 times 2 is ___.”
  “9 times 3 is ___.”

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Apply

• Real-world sorting activity:
  Provide pictures/cards of items grouped in 7s and 9s (e.g., buses with 7 seats, posters with 9 pictures).
  Students sort cards into “Multiple of 7” and “Multiple of 9” piles with support.

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Challenge

• Encourage “thinking outside the box” by asking:
  “Can you find other multiples of 7 or 9 if we double or triple the packs?”
• Introduce simple word problems such as:
  “If there are 7 candies in one bag, how many candies are there in 6 bags?”
• For more advanced students, introduce concept of common multiples:
  “What is the smallest number that is a multiple of both 7 and 9?”

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Resources

• Number lines (large and colour-coded)
• Counters and/or small objects (buttons, blocks)
• Packs/cards with pictures representing multiples of 7 and 9
• Sentence starter sheets
• Whiteboards and markers

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Key Vocabulary

• Multiple, times, packs, groups, total, times table, number line

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Deployment of Staff

• Teacher: Leads introduction, models problem solving, monitors group work and provides prompts during practice and apply stages.
• TA: Supports individual and pairs during practice and apply, helps with reading and writing responses, provides reassurance and scaffolding for learners.

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Notes for Teachers

• Use visual aids and multisensory learning to reinforce understanding.
• Keep instructions clear, concise, avoid abstract language.
• Ensure routine and predictability through consistent lesson structure.
• Frequent positive reinforcement is essential to build confidence.

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Multiples Practice

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Lesson 2: Recognising and Writing Multiples of 7 and 9

Learning Objective (LO)

• To read, write and identify multiples of 7 and 9 within 100.
  (National Curriculum ref: Number - Multiples, factors and primes – KS3 Maths Programme of Study)

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Personalisation

Begin by reviewing what was learnt yesterday. Ask students:

• “Can you show me a multiple of 7 with your fingers?”
• “What about a multiple of 9?”
  Use their responses as a warm-up.

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Recap

• Quick oral recall of multiples of 7 and 9 (using number line or flashcards).
• Reiterate what a multiple means; reinforce the connection to times tables.

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Introduce

• Demonstrate writing multiples on individual whiteboards:
  Show “7, 14, __, 28...” and prompt students to fill in the missing multiples.
  Repeat with multiples of 9.

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Model

• Show how to write a simple functional question:
  “James has 7 biscuits in one pack. He buys 3 packs. How many biscuits altogether?”
• Write the multiplication sentence and solve it orally.
• Present a matching “number sentence” to the word problem so students understand how to link text to numbers.

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Practice

• Worksheets with simple questions involving multiples of 7 and 9, e.g.:
  • "Circle all the multiples of 7 below: 5, 14, 18, 21, 28"
  • “Write the next 3 multiples of 9 after 45”
• Include pictures to connect to the question (e.g., 7 apples, 9 pencils).

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Apply

• Real-life role play:
  Create a ‘shop’ scenario where students buy items in packs of 7 or 9.
  Ask: “If you buy 4 packs of snacks with 7 items in each pack, how many will you have?”
  Use play money, counters or drawings.

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Challenge

• Explore missing number puzzles:
  “7 x __ = 42” or “9 x __ = 63”
• For advanced learners, introduce basic division with multiples, e.g.:
  “If Tom has 63 sweets and he puts them in packs of 9, how many packs does he have?”

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Resources

• Whiteboards and markers
• Worksheets with visuals and simple questions
• Counters or play items for role play
• Flashcards with multiples of 7 and 9

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Key Vocabulary

• Multiply, times, pack, total, equal, product, missing number

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Deployment of Staff

• Teacher: Leads instruction and models writing sentences and solving problems.
• TA: Supports reading and comprehension, encourages attempts, assists in role play.

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Multiples Application

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Lesson 3: Using Multiples of 7 and 9 in Everyday Contexts

Learning Objective (LO)

• To use multiples of 7 and 9 to solve functional real-world problems.
  (National Curriculum ref: Number - Multiples, factors and primes; Problem Solving and Reasoning – KS3 Maths Programme of Study)

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Personalisation

Discuss where students may see 7 and 9 in their life:

• Days in a week (7), fingers/thumbs on hands (5+2 fingers on feet?), number of seats in a row, sports teams, etc.

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Recap

• Quick review of multiples of 7 and 9 using a visual counting game.

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Introduce

• Present a simple problem on the board:
  “The sports coach has 7 cones in a set. How many cones are there in 6 sets?”
• Discuss question and possible steps to solve.

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Model

• Demonstrate breaking down problem:
  Multiply 7 x 6.
• Use objects to represent cones, count out 6 groups of 7.
• Write maths sentence and say the answer aloud clearly.

