Understanding Numbers

Overview

In this first lesson of the unit, students explore how place value helps them understand numbers, move along number lines, and use counting-on strategies. Students will represent numbers in partitions (hundreds, tens, ones) and connect those partitions to jumps on a number line.

Learning intentions

• Students will use place value to partition two- and three-digit numbers into hundreds, tens and ones.
• Students will represent numbers on a number line and describe what each jump means.
• Students will use counting strategies (counting on and regrouping by place value) to solve addition and subtraction without a calculator.
• Students will explain their thinking using number sentences, diagrams and words.

Success criteria

• I can partition a number into hundreds, tens and ones and write the parts.
• I can show a number on a number line and state how many jumps I made and why.
• I can use counting on to solve a number sentence and check if my answer makes sense.
• I can explain how place value helps me calculate efficiently.

Curriculum links

• Number — VC2M3N04: add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist calculations without a calculator.
• Number — VC2M3N04: use part-part-whole reasoning and the inverse relationship between addition and subtraction to solve problems.
• Number — VC2M3N04: choose place value partitions to help calculations (for example, partition and regroup for 485 + 365).
• Number — Number line and place value models support VC2M3N04 (use diagrams/models to assist calculations).

Lesson structure (60 minutes)

1. 0–5 min · Welcome and learning hook. Teacher writes: “What number is one more than 299? How do you know?” and shows two quick examples on the board. Students share strategies in pairs, then volunteer one explanation.

2. 5–15 min · Activate prior knowledge (place value). Teacher models partitioning using a place value chart (hundreds/tens/ones) with a 3-digit number (e.g., 238) and asks: “How many hundreds? Tens? Ones?” Students use counters or base-ten blocks to partition a number on their own mini-whiteboard, then check with a partner.

3. 15–25 min · Direct teach: number line moves. Teacher draws a number line segment from 200 to 320, labels key points (e.g., 200, 210, 220), and demonstrates a counting-on problem such as 214 + 30 by making three jumps of 10. Students follow, then complete a similar model: 206 + 20, describing “each jump is tens” in sentence starters.

4. 25–40 min · Guided practice: add using place value partitioning. Teacher writes a set of two calculations:

• 148 + 50
• 176 + 40 Teacher prompts partitioning (148 = 100 + 40 + 8) and then shows regrouping as needed (add tens to the tens part; ones stay the same). Students work in pairs at a place-value mat and number-line template, using counters to show partitions and then drawing their jumps on the number line. Teacher circulates, listening for correct language (hundreds/tens/ones, jumps, count on).

5. 40–50 min · Quick check: subtraction as the inverse. Teacher shows: “If 148 + 50 = 198, what is 198 − 50?” and highlights inverse thinking (undo the same tens). Students practise with one guided question: “200 − 30” using the same number line idea (three jumps back). Students hold up thumbs (1–3) to show confidence.

6. 50–58 min · Independent task: show and explain. Students complete 3 questions (teacher selects based on class readiness):

• Partition a 3-digit number (e.g., 325) into hundreds/tens/ones.
• Place a given number on a provided number line (choose a jump-based location).
• Solve one addition using counting-on by tens and one subtraction using inverse thinking. Students must write either a short explanation or a number sentence with a diagram.

7. 58–60 min · Exit ticket. Teacher asks students to answer: “Solve: 245 + 30. Show your counting-on jumps and explain using place value.” Students submit on paper or a mini-whiteboard.

Resources

• Place value mats (hundreds, tens, ones) for every student
• Base-ten blocks or counters
• Number line templates (e.g., 200–320 and 0–200 segments as needed)
• Mini-whiteboards and markers
• Teacher number line and place value chart (large)
• Student worksheet/exit ticket (3 questions)
• Sentence starter strips (e.g., “I counted on by… because…”)

Assessment

• Teacher observation during pair work: correct partitioning and clear counting-on language.
• Guided questioning checks at 15–25 min and 40–50 min (students can describe jump size and inverse relationship).
• Exit ticket: accuracy of the answer plus evidence of number-line jumps/place value explanation.

Differentiation

• Support:
• Provide sentence starters for explanations (“I partitioned…”, “Each jump is…”, “I counted on…”).
• Use partially completed number lines with only 10s marked first; later add 1s if ready.
• Offer a reduced set of calculations for students needing extra time.
• Extension (for advanced learners):
• Add a mixed problem requiring regrouping by place value (e.g., 248 + 70) and ask students to explain which part changes and why.
• Challenge students to create their own addition and subtraction pair that are inverses using a given number-line range.
• EAL considerations:
• Emphasise consistent terms: “hundreds”, “tens”, “ones”, “count on”, “jumps”.
• Allow oral explanations recorded by the teacher or using short written words.
• SEN considerations:
• Use tactile supports (base-ten blocks) and limit working memory by keeping the number line range small.
• Provide a checklist for success criteria (partition, place on line, explain).

Extension (optional)

• SKIP (not requested).