Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Two-Step Word Problems

Active learning works well for two-step word problems because students need to slow down and process each part of the problem. Movement and visual models help them break the problem into manageable steps, reducing the chance of skipping or mixing operations. When children act out or draw each step, they build the habit of careful reading and checking.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Problem Solving

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 30 min · Pairs

Pair Drawing Relay: Step-by-Step Models

Pairs read a two-step problem. One partner draws the first step with counters or bars, passes to the other for the second step. They discuss and solve together, then swap roles for a new problem. Share one model with the class.

What are the two things you need to work out to solve this problem?

Facilitation Tip

During Pair Drawing Relay, circulate to ensure both partners sketch each step before moving on, not just the final answer.

What to look for

Present students with a word problem like: 'Sarah had 15 crayons. She gave 5 to her friend and then found 3 more. How many crayons does Sarah have now?' Ask students to write down the two numbers they need to calculate and the operation for each step.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 45 min · Small Groups

Small Group Story Chains: Problem Creation

In small groups, students take turns adding a sentence to build a two-step story, like starting with toys then giving some away. Each group solves their chain using objects, records steps, and presents to another group for checking.

How can drawing a picture or using objects help you work through each step?

Facilitation Tip

In Small Group Story Chains, model how to ask, 'What do we need to find first?' to guide students through the problem.

What to look for

Give each student a simple two-step word problem. Ask them to draw a picture or use counters to solve the first step, write the answer, then solve the second step and write the final answer. They should also write one sentence explaining how they checked their answer.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 25 min · Whole Class

Whole Class Act-Out: Human Number Line

Display a problem on the board. Select students to represent numbers on a floor number line, acting out addition then subtraction steps as a class. Everyone predicts outcomes, then verifies with counters.

Can you check your answer by reading the problem again carefully?

Facilitation Tip

For Whole Class Act-Out, assign roles so every student participates in modeling the first and second steps.

What to look for

Pose a problem to the class: 'Tom had 12 stickers. He bought 6 more, and then gave 4 to his sister. How many stickers does Tom have?' Ask students to share how they figured out what to do first and second. Encourage them to explain why they chose addition or subtraction for each step.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 20 min · Individual

Individual Journal Solve: Check and Reflect

Students solve three two-step problems in journals, drawing each step and writing checks. Circulate to prompt questions like the key ones provided. End with a quick share of favorite strategies.

What are the two things you need to work out to solve this problem?

Facilitation Tip

During Individual Journal Solve, give sentence starters like 'First I ____, so I ____.' to scaffold writing steps.

What to look for

Present students with a word problem like: 'Sarah had 15 crayons. She gave 5 to her friend and then found 3 more. How many crayons does Sarah have now?' Ask students to write down the two numbers they need to calculate and the operation for each step.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teach this topic by having students physically or visually model each step before writing numbers. Avoid rushing to the final answer; instead, pause after each operation to ask, 'Does this make sense?' Research shows that concrete representations reduce errors in operation choice and sequence. Use think-alouds to model how to reread the problem after each step to check for reasonableness.

Successful learning looks like students identifying the two operations needed, solving each step in order, and verifying their final answer matches the context. They should use drawings or counters to explain their thinking and correct mistakes when peers point them out. Clear steps and explanations in their work show they can transfer the method to new problems.

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Watch Out for These Misconceptions

• During Pair Drawing Relay, watch for students who sketch the final number of items without showing the separate steps.

  Prompt them to label each drawing with 'After step 1' and 'After step 2' and explain what each picture represents before moving forward.

• During Small Group Story Chains, watch for groups that choose operations based on the last number mentioned instead of the context.

  Have them act out the story with counters and pause to ask, 'What is happening in the problem? Does adding or taking away fit here?' until they agree on the correct operation.

• During Whole Class Act-Out, watch for students who perform both steps at once instead of pausing between them.

  Freeze the action after the first step and ask, 'How many are there now? What needs to happen next?' before continuing.

• During Individual Journal Solve, watch for students whose final answer matches the context but the steps do not.

  Have them use a highlighter to trace the numbers in the problem to the steps in their work, then reread the question to see if their steps match the wording.

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Methods used in this brief

• Collaborative Problem-Solving