Counting Together

Title: Counting Together
Current Content:

Learning Objectives

• Understand and demonstrate simple addition facts up to 20, including doubles and related subtraction facts, building on prior knowledge.
• Use concrete materials such as PV (place value) blocks, counters, and 10s frames to model addition problems and connect symbols and equations with practical problems
• Explain addition as ‘joining’ or ‘adding on’ using correct mathematical vocabulary such as “add”, “plus”, and “join”
• Solve word problems involving addition within 20 in contexts relevant to their everyday life
• Estimate and check addition results using mental strategies (reasonableness, known facts) with guidance
• Develop fluency with addition facts through hands-on activities and games
• Understand the concept of place value in addition by connecting single-digit addition to tens and ones addition (e.g., if 2 + 3 = 5, then 20 + 30 = 50) using PV blocks and visual aids

Curriculum Links

• Number Knowledge and Strategies (Level 2, Year 3) from the New Zealand Curriculum Refresh:
  • Recall addition facts to 20, and connect to subtraction facts (families of facts, doubles, halves)
  • Use materials to explore addition and subtraction
  • Solve problems using addition and subtraction up to 100 (start unknown, change, result)
  • Connect symbols and equations to practical problems
• Key Competencies: Thinking, Participating and Contributing, Relating to Others (shared group activities for learning)

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Resources Needed

• PV blocks, counting cubes, or multilink cubes (sets of ~20 cubes per student set)
• 10s frames printable or magnetic boards
• Counters or small objects (e.g., blocks, counters)
• A whiteboard and markers
• Flashcards with addition problems up to 20
• Everyday life context items (toy groceries, fruit images, play money)
• Worksheets with number sentences and blank spaces for answers
• A set of story/word problem cards connected to everyday life contexts (shopping, sharing fruit, etc.)
• Tens and ones charts or place value mats for visualizing tens and ones

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Lesson Breakdown (60 minutes)

Introduction & Warm-up (10 minutes)

• Begin with a discussion: “Can you think of times when you add things together in real life?” (e.g., putting apples in a basket, counting toys)
• Introduce the concept of addition as joining or adding more.
• Use simple, relatable examples (e.g., “I have 3 apples, and my friend gives me 4 more — how many apples do I have now?”)
• Quick mental math warm-up: Show several flashcards with addition facts to 10 for rapid recall practice.
• Emphasise correct vocabulary: add, plus, total, count on.

Activity 1: Hands-On Addition Using Counters & PV Blocks (15 minutes)

• Divide students into small groups (4-5 per group with shared materials).
• Task: Using counters and PV blocks, model addition problems like 7 + 8 or 9 + 6.
• Encourage students to ‘join’ two groups of objects physically, then count the total.
• Use 10s frames to visualise numbers and facilitate ‘making ten’ strategies.
• Teacher circulates asking groups to explain their thinking, use correct terms, and represent the equation (e.g., 7 + 8 = 15).
• Link physical addition to horizontal number sentences.

Activity 2: Understanding Place Value in Addition (10 minutes)

• Teaching Point: Explain that addition works the same way with tens as it does with ones. If 2 + 3 = 5, then 20 + 30 = 50 because 20 is 2 tens and 30 is 3 tens.
• Use PV blocks to show 2 single cubes plus 3 single cubes equals 5 cubes. Then show 2 ten-blocks plus 3 ten-blocks equals 5 ten-blocks (50).
• Display a tens and ones chart or place value mat to visually separate tens and ones.
• Guided example: Write on the board “2 + 3 = 5” and then “20 + 30 = 50” and explain how the place value changes the number but the addition concept is the same.
• Provide example problems for students to model with PV blocks and place value charts:
  • 4 + 5 and 40 + 50
  • 3 + 6 and 30 + 60
• Ask students to explain the connection between the single-digit addition and the tens addition using the materials and charts.
• Emphasise correct vocabulary: tens, ones, place value, add, plus, equals.

Activity 3: Real-Life Context Addition Problems (15 minutes)

• Use play money or grocery items to create story problems, e.g., “You have $5; you earn $7 more. How much do you have now?”
• Students work in pairs taking turns creating their own addition stories and solving.
• Encourage use of drawings or materials to show their thinking.
• Guide them to write and say the addition equations.
• Share examples aloud as a class for peer learning.

Activity 4: Number Sentence Game (10 minutes)

• Play a group game where students solve addition facts up to 20 on flashcards.
• Students write answers on mini-whiteboards or say them aloud quickly.
• Vary difficulty, starting with known facts and moving to slightly larger numbers (e.g., 12 + 6).
• Highlight strategies: counting on, making tens, doubles (4+4), and commutative property (5 + 9 = 9 + 5).
• Reinforce fluency and confidence.

Consolidation and Reflection (10 minutes)

• Review key language: add, plus, total, equals, join, plus sign (+), equals sign (=), tens, ones, place value.
• Use a word problem from earlier and solve it as a class on the whiteboard using PV blocks and number lines.
• Invite students to explain the steps in their own words.
• Discuss how addition helps solve real-life problems.
• Quick individual exit task: Write one addition sentence that matches a story they make up.

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Assessment Ideas

• Formative observation during group activities: note students’ ability to model addition physically, use vocabulary appropriately, and write correct number sentences.
• Check mental recall of simple facts with flashcard rounds.
• Collect exit tasks to assess individual understanding of addition sentences in everyday contexts.
• Ask students to explain strategies used verbally for solving addition problems, including place value understanding.
• Use a few written word problems as an informal quiz in the next lesson for progress monitoring.

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Teaching Considerations

• Differentiate by providing extra support with more hands-on materials for students needing concrete representations.
• Challenge rapid recallers with addition facts up to 20 and related subtraction facts.
• Use think-aloud strategies to model efficient addition strategies for all students.
• Encourage cooperative learning and talk in pairs to build communication skills and deepen understanding.
• Link learning to students’ cultural and community contexts for relevance and engagement.

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This lesson plan is tightly aligned with the New Zealand Curriculum Refresh (Te Mātaiaho Mathematics and Statistics phase 1, Years 2-3) focusing on number operations and practical problem solving with addition, emphasising hands-on materials, everyday contexts, place value understanding, and fluency with facts.