Math // Fractions

Addition and subtraction word problems

Solve word problems involving addition and subtraction of fractions with like denominators, using visual models and equations

Ages
9 to 10
Type
Method
Builds on
1 topic
Leads to
1 topic
Standards
1 code

Quick check

If the learner reads that one section of a nature trail is 3/8 km and another is 5/8 km, can they work out the total distance without a calculator?

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.
  • A jug contains 3/4 litre of juice; 2/4 litre is poured out — how much remains?
  • Two pieces of ribbon are 2 3/8 and 1 5/8 inches — what is their total length?
  • Draw a fraction model to represent and solve a fraction word 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

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Addition and subtraction word problems

Ages 9 to 10 // Method

Leads to

1 topic
  • Fraction Word ProblemsHelpful

    Fractions // Ages 10 to 11

    Extends Y5 fraction word problems to unlike denominators

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

Learners apply like-denominator addition and subtraction of fractions and mixed numbers to word problems (juice poured from a jug = separate/subtract; ribbons joined end to end = combine/add). The computation is already secured; the new demand is READING the situation to choose join versus separate, drawing a matching model, computing with the denominator held as a fixed unit, regrouping a fraction sum that crosses a whole (e.g. 2 3/8 + 1 5/8 = 4), and interpreting the result back in context. Core approach: draw the story on a bar or number line before writing symbols, keep eighths as eighths to block adding across, and estimate with whole numbers to sanity-check.

Common misconceptions

  • Adds across denominators when combining (2 3/8 + 1 5/8 → 3 8/16)
  • Chooses the wrong operation — adds when the story separates, or vice versa
  • Leaves a crossing sum unregrouped (3 8/8 rather than 4)
  • Misreads which quantity is removed or kept in the context

Useful representations

  • Bar model of the jug (part poured out shaded) or the ribbons laid end to end
  • Number line for combining/removing lengths
  • Story ↔ equation ↔ picture triple
  • Regroup of a fraction sum crossing a whole (8/8 = 1)

Teaching practices

  • Model the story on a bar/number line before writing the equation — draw the jug emptying or the ribbons joining
  • Decide join (+) vs separate (−) from the situation, and say which quantity is being removed or combined
  • Hold the denominator as a fixed unit (eighths stay eighths) to block add-across
  • Estimate with whole numbers first, then check the exact answer against it
  • Interpret the result in context and regroup a crossing sum (8/8 → 1 whole)

Activities to try

  1. 1

    Model the story before you compute

    Why it works: The story tells you the operation; a picture drawn first makes join-versus-separate visible, and holding the denominator as a fixed unit means combining 3/8 and 5/8 gives 8/8 = one whole, never 8/16.

    1. Read: 'A jug holds 3/4 of a litre of juice; 2/4 of a litre is poured out — how much is left?' Draw a bar showing 3/4, shade the 2/4 poured away, and read the remaining 1/4 off your picture.
    2. Read: 'Two ribbons are 2 3/8 inches and 1 5/8 inches long — what is their total length?' Draw the two ribbons laid end to end on a bar marked in eighths.
    3. Before writing any symbols, say aloud whether the story is a 'take away' or a 'combine', and name which quantity is removed or joined.
    4. Write the matching equation, keeping the denominator fixed (quarters stay quarters, eighths stay eighths): 3/4 − 2/4 = 1/4; 2 3/8 + 1 5/8 = 3 + 8/8 = 4.
    5. When the fraction parts reach 8/8, regroup that whole into the whole-number count so the total reads 4 inches, not 3 8/8.
  2. 2

    Act out pouring and joining with a locked-unit model

    Why it works: Combining the fraction parts can make a whole appear in the whole-number count (8/8 → 1 whole), and when the pieces are kept as fixed eighths, adding across into sixteenths is not even a possible move.

    1. In a story workspace, pick the jug context and pour 2/4 out of a 3/4-litre jug; watch the removed part grey out, leaving 1/4, and read 'take away' straight off the picture.
    2. Switch to the ribbon context and drag two ribbons (marked in eighths) end to end; watch the eighths auto-count as they join.
    3. Notice that when 3/8 and 5/8 meet at 8/8 the eighths fuse into one whole inch and the total snaps to 4 inches.
    4. Read the matching ± equation that the picture produces, and use a 'more or fewer than you started with?' check to confirm the direction of the operation.
  3. 3

    Study then classify the two story structures

    Why it works: Pour-out stories separate (subtract) and joining stories combine (add); naming the structure first makes the correct operation and any crossing-sum regroup predictable.

    1. Study a worked pour-out (jug: 3/4 − 2/4 = 1/4) and a worked join (ribbons: 2 3/8 + 1 5/8 = 4), revealing the shaded/combined model and then the answer for each.
    2. Answer 'what does 8/8 make?' for the ribbon total and explain where that whole goes in the answer.
    3. Sort a set of new stories into 'combine' versus 'take away', then match each story to the ± equation that solves it.
    4. Fill in a missing answer that requires a regroup step, and explain the regroup in words.

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
4.NF.3.d

Math // Fractions

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