Mathematics · Grade 2

Active learning ideas

Solving Length Word Problems

Active learning works well for length word problems because students need to physically manipulate objects to understand measurement units. Moving and comparing lengths helps them transition from abstract numbers to concrete understanding, which builds confidence in solving real-world problems.

• Ontario Curriculum Expectations
• 2.MD.B.5

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Numbered Heads Together
• 30 min · Pairs

Manipulative Build: Length Problems

Provide paper strips or linking cubes for lengths. Students read word problem cards, build models to represent lengths, add or subtract physically, then write number sentences and check with rulers. Partners discuss and record solutions on charts.

Analyze a word problem to determine if addition or subtraction is needed for lengths.

Facilitation Tip

During Manipulative Build, circulate to ask guiding questions like, 'How did you decide to add or subtract?' to push students' reasoning.

What to look for

Provide students with a word problem: 'Sarah has a ribbon that is 25 cm long. She cuts off 10 cm. How long is the ribbon now?' Ask students to write the number sentence and the answer, and to draw a picture showing the ribbon's length.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 02

• Numbered Heads Together
• 35 min · Small Groups

Ruler Hunt: Solve and Share

Students search classroom for objects matching problem clues, like 'two items totaling 15 cm'. They measure with rulers, solve using addition or subtraction, and justify choices. Groups share one solution with the class.

Construct a number sentence to represent a length word problem.

Facilitation Tip

For Ruler Hunt, model how to align objects carefully on the ruler to avoid gaps or overlaps.

What to look for

Present students with two objects, e.g., a pencil (15 cm) and an eraser (5 cm). Ask: 'How much longer is the pencil than the eraser?' Observe if students correctly identify subtraction and write the number sentence (15 - 5 = ?).

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Operation Sort and Solve

Set up stations: sort word problems by add/subtract, write number sentences, measure to verify, explain with drawings. Groups rotate every 10 minutes, completing a problem sheet at each.

Explain how to use a ruler to solve a problem about combining lengths.

Facilitation Tip

In Station Rotation, provide a quick checklist for students to self-assess their operation choices before moving on.

What to look for

Pose a problem: 'Tom used 12 cm of string to tie a package and 8 cm to make a bow. How much string did he use in total?' Ask students to explain in their own words how they would solve this problem, encouraging them to mention the operation they would use and why.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Numbered Heads Together
• 25 min · Pairs

Partner Story Problems: Create and Solve

Pairs draw pictures of lengths, write their own word problems, swap with another pair to solve using rulers. They check answers together and revise if needed.

Analyze a word problem to determine if addition or subtraction is needed for lengths.

What to look for

Provide students with a word problem: 'Sarah has a ribbon that is 25 cm long. She cuts off 10 cm. How long is the ribbon now?' Ask students to write the number sentence and the answer, and to draw a picture showing the ribbon's length.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teachers should model the process of reading a problem carefully, drawing a quick sketch, and writing a number sentence. Avoid rushing to calculations; instead, emphasize connecting the problem's context to the operation. Research shows that students who explain their steps aloud in small groups retain concepts longer.

Students will confidently identify the correct operation for word problems, measure lengths accurately with rulers, and explain their thinking using number sentences and visual models. They will also discuss their reasoning with peers to deepen understanding.

---

Watch Out for These Misconceptions

• During Manipulative Build, watch for students who automatically add lengths regardless of the problem's wording.

  Have them act out the problem with string or strips, removing the shorter length to model subtraction scenarios like 'how much shorter'.

• During Ruler Hunt, watch for students who estimate lengths instead of measuring carefully.

  Pair students to compare their measurements side-by-side and discuss discrepancies to reinforce precision.

• During Station Rotation, watch for students who skip drawing models or writing number sentences.

  Circulate and ask, 'What does the problem ask you to find?' to prompt them to connect the question to their work.

---

Methods used in this brief

• Numbered Heads Together
• Stations Rotation