Math // Addition & Subtraction

Addition and subtraction strategies

Use counting on and counting back as strategies for addition and subtraction

Ages
6 to 7
Type
Method
Builds on
3 topics
Leads to
0 topics
Standards
1 code

Quick check

If the learner needs to work out '8 + 5', can they start from 8 and count up five more — rather than starting from 1 every time?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Add 8 + 3 by starting at 8 and counting on 3 (9, 10, 11)
  • Subtract 12 − 3 by counting back 3 from 12 (11, 10, 9)
  • Explain that counting on is a way to add

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

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Addition and subtraction strategies

Ages 6 to 7 // Method

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Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For ages 6–7, teach counting on for addition and counting back for subtraction as the efficiency step beyond counting-all. The core skills: start from the larger number (e.g. begin at 8 for 8+3), say the NEXT number as the first count ('9'), and track the number of steps so the start isn't miscounted. Best anchored on a visible number line/track where hops are seen and counted, then gradually replaced by known and derived facts. Target sums: 8+3=11 (count on), 12−3=9 (count back), 2+9 (start from the larger addend, 9).

Common misconceptions

  • Counting all from one instead of counting on from a number (a normal earlier stage).
  • Counting the starting number as the first step (8 + 3 → 8,9,10 = 10), an off-by-one error.
  • Counting on from the first-written number rather than the larger one, making more steps than needed.
  • Counting in the wrong direction for subtraction.
  • Over-relying on counting for facts that should become instant recall.

Useful representations

  • Number line / number track with hops
  • Fingers used to keep track of the count of steps
  • Hundred square for later extension
  • Bead string showing jumps
  • 'Start big, count on' prompt card

Teaching practices

  • Teach counting ON from the larger addend, not counting all from one, as the efficiency step.
  • Use a number line or number track so jumps are visible and the start number isn't miscounted as a step.
  • Track the number of steps with fingers or marks to prevent off-by-one errors.
  • Model counting back for subtraction and connect it to 'one less each time'.
  • Treat counting on/back as a transitional strategy — celebrate it, then nudge toward known and derived facts for efficiency.

Activities to try

  1. 1

    Hop along the number line: count on and count back

    Why it works: Starting AT the larger number and taking just a few hops lands on the same answer as counting everything from one, but is faster; the first count is the next number along from the start (9 for 8+3; 11 when counting back from 12 for 12−3), not the start number.

    1. On a number line or number track, set the start at the larger number (8 for 8+3) and make three hops forward, saying the number you LAND on each time: '9, 10, 11' — not '8'.
    2. Keep track of how many hops you have made using fingers or marks, so you take exactly three.
    3. Switch to count-back mode for 12−3: start at 12 and hop backward three times, saying '11, 10, 9'.
    4. For 2+9, decide which number to start from and explain why you start at 9, not 2.
    5. Narrate out loud where you start and how many steps you take.
  2. 2

    Spaced practice: draw the hops and choose the start

    Why it works: Repeated, varied practice consolidates counting on from the larger addend and counting back accurately, reinforcing where the count begins.

    1. Draw the jumps on a number line for 8+3 and for 12−3, labelling each landing number.
    2. Answer: 'Which number should you start counting from for 2+9?' and justify the choice.
    3. Fill in results for several count-on and count-back sums (for example 6+2), checking you did not count the start as a step.
  3. 3

    Talk it through: why start at the bigger number?

    Why it works: Articulating why you start from the larger number and that counting on is adding surfaces (and helps move past) a counting-all habit.

    1. Work out a sum and narrate where you start and how many steps you take.
    2. Answer questions like 'Why did you start at 8 and not at 1?' and 'Which is quicker for 8+3 — counting everything or counting on? Why?'.
    3. Explain in your own words how counting on is a way of adding.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
1.OA.5

Math // Addition & Subtraction

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