Represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences

Standards Alignment

• TEKS.MATH.1.05D primary
  represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences;
• TEKS.MATH.1.05E primary
  understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s);
• TEKS.MATH.1.05F primary
  determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation; and

Lesson Overview

This Grade 1 mathematics lesson focuses on helping students represent word problems involving addition and subtraction of whole numbers up to 20. Students will use concrete objects, pictorial models, and number sentences to solve problems. They will also learn the meaning of the equal sign as a relationship between expressions and determine unknown numbers in addition or subtraction equations. This lesson supports algebraic reasoning by applying number patterns and properties of operations to describe relationships.

Learning Objectives

• Represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences.
• Understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).
• Determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation.

Success Criteria

• Students can use objects or drawings to model addition and subtraction word problems with numbers up to 20.
• Students can write number sentences that correctly represent addition or subtraction problems.
• Students can explain that the equal sign means both sides have the same value.
• Students can find the missing number in an addition or subtraction equation regardless of its position.

Prerequisite Knowledge

Students should know basic counting skills and be familiar with addition and subtraction within 20. They should recognize numbers and understand simple addition and subtraction concepts.

Key Vocabulary

• Addition
• Subtraction
• Word problem
• Concrete model
• Pictorial model
• Number sentence
• Equal sign
• Unknown number

Materials and Resources

• Counters or small objects (e.g., blocks, buttons)
• Paper and pencils
• Whiteboard and markers
• Printed word problem cards or prepared story problems
• Drawing paper or notebooks

Teacher Preparation

• Prepare simple addition and subtraction word problems with sums or differences up to 20.
• Gather enough counters or small objects for each student or group.
• Prepare pictorial model examples on the board or chart paper.
• Prepare number sentence templates showing addition and subtraction with an equal sign.
• Plan questions to guide students in understanding the equal sign and unknown numbers.

Detailed Lesson Notes

Understanding Addition and Subtraction Word Problems

Addition word problems describe situations where quantities are combined or joined together, such as "There are 8 apples, and 5 more are added. How many apples are there now?" Subtraction word problems describe situations where some quantity is taken away or compared, such as "There are 15 cookies, and 7 are eaten. How many cookies are left?" Students need to identify the operation required by the problem context.

Using Concrete Models to Represent Problems

Concrete models involve using physical objects like counters or blocks to represent the quantities in the problem. For example, if the problem says 8 apples plus 5 apples, students can place 8 counters, then add 5 more counters, and count the total. This hands-on approach helps students visualize the problem and understand the addition or subtraction process.

Using Pictorial Models to Represent Problems

Pictorial models are drawings or pictures that represent the quantities in the problem. Students can draw circles, dots, or other symbols to show the numbers involved. For example, drawing 8 circles and then 5 more circles to represent 8 + 5. This bridges the concrete experience to abstract thinking and supports writing number sentences.

Writing Number Sentences

A number sentence is a mathematical expression that uses numbers and symbols to represent a problem. For addition and subtraction, it includes numbers, plus or minus signs, and an equal sign. For example, 8 + 5 = 13. Students learn that the equal sign means both sides have the same value, not just the answer comes next. Understanding this helps them solve equations with unknowns.

Understanding the Equal Sign as a Relationship

The equal sign (=) means that the value on the left side is the same as the value on the right side. For example, in 7 + 3 = 10, the sum of 7 and 3 is equal to 10. Students often mistakenly think the equal sign means 'the answer comes next,' so teaching the equal sign as a balance or relationship is important for algebraic reasoning.

Determining the Unknown Number in Equations

Students will learn to find the missing number in addition or subtraction equations where the unknown can be any term. For example, in 9 + ? = 15, students determine the missing addend by thinking about what number added to 9 equals 15. Similarly, in 20 - ? = 13, they find the missing subtrahend. This skill builds early algebraic thinking and problem-solving.

Worked Examples

Classroom Activity

Work individually or in pairs to solve word problems using concrete or pictorial models and write number sentences.

