Fact Families

Overview

In this lesson (Lesson 1 of 7), students build two-digit fact families using hands-on materials. They investigate how addition and subtraction are related when the same numbers are used in different equations.

Learning intentions

• Students will explore how subtraction is the inverse of addition in a two-digit fact family.
• Students will represent related equations using the same three numbers.
• Students will use efficient strategies (counting on/back, or known facts) to solve equations.
• Students will create and explain a fact family set using appropriate mathematical language.

Success criteria

• I can write three related equations in a two-digit fact family using the same three numbers.
• I can explain (using words or drawings) how the subtraction answers connect to the addition equation.
• I can solve two-digit addition and subtraction problems using a chosen strategy.
• I can check my fact family by comparing the numbers in each equation.

Curriculum links

• Number and Algebra: develop understanding of addition and subtraction and solve problems using efficient strategies.
  • AC9M2A02
  • AC9M2N04
  • AC9M2N06
  • AC9M3A01
  • AC9M3A02
  • AC9M4N06
  • AC9M4A01
• Number and Algebra: use representations to model and connect addition and subtraction relationships.
  • AC9M2A02
  • AC9M2N04
  • AC9M2N06
  • AC9M3A01
  • AC9M3A02
  • AC9M4N06
  • AC9M4A01
• General capabilities: Critical and Creative Thinking (reason about relationships), Personal and Social Capability (work respectfully in a group), Digital Literacy (optional later for recording, if used).
  • AC9M2A02
  • AC9M2N04
  • AC9M2N06
  • AC9M3A01
  • AC9M3A02
  • AC9M4N06
  • AC9M4A01
• Cross-curriculum priorities: Sustainability and Asia & Australia’s Engagement with Asia (embedded through short, real-world contexts like budgeting or counting items for a community event).
  • AC9M2A02
  • AC9M2N04
  • AC9M2N06
  • AC9M3A01
  • AC9M3A02
  • AC9M4N06
  • AC9M4A01

Lesson structure (45 minutes)

1. 0–5 min | Hook: “Same numbers, different jobs” Show the introduction slides. Display one set of three numbers (e.g., 23, 45, 68). Ask: “How could these same numbers appear in an addition and two subtraction equations?” Students discuss with a partner, then share one idea.

2. 5–12 min | Mini-teach: what is a fact family? Use the introduction slides to model a fact family with equations written under a visual (bar/number bond style or fact-family “triangle”). Emphasise:

• Addition combines two parts to make a whole.
• Subtraction finds a missing part, using the same whole and one part. Use inverse language simply: “If you know the addition, subtraction can reverse it.”

3. 12–20 min | Hands-on build: make the fact family Give each group materials (place value blocks or base-10 bundles, or counters with tens and ones). Assign numbers in a fact family range appropriate for Year 2–4 (keep digits to two tens/ones totals; avoid very large complexity). Students build the whole with addition, then cover one part to show the missing number for subtraction. Teacher circulates and prompts: “Which part did you cover? What equation matches?”

4. 20–28 min | Write & check equations (teacher-guided) Return to the introduction slides for the “check” routine:

• Do the three equations use the same three numbers?
• Does the addition answer equal each subtraction’s starting whole? Students work at their desks (still in their small group). They write the three equations from their built model.

5. 28–38 min | Independent/paired task: fact family worksheet Distribute the photosynthesis labelling worksheet to pairs (each pair creates one fact family and solves the three equations). Include a short prompt: “Circle the whole number. Underline the parts.” Teacher uses a quick “show your thinking” strategy: students explain their subtraction link to their partner using sentence stems:

• “Because 23 + 45 = 68, I know 68 − 45 = 23.” For ADHD/Autism support, allow drawing/using materials for one extra equation if needed.

6. 38–43 min | Plenary: Fact family gallery Choose 3–4 student sets to display (on a board or document camera). Use the introduction slides to guide discussion: “Which equation is the ‘whole’? Which subtraction is removing part A? How do you know?” Students use thumbs-up/check to show whether the numbers match all three equations.

7. 43–45 min | Exit ticket: one true fact family On the same the photosynthesis labelling worksheet page (or a small bottom slip if preferred), students complete one missing equation so the fact family is correct. Collect as an exit check.

Resources

• the introduction slides (about 10 slides, hook + model + check routine + plenary prompts)
• the photosynthesis labelling worksheet (one-page fact family creation and solve)
• Place value blocks / base-10 bundles (tens and ones) OR tens-and-ones counters
• Mini whiteboards or scrap paper for equation checking
• Number cards for three-number fact families (teacher prepared)
• Sentence stems printed or on board (“Because…, I know…”)
• Timer and a simple group-work routine prompt card
• Display board/clipboard for “gallery” work

Assessment

• Observation checklist during hands-on build: students correctly link addition to subtraction (inverse reasoning).
• Worksheet evidence: three correct equations using the same three numbers, with correct answers.
• Exit ticket: one correct missing equation that confirms understanding of fact family structure.

Differentiation

• Support (ADHD/Autism): provide materials for the full first fact family; allow drawing; use sentence stems; reduce writing load by offering equation frames (e.g., __ + __ = __).
• Support (Year 2): use smaller two-digit numbers within a narrower range; include one partially completed fact family for scaffolding.
• Extension (Year 4): ask students to create a second fact family using the same whole, or to explain which subtraction corresponds to “remove tens” vs “remove ones” using their model.
• EAL/SEN: highlight key words on posters (“whole”, “part”, “missing”, “inverse”) and allow oral explanation before writing.