Math // Measurement

Addition and subtraction word problems

Solve word problems involving lengths within 100, using addition and subtraction with drawings and equations

Ages
7 to 8
Type
Method
Builds on
2 topics
Leads to
1 topic
Standards
1 code

Quick check

If the learner has a piece of rope 75 cm long and cuts off 28 cm, can they work out how much rope is left — and draw a number-line diagram to show it?

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.
  • Solve 'The rope is 45 cm long. I cut off 18 cm. How long is it now?'
  • Draw a diagram (e.g. a ruler drawing) to represent a length word problem
  • Write an equation with a symbol for the unknown to represent the problem

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

Before this

2 topics

You are here

Addition and subtraction word problems

Ages 7 to 8 // Method

Leads to

1 topic
  • Working with moneyHelpful

    Mathematical Thinking // Ages 7 to 8

    Length word problems exercise real-world modelling

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

Year 2 / Grade 2 (age 7–8) pupils solve one-step length word problems within 100 using addition and subtraction, representing each situation with a drawing (such as a ruler or bar drawing) and an equation that uses a symbol (□ or ?) for the unknown — including missing-addend forms like 18 + □ = 45. The core skill is modelling: the child builds a picture of the problem structure (whole and parts, or two lengths compared) and reads the number sentence off that picture, rather than grabbing the two numbers and applying an operation cued by a keyword. This maps CCSS 2.MD.B.5, with 2.MD.B.6 adding the length-from-0 number-line model.

Common misconceptions

  • Chooses the operation from a keyword ('longer'/'altogether' → add; 'cut off'/'left' → subtract) without modelling the situation, so comparison and missing-addend problems are miscalculated.
  • Writes the answer where the unknown symbol should go, reading '=' as 'the answer is' rather than 'has the same value as', so cannot represent 18 + □ = 45 before solving.
  • When drawing/using a ruler, counts the marks or starts at 1 instead of 0, so the represented length is off by one.
  • Drops the unit or draws a picture that doesn't match the quantities.

Useful representations

  • Bar model (whole split into known part + unknown □)
  • Ruler / number-line drawing with jumps from 0
  • Equation with a symbol for the unknown (□ or ?)
  • Comparison bars stacked to show 'how much longer'

Teaching practices

  • Model the situation before calculating — use a bar model or a ruler/number-line drawing to show the whole and its parts (or the two lengths being compared), so the operation follows from the structure, not from a keyword.
  • Teach the symbol-for-the-unknown explicitly: write 45 − 18 = □ AND 18 + □ = 45 for the same rope, showing both describe the same picture and that '=' means 'has the same value as', not 'the answer comes next'.
  • Deliberately include comparison ('12 cm longer') and missing-addend ('how much was cut off?') problems, not just result-unknown take-aways, so keyword strategies break down.
  • Represent lengths from 0 on a number line with equally spaced points, and show sums/differences as jumps (2.MD.B.6).
  • Insist on units in the answer (cm) and on a drawing that matches the numbers, so the model and the equation stay tied to the quantity.

Activities to try

  1. 1

    Build a bar or ruler model, then read the equation off it

    Why it works: The unknown is a visible piece of the bar or ruler you can point to before you know its number, so the equation is a description of the picture — not a guess triggered by a word like 'cut off'.

    1. Read a result-unknown story, e.g. 'A rope is 45 cm long. I cut off 18 cm. How long is it now?'
    2. Draw a bar (or ruler line) labelled 45, mark off the 18 cm that was cut, and mark the leftover piece with a □ to show it is the length you do not yet know.
    3. Write a number sentence that matches the drawing, using a symbol for the unknown: 45 − 18 = □ AND 18 + □ = 45.
    4. Solve and label the answer with its unit: 27 cm.
    5. Show the two equations against the same drawing and explain why both describe one picture.
  2. 2

    Model comparison stories with stacked bars

    Why it works: In a comparison the operation comes from where the lengths line up and which piece of the drawing is unknown. The word 'longer' always points to the overhang (the difference). Whether you add or subtract depends on whether the unknown is the longer bar, the shorter bar or the overhang itself.

    1. Read a comparison story, e.g. 'Sam's ribbon is 30 cm. Mia's is 12 cm longer. How long is Mia's?'
    2. Draw two bars stacked so they start level; make Mia's bar stick out past Sam's, and mark the extra gap as 12 cm.
    3. Point to where the 12 cm sits in the picture (the overhang), not just the word 'longer'.
    4. Write the matching equation with a symbol for the unknown total and solve: 30 + 12 = □, so □ = 42 cm.
    5. Compare a 'how much longer?' version where the gap itself is the unknown, and show the gap is what the □ marks this time.
  3. 3

    Lengths from 0 on a number line, with jumps

    Why it works: Length accumulates from 0, and it is the intervals (the spaces between marks) that count — starting from 1, or counting marks instead of spaces, gives a length that is off by one.

    1. Draw a number line with equally spaced points and label the start point 0.
    2. Place a length by counting the intervals (spaces) from 0, not the marks, so a length of 18 cm ends at the mark labelled 18 after 18 intervals, rather than by counting 18 marks (which lands short).
    3. Show a sum or difference as a jump along the line (e.g. jump back 18 from 45, landing on 27).
    4. Say aloud where each length begins and ends, confirming it accumulates from 0.

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
2.MD.5

Math // Measurement

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