Foundations of Mathematical Thinking · 1st Class · Addition of Numbers to 20 · Autumn Term

Two-Step Word Problems

Apply addition and subtraction skills to solve multi-step word problems.

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

About This Topic

Two-step word problems build on addition and subtraction within 20 by asking students to solve real-world scenarios that require two operations. For example, a child might first add apples to a basket, then subtract some that roll away. Students learn to identify the sequence of steps, use drawings or counters to model each part, and verify answers by rereading the problem. This aligns with NCCA Primary Number and Problem Solving strands, fostering logical thinking from the Autumn Term unit.

These problems connect number operations to everyday contexts like sharing toys or counting snacks, which helps students see math as practical. They develop key skills: parsing language for clues, planning multi-step solutions, and self-checking. Group discussions reveal how different strategies, such as bar models or number lines, lead to the same answer, building confidence and flexibility.

Active learning suits this topic well. When students act out problems with objects or create their own stories in pairs, they experience the steps kinesthetically. This makes abstract sequencing tangible, reduces errors from rushing, and encourages peer teaching that solidifies understanding for all.

Key Questions

1. What are the two things you need to work out to solve this problem?
2. How can drawing a picture or using objects help you work through each step?
3. Can you check your answer by reading the problem again carefully?

Learning Objectives

• Identify the two separate calculations needed to solve a given two-step word problem.
• Calculate the answer to the first step of a two-step word problem involving addition or subtraction within 20.
• Calculate the answer to the second step of a two-step word problem involving addition or subtraction within 20.
• Demonstrate a strategy, such as drawing or using manipulatives, to represent each step of a two-step word problem.
• Verify the final answer to a two-step word problem by rereading the problem and checking calculations.

Before You Start

Addition of Numbers to 20

Why: Students need to be proficient with single-step addition problems before they can tackle the first step of a two-step problem.

Subtraction of Numbers to 20

Why: Students need to be proficient with single-step subtraction problems before they can tackle the first step of a two-step problem.

Key Vocabulary

two-step problem	A word problem that requires two separate calculations, usually addition and subtraction, to find the final answer.
operation	A mathematical process, such as addition or subtraction, used to solve a problem.
sequence	The order in which steps or events happen. In a two-step problem, this means figuring out which calculation to do first.
model	A visual representation, like a drawing or using counters, that helps to understand and solve a math problem.

Watch Out for These Misconceptions

Common Misconception

Students skip the first or second step entirely.

What to Teach Instead

This happens when they rush to the end number. Acting out problems with objects or drawings forces them to pause at each step. Peer review in pairs helps them spot skips by retracing aloud.

Common Misconception

Choosing the wrong operation for a step.

What to Teach Instead

Words like 'more' signal addition, but context confuses some. Hands-on trials with counters let students test operations and see results mismatch until correct. Group modeling discussions clarify cues.

Common Misconception

Answer seems right but does not match on recheck.

What to Teach Instead

They overlook the final question. Rereading protocols in think-pair-share build this habit. Visual bar models make discrepancies obvious during partner checks.

Active Learning Ideas

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.

30 min·Pairs

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.

45 min·Small Groups

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.

25 min·Whole Class

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.

20 min·Individual

Real-World Connections

• A baker might first add flour to a bowl, then subtract some that is spilled, to figure out how much flour is left for the recipe.
• A shopkeeper might count the number of apples received in a delivery, then subtract the number sold that day, to know how many apples remain in stock.

Assessment Ideas

Quick Check

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.

Exit Ticket

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.

Discussion Prompt

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.

Frequently Asked Questions

How do you introduce two-step word problems in 1st class?

Start with familiar contexts like snacks or toys, using visuals and objects. Model one problem whole class: identify steps, draw, solve, check. Provide scaffolds like sentence frames. Gradually release to pairs for supported practice, ensuring all use the key questions to guide thinking.

What are common errors in two-step problems?

Errors include skipping steps, picking wrong operations, or not rereading for the final question. Address with explicit modeling of bar drawings and object manipulations. Daily quick checks in journals track progress, while peer feedback highlights patterns across the class.

How can active learning help with two-step word problems?

Active approaches like acting out scenarios with props or relay drawings make steps concrete and sequential. Students manipulate objects to test ideas, reducing cognitive load. Collaborative creation of problems builds ownership, and movement keeps engagement high, leading to deeper retention of strategies.

How to differentiate two-step word problems?

Offer tiered problems: simple add-subtract for some, mixed operations for others. Provide drawing templates or counters as needed. Extension tasks include writing original problems. Pair stronger students with those needing support for mutual teaching during activities.