Guided Practice

Independent Practice

1. Foundational: Use counters to show the problem: "There are 4 apples, and 3 more are added. How many apples are there now?" Write the number sentence.
2. Developing: Draw a picture to represent: "There are 10 birds on a tree. 6 fly away. How many birds are left?" Write the number sentence.
3. Application: Write the number sentence and solve: "8 + ? = 13". Use a drawing or counters to find the unknown number.
4. Analysis: Explain what the equal sign means in the number sentence: 7 + 4 = 11. Why is it important to understand this?
5. Challenge: Find the unknown number: ? - 5 = 8. Use a pictorial model or number sentence to explain your answer.

Independent Practice Teacher Answer Key

1. 1. Place 4 counters, then add 3 more counters. Count all counters: 7. Number sentence: 4 + 3 = 7.
2. 2. Draw 10 birds, cross out 6 birds. Count remaining birds: 4. Number sentence: 10 - 6 = 4.
3. 3. Draw 8 objects, then add some more until total is 13. The number added is 5. Number sentence: 8 + 5 = 13.
4. 4. The equal sign means the value on the left (7 + 4) is the same as the value on the right (11). Understanding this helps students see equations as balanced relationships, not just a signal that the answer comes next.
5. 5. Since subtracting 5 gives 8, the unknown number must be 13 because 13 - 5 = 8. Draw 13 objects, cross out 5, 8 remain.

Guiding Questions

• What does the problem ask you to find?
• How can you show the problem with objects or pictures?
• What number sentence matches your model?
• What does the equal sign mean here?
• How can you find the missing number in this equation?

Common Misconceptions

• Students may think the equal sign means 'the answer comes next' rather than a balance between two expressions.
• Students may always expect the unknown number to be at the end of the equation and struggle when it is at the beginning or middle.
• Students might confuse addition and subtraction operations in word problems if the context is unclear.

Differentiation

Assessment

• Observe students as they use counters and drawings to solve problems.
• Ask students to explain what the equal sign means during guided practice.
• Check students' number sentences for correct use of symbols and numbers.
• Solve this word problem: "There are 9 pencils. 4 are given away. How many pencils are left? Show your work with a drawing and write the number sentence."
• Find the unknown number: 6 + ? = 14. Use a model or drawing to explain your answer.
• Create a short quiz with addition and subtraction word problems up to 20, including problems with unknown numbers.
• Have students explain the meaning of the equal sign in their own words and give examples.

Answer Guide

• Use counters to show the problem: "There are 4 apples, and 3 more are added. How many apples are there now?" Write the number sentence.
  Answer: Place 4 counters, then add 3 more counters. Count all counters: 7. Number sentence: 4 + 3 = 7.
• Draw a picture to represent: "There are 10 birds on a tree. 6 fly away. How many birds are left?" Write the number sentence.
  Answer: Draw 10 birds, cross out 6 birds. Count remaining birds: 4. Number sentence: 10 - 6 = 4.
• Write the number sentence and solve: "8 + ? = 13". Use a drawing or counters to find the unknown number.
  Answer: Draw 8 objects, then add some more until total is 13. The number added is 5. Number sentence: 8 + 5 = 13.
• Explain what the equal sign means in the number sentence: 7 + 4 = 11. Why is it important to understand this?
  Answer: The equal sign means the value on the left (7 + 4) is the same as the value on the right (11). Understanding this helps students see equations as balanced relationships, not just a signal that the answer comes next.
• Find the unknown number: ? - 5 = 8. Use a pictorial model or number sentence to explain your answer.
  Answer: Since subtracting 5 gives 8, the unknown number must be 13 because 13 - 5 = 8. Draw 13 objects, cross out 5, 8 remain.

Real-Life Application

Ask families to help students find and solve simple addition or subtraction word problems at home, such as counting toys or snacks. Students can draw pictures or use objects to show their solutions and share their number sentences with family members.

Homework or Home Connection

• Ask families to help students find and solve simple addition or subtraction word problems at home, such as counting toys or snacks. Students can draw pictures or use objects to show their solutions and share their number sentences with family members.

Lesson Summary

In this lesson, students learned to represent addition and subtraction word problems with whole numbers up