Subtraction Strategies

Overview

In this lesson (Lesson 4 of 10) students practise mental subtraction strategies, focusing on counting back and using a number line to support accurate calculation. They apply strategies to solve subtraction problems within their known number range.

Learning intentions

• Students will be able to use counting back to subtract a small number.
• Students will be able to use a number line to model subtraction and record working.
• Students will be able to choose an efficient strategy for a given subtraction problem.
• Students will explain their thinking using correct mathematical language (for example, “start at”, “count back”, “distance between numbers”).

Success criteria

• I can count back from the starting number to find the answer.
• I can use a number line to solve subtraction problems and check my result.
• I can describe which strategy I used and why it helps.

Curriculum links

• Number and Algebra: represent and calculate with whole numbers using efficient mental and written strategies.
• Number and Algebra: use counting strategies and apply them to subtraction situations.
• Measurement and Geometry / Algebraic thinking (through communication): explain and justify mathematical reasoning and representations.

Lesson structure (45 minutes)

1. (0–5 min) Warm-up: “Count Back Sprint” Teacher shows quick oral prompts (e.g., 12−3, 20−5). Students show answers with fingers or mini-whiteboards while practising counting back from the starting number. Teacher reinforces: “Start at the first number and count back.”

2. (5–12 min) Explicit teaching: Counting back Model two examples step-by-step:

• 14 − 2: start at 14, count back 2 (13, 12).
• 21 − 4: start at 21, count back 4 (20, 19, 18, 17). Students repeat chorally with the teacher, then independently for one example each.

3. (12–20 min) Guided practice: Number line meaning Draw a short number line on the board (e.g., 8 to 16 or 18 to 26 depending on class range). Model how subtraction becomes “move left”:

• 15 − 6: start at 15, jump left 6 steps to land on 9. Students come to the board to add the jumps (or teacher does for the class while students indicate each jump). Emphasise accurate “landing” on the correct number.

4. (20–28 min) Strategy choice: Sort and solve Provide 6 subtraction cards or task items (mix of facts and word problems). In pairs, students choose whether to use counting back or a number line. They must:

• Solve the problem
• Record a method (counting-back steps OR a number line with jumps)
• Write one sentence: “I chose ____ because ____.”

5. (28–36 min) Independent fluency: Number line stations Set up 3 short stations (about 2–3 minutes each, then rotate once):

• Station A: “Count back blanks” (students fill missing numbers in a counting-back sequence).
• Station B: “Jump left” (students draw a number line and mark jumps).
• Station C: “Check it” (students solve using their preferred method, then verify with the opposite method for one question). Teacher circulates with a focus on correct counting, correct direction on the number line, and clear explanations.

6. (36–42 min) Whole-class share: Compare strategies Invite a few students (or groups) to share how they solved one question. Teacher highlights differences: sometimes counting back is faster; sometimes the number line helps with larger jumps or tricky starting points.

7. (42–45 min) Exit ticket: One strategy, one explanation Students complete 2 subtraction questions on mini-whiteboards (or paper): one suited to counting back and one suited to a number line. They also add: “I used ____.” and one reason (“It helped me see how many steps.”).

Resources

• Mini-whiteboards, markers, and erasers
• Prepared subtraction cards and/or problem slides
• Number line templates (short range appropriate to class, e.g., 0–30 or 10–50)
• Student worksheet: strategy recording section (counting back OR number line)
• Coloured counters or Unifix cubes for modelling (optional)
• Timer for rotations and “sprint” warm-up
• Teacher visual examples (counting back steps; jump-left number line)
• Exit ticket slips

Assessment

• Formative checks during the warm-up and guided practice: observe counting accuracy and correct direction.
• During strategy choice and stations: review recorded methods and explanations for clarity and correctness.
• Exit ticket: confirm each student can solve using an appropriate strategy and justify it briefly.

Differentiation

• Support: provide a pre-drawn number line for students who need the structure; limit to subtraction with smaller numbers to practise confidence before larger jumps.
• Support: sentence starters for explanations (for example, “I started at ___ and counted back ___.” / “I moved left ___ steps.”).
• Extension: include subtraction where students compare two strategies (for example, “Which is faster: counting back or number line?”) and require an additional check.
• EAL/SEN: allow oral explanation first, then provide matching sentence frames and word banks for key phrases like “start at”, “count back”, “steps”, “landing number”.