Word Problems

What this covers

• Restating a problem in your own words and naming exactly what is being asked before touching any numbers
• Choosing the operation from the situation type — equal groups, comparison, part-whole, and 'how many times as many'
• Two-step problems: identifying the hidden intermediate answer and keeping it labelled so it isn't mistaken for the final one
• Drawing a bar model or tape diagram to show which quantity is the whole and which are the parts
• Interpreting division remainders in context — round up, drop, or report the remainder itself
• Checking reasonableness with estimation and by rereading the question, plus writing the answer with correct units

Where learners get stuck

Grabbing every number in the problem and operating on all of them

Younger students learn that problems have a tidy answer, so extra or unused information feels like a mistake. Multi-step and distractor problems in grades 4-5 break that habit for the first time, and the child needs practice deciding a number isn't needed.

Treating keywords as rules — 'altogether' means add, 'left' means subtract, 'each' means multiply

Keyword lists work on the simple one-step problems of grade 2 and then fail. 'Ben has 3 fewer than Maya; Ben has 12' requires addition despite 'fewer'. The fix is asking what is happening in the story rather than scanning for trigger words.

Writing a remainder as the answer when the question needs a whole number

Division practice is usually taught as 'quotient R remainder', so the child reports the form they were drilled on. Whether 26 children needing seats-of-4 means 6 buses or 7 depends on the story, and that judgement step is separate from the arithmetic.

What a session looks like

A typical 25-30 minute session runs three or four problems at increasing difficulty. Evelyn reads the problem aloud, asks the learner to say back what is happening and what the question wants, then waits while they choose an operation and explain the choice. When an answer is wrong, the tutor goes to the reasoning step rather than giving the correct number — often by asking the child to estimate first, or to say what their answer would mean in the story. Diagrams are described verbally and the learner sketches on paper. Sessions end with the learner explaining one solved problem back from start to finish.

Helpful to know first

• Fluent addition and subtraction within 1000
• Knows multiplication and division facts through 10 x 10, or is actively learning them
• Can read a short paragraph independently, or has an adult nearby to read it aloud
• Comfortable writing numbers and simple equations on paper during the session

Questions

My child can do the math but freezes on word problems — is this normal?

It is very common in grades 3-5. Computation and problem interpretation are different skills, and word problems add reading load, working memory, and the decision of which operation to use. Sessions focus on the interpretation step, with arithmetic kept easy at first so the child isn't juggling both.

How do you teach two-step word problems?

By making the intermediate answer explicit. The learner is asked to state what they need to find out first, label it, and only then look at what the question actually wants. Most two-step errors are stopping after step one, so the routine of rereading the question at the end is practised every session.

Do you use bar models or the same method as our school?

Bar models and tape diagrams are used because they show part-whole and comparison structures clearly, and they appear in most grade 3-5 curricula. If your school uses a different diagram or a specific phrasing, mention it at the start of a session and the tutor will follow it.

How long before word problems get easier?

That varies by child. Progress usually shows up as the learner starting to restate the problem unprompted and estimate before calculating, rather than as a jump in scores. Regular short sessions on a small number of problems tend to work better than long ones.