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Practice

• Functionally based questions relevant to students, for example:

  1. How many cupcakes if 7 cupcakes in each box and you have 5 boxes?
  2. There are 9 plates on one table. How many plates on 7 tables?

• Use drawings and physical objects to support understanding.

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Apply

• Group activity: students create their own practical problems involving multiples of 7 or 9 using objects provided.
• Each group shares their problem verbally with the rest of the class.

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Challenge

• For those advanced, introduce combining multiples:
  “If a pack has 7 sweets and another pack has 9 sweets, how many sweets in total if you have 2 packs of each?”
• Begin to explore addition of multiples and recording answers in sentence form.

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Resources

• Counters, cones or classroom objects
• Worksheets with picture-based problems
• Large display number sentences
• Blank cards for creating questions

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Key Vocabulary

• Multiply, groups, total, sets, packs, each, sum, problem

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Deployment of Staff

• Teacher: Guides problem-solving and supports explanation of maths sentences.
• TA: Supports learners in creating and sharing problems, offers reading support and helps manage materials.

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Multiples Consolidation

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Lesson 4: Consolidating Multiples through Practical Tasks

Learning Objective (LO)

• To consolidate understanding and recall of multiples of 7 and 9 through practical and sensory activities.
  (National Curriculum ref: Number - Recall multiplication facts, Problem Solving and Reasoning)

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Personalisation

Discuss which multiples have been easiest and hardest for each student, use this to encourage confidence.

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Recap

• Play a “Multiple Hunt” game: teacher calls a multiple of 7 or 9, students find that number on displayed charts or flashcards.

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Introduce

• Explain practical tasks for the session: using real items, students will count and sort multiples of 7 and 9.

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Model

• Show how to group objects in sevens or nines and count totals, modeling communication about their findings.

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Practice

• Sensory table: students handle beans or blocks in groups of 7 and 9, counting totals aloud or with prompts.
• Matching cards: match number sentences to pictures of grouped objects.

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Apply

• Tick chart: Students independently identify and tick which numbers in a sequence are multiples of 7 or 9.

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Challenge

• Introduce simple problem-solving with missing numbers:
  “I have ___ boxes of 7. Total sweets are 35. How many boxes do I have?”
• Encourage learners to use physical counters to check their answer.

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Resources

• Counters, blocks or beans
• Flashcards, worksheets, tick charts
• Visual number lines on display

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Key Vocabulary

• Multiple, group, count, total, number sentence, missing number

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Deployment of Staff

• Teacher: Facilitates group and independent work, assists with explanations.
• TA: Supports learners with sensory engagement and recording work.

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Multiples Extension

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Lesson 5: Extension and Problem Solving with Multiples

Learning Objective (LO)

• To deepen understanding of multiples through extension problems and introducing least common multiples (LCM) in an accessible way.
  (National Curriculum ref: Number - Understanding multiples, factors, and LCM – KS3)

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Personalisation

Begin with personal goal setting:
“What would you like to get better at with multiples?”

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Recap

• Recap multiples of 7 and 9 verbally with fun actions (clap on multiples of 7, stamp on multiples of 9).

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Introduce

• Introduce simple concept of common multiples:
  “Some numbers can be multiples of both 7 and 9.”
  Show example — 63 (7 x 9 and 9 x 7).

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Model

• Use a Venn diagram (overlapping circles) with multiples of 7 on one side and multiples of 9 on the other.
• Place common multiples in overlapping section with hands-on sorting cards.

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Practice

• Sorting game: Students sort a set of number cards into three piles: multiples of 7 only, multiples of 9 only, and multiples of both.
• Use sentence starters: “___ is a multiple of 7 because...”

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Apply

• Present simple word problems that involve both multiples:
  “If you have 7 apples and 9 oranges, and you get 7 more apples and 9 more oranges, how many do you have?”

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Challenge

• For advanced learners, explore predicting multiples by adding sequences, e.g.:
  “Start at 7 and add 7 each time: what are the first 5 multiples?”
• Introduce asking: “Is 45 a multiple of 7 or 9?”

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Resources

• Venn diagram posters
• Number cards (multiples of 7 and 9 up to 100)
• Sentence starter sheets
• Counters or physical objects

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Key Vocabulary

• Multiple, common multiple, both, sort, sequence

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Deployment of Staff

• Teacher: Introduces common multiples with visual aids, facilitates group discussion.
• TA: Assists learners with sorting activity, supports understanding of Venn diagrams and sentence construction.

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End of Week Overview:
This week’s lessons focus on embedding, consolidating, and extending understanding of multiples of 7 and 9 using a multi-sensory, practical approach tailored to students with autism and low reading levels. Functional maths contexts build real-life relevance and confidence in numeracy skills, fully aligned with the National Curriculum for KS3.