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

Solving Simple Word Problems

Explore division of integers, fractions, and decimals, including understanding remainders, dividing by powers of ten, and the concept of reciprocals.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.1
• NCCA: Junior Cycle - Strand 3: Number - N.1.2

About This Topic

Solving simple word problems helps 1st Class students apply addition and subtraction within 20 to everyday stories. They read problems about combining items, taking away, or comparing quantities, deciding the operation by asking: 'What is happening, and what do we need to find?' Drawing pictures or using counters models sharing equally, with attention to remainders when items do not divide evenly.

This topic supports NCCA primary mathematics in the Number strand, building early reasoning and representation skills that lead to Junior Cycle standards like N.1.1 and N.1.2. Students practice key questions to parse problem structure, choose strategies like counting on or partitioning, and explain their thinking, fostering clear communication.

Active learning suits this topic perfectly. When students draw bar models, act out scenarios with objects, or discuss solutions in pairs, problems shift from confusing text to tangible experiences. These methods reveal misunderstandings quickly, encourage multiple solution paths, and build confidence in tackling real-world math.

Key Questions

1. What is happening in this story problem, and what do you need to find out?
2. How do you know whether to add or take away to solve a word problem?
3. Can you draw a picture to help you solve a word problem about sharing?

Learning Objectives

• Calculate the number of items each person receives when sharing a total quantity within 20.
• Identify the remainder when a quantity cannot be shared equally among a given number of people.
• Explain the process of solving a word problem by drawing a picture to represent sharing.
• Compare the results of sharing a quantity in different ways to solve a word problem.

Before You Start

Counting to 20

Why: Students need to be able to count reliably up to 20 to understand the quantities involved in sharing problems.

Introduction to Subtraction

Why: Understanding subtraction helps students conceptualize taking away items as they are shared or when identifying a remainder.

Key Vocabulary

Share	To divide something into equal parts so that each person or group gets the same amount.
Equal parts	When a whole is divided into pieces that are exactly the same size.
Remainder	The amount left over after dividing something into equal parts, when it cannot be divided any further equally.
Word problem	A story that describes a mathematical situation that needs to be solved using numbers and operations.

Watch Out for These Misconceptions

Common Misconception

Always add when words like 'more' appear.

What to Teach Instead

Many problems use 'more' for subtraction, like 'how many more to reach 10.' Pair discussions of examples clarify context; drawing pictures shows the comparison visually, helping students self-correct during sharing.

Common Misconception

Sharing always results in exact equals, ignoring remainders.

What to Teach Instead

Real sharing often leaves extras. Hands-on division with counters lets students see and count remainders naturally. Group role plays reinforce expressing solutions as 'each gets X with Y left,' building accurate language.

Common Misconception

Skip reading fully; just spot numbers and operate.

What to Teach Instead

Problems require understanding the story. Requiring initial sketches before calculating ensures comprehension. Peer reviews in small groups prompt questions like 'What does it ask?', catching skips early.

Active Learning Ideas

Pair Draw: Story Problem Solver

Provide word problem cards about sharing toys or adding fruits. Partners draw pictures to show the story, solve using counters, and explain their steps to each other. Pairs then create one new problem for the next duo.

20 min·Pairs

Small Group: Role Play Problems

Give groups props like blocks or teddies matching a word problem script. Students act it out, decide add or subtract, solve with objects, and note remainders. Groups present their skit and solution to the class.

30 min·Small Groups

Whole Class: Think-Pair-Share Challenge

Display a daily word problem on the board. Students think alone for 2 minutes, pair to discuss and draw solutions, then share strategies with the class. Vote on the clearest picture representation.

15 min·Whole Class

Individual: My Word Problem Journal

Students draw or write a personal word problem from home life, like sharing sweets. They solve it with a picture, label the operation, and note any remainder. Collect for a class problem bank.

25 min·Individual

Real-World Connections

• When planning a party, a child might need to figure out how many sweets each friend can have if there are 15 sweets and 6 friends, and if there will be any left over.
• A teacher might need to share 18 crayons equally among 4 students, determining how many crayons each student gets and if any remain.

Assessment Ideas

Exit Ticket

Give each student a card with a simple sharing problem, such as 'There are 10 cookies to share among 3 friends. How many cookies does each friend get? How many are left over?' Students draw a picture to solve and write the answer.

Quick Check

Present a word problem on the board, for example, 'Sarah has 12 stickers and wants to give an equal amount to her 4 friends.' Ask students to hold up fingers to show how many stickers each friend gets. Then ask them to show with their fingers how many stickers are left over.

Discussion Prompt

Pose the question: 'If you have 7 apples to share with 2 people, how can you do it? What if you had 8 apples?' Encourage students to explain their strategies and discuss why there is a remainder in one case but not the other.

Frequently Asked Questions

How do I teach 1st Class students to choose addition or subtraction in word problems?

Start with signal words but emphasize story context through key questions: 'What is happening?' Use visuals like bar models. Practice with sorted problem types, then mixed sets. Daily think-alouds model decisions, gradually releasing to student-led solving with drawings for support.

How to introduce remainders in simple sharing word problems for beginners?

Frame as 'extras left over' using concrete objects like sweets. Students share physically, count remainders, and draw them. Progress to problems stating 'as equal as possible.' Discussions normalize remainders as common, linking to fair sharing in life.

How can active learning help with solving simple word problems?

Active methods like drawing, manipulatives, and role play make abstract stories concrete for young learners. Pairs or groups discussing strategies expose varied approaches, reducing errors from misreading. Creating their own problems deepens ownership, while sharing builds justification skills essential for NCCA progression.

What differentiation strategies work for word problems in 1st Class?

Offer tiered problems: basic for adding/subtracting facts, advanced with remainders or multi-steps. Provide scaffolds like sentence stems or visuals for some, extensions like inventing problems for others. Flexible grouping pairs stronger readers with visual thinkers, ensuring all access success.