Mathematics · Grade 1

Active learning ideas

Comparing Lengths Indirectly

Hands-on comparisons of lengths build spatial reasoning skills that students use daily, from arranging materials to understanding classroom space. Active learning lets students test ideas with concrete tools like strings and paper strips, turning abstract comparisons into visible evidence they can justify to peers.

• Ontario Curriculum Expectations
• 1.MD.A.1

• 15–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Mystery Object
• 20 min · Pairs

Pairs with String: Desk to Whiteboard

Pairs cut equal strings to match desk length, then stretch along whiteboard and compare ends. They mark endpoints with tape and discuss differences. Extend by swapping partners to verify.

Explain how we can compare the height of two tables if we cannot move them next to each other.

Facilitation Tip

During Pairs with String, remind students to align one end of the string exactly at the start of the first object before wrapping it to the end.

What to look for

Provide students with two objects that cannot be easily placed together (e.g., a book and a classroom door). Ask them to draw or write the steps they would take to compare their lengths using a piece of string, and then state which object is longer.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 02

• Mystery Object
• 30 min · Small Groups

Small Groups: Table Height Challenge

Groups use yarn to measure one table height, transfer to floor, and chain paper clips along yarn for portable units. Compare to second table by laying chains side by side. Record longer/shorter.

Construct a method to compare the length of your desk to the length of the whiteboard using a string.

Facilitation Tip

In Small Groups: Table Height Challenge, circulate to ensure groups use the same starting point on the wall, such as the floor, when marking heights.

What to look for

Present students with a scenario: 'Imagine you need to know if your desk is longer than the teacher's desk, but you cannot move them. How could you find out for sure?' Listen for explanations involving a third object to transfer length.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 03

• Mystery Object
• 40 min · Whole Class

Whole Class: Playground Paths

Class measures two paths with sidewalk chalk lines as units, walks heel-toe to count steps indirectly. Compare totals on board. Justify if paths equal.

Justify why indirect measurement is sometimes necessary.

Facilitation Tip

For Whole Class: Playground Paths, demonstrate how to lay string flat without twisting to prevent measurement errors when transferring lengths.

What to look for

Give pairs of students a collection of objects (e.g., pencil, crayon, marker). Ask them to select two objects that are difficult to compare directly. Have them use a paper strip to compare the lengths and then record which object is longer and why.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 04

• Mystery Object
• 15 min · Individual

Individual: Book Shelf Sort

Each student uses a straw chain to compare shelf heights without touching books. Lay chains flat to order shelves from shortest to tallest.

Explain how we can compare the height of two tables if we cannot move them next to each other.

Facilitation Tip

During Individual: Book Shelf Sort, encourage students to label their strips with the book titles to track comparisons during sharing.

What to look for

Provide students with two objects that cannot be easily placed together (e.g., a book and a classroom door). Ask them to draw or write the steps they would take to compare their lengths using a piece of string, and then state which object is longer.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teachers should model the transfer process slowly, emphasizing precision in starting points and alignment. Avoid rushing to conclusions; instead, guide students to repeat measurements and compare results with peers. Research shows that students learn indirect comparison best when they physically manipulate tools and explain their steps aloud to others.

Students will measure and compare lengths indirectly using a third object, explain their comparison methods clearly, and defend why their approach works. Observations should show students selecting appropriate tools, transferring lengths accurately, and checking results with classmates.

---

Watch Out for These Misconceptions

• During Pairs with String: Desk to Whiteboard, watch for students who leave gaps between the string and the object edges, assuming the string must just 'reach' the end without tight alignment.

  Prompt students to lay the string flat against the desk edge and pull it taut to the whiteboard edge before cutting or marking, demonstrating how tight alignment ensures accuracy.

• During Small Groups: Table Height Challenge, watch for students who assume a longer cube chain automatically means the table is taller.

  Have students compare cube chains of the same length directly and discuss why identical chains must produce identical height marks, reinforcing tool standardization.

• During Whole Class: Playground Paths, watch for students who doubt the string’s accuracy because they cannot see both ends at once.

  Ask students to fold the string in half to match the transferred length, then compare the folded ends visually to confirm the path lengths are equal.

---

Methods used in this brief

• Mystery Object