Lesson 8 — Two-Step Word Problems

Summary

Learners solve two-step word problems by acting them out, drawing a bar diagram, and recording the first step and then the second — using any of the four operations. They discover that a two-step problem is just two one-step problems in a row.

Objectives

• Solve two-step word problems using the four operations and explain the relationship between addition and subtraction or multiplication and division. (D05.S2.03.02)

Connection

A market seller starts the day with 45 mangoes, sells 18 in the morning, then gets 12 more; how many now? A family rides a bus 6 kilometers, then walks 3 more, then comes home the long way; how far in all? Real life does not come in one neat step — it comes in a story, and you solve the story by taking it one step at a time. That is a two-step problem, and people solve them in every market, kitchen, and journey on Earth.

Materials

• About 60 small objects
• A set of two-step story cards
• Paper or slate and a drawing tool

Preparation

• Give each learner or pair about 60 objects and a set of story cards.
• Clear space to act out stories.
• Prepare a worked example (for example: “A seller has 45 mangoes, sells 18, then gets 12 more. How many now?”).

Facilitator note

This lesson is written to the learner (“you”). It is the learner’s first formal two-step problem — the new skill is decomposing a story into a first step and a then-step, choosing the right operation for each. Teach with a worked example (philosophy §13): read the story, act it out with objects, draw a bar diagram, then record step 1 and step 2 before learners try their own. Children make sense of word problems by acting them out and drawing them, long before symbols (Carpenter et al., 2015). The story, the drawing, and the numbers are three ways to the same meaning. No one’s speed at solving measures their smartness; a child who acts it out and tells the story has understood it even before writing numbers. Choose stories from many real lives — market, farm, sea, kitchen, bus — so no single world is the default. Count in the home language. For learners who are Deaf or hard of hearing, act the story in sign and pictures; for learners who are blind or low-vision, move objects in two steps the hands can follow. Learners with limited movement direct a partner. Mastery arrives at its own pace.

Procedure

1. Gather — a story, not a sum (5 min). Today our numbers come inside a story. When a story has two parts, we solve it two steps.
2. Worked example — the fruit seller (10 min). Listen: “A seller has 45 mangoes. She sells 18 in the morning. Then a farmer brings her 12 more. How many does she have now?” Act it out with objects. Step 1: take away 18 — 45 − 18 = 27. Step 2: add 12 — 27 + 12 = 39. She has 39 mangoes. Draw a bar diagram of it.
3. Guided practice — act, draw, write (20 min). Choose story cards. For each: read the story, act it out, draw the bar, then write step 1 and step 2 as number sentences. Underline the answer in a sentence: “She has 39 mangoes.”
4. Check with a friend (8 min). Trade stories and answers. Do you agree on both steps? Act it out again together, kindly, if you differ.
5. Close (7 min). Remember: a two-step problem is two one-step problems in a row. Read, act, draw — then write the first step and the second.

Differentiation

• Support: Use two-step stories that use only addition and subtraction today; add multiplication and division another day.
• Support (blind/low-vision): Act out both steps with objects in cups; say each number sentence aloud.
• Extension: Write your own two-step story, solve it, and read it for a friend to try.

Assessment

• Formative (observation): Can the learner decompose a two-step story, choose the right operation for each step, and record both number sentences?
• Artifact (portfolio): The learner’s bar diagram and two-step solution, kept as a record of reasoning.

Home connection

At home, make up a two-step story from your day (“we had 10 cups, used 3, washed 2 more — how many now?”) and solve it with a grown-up.

Resources

• Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children’s Mathematics: Cognitively Guided Instruction (2nd ed.). Heinemann. (Children solving word problems by acting out and drawing before writing symbols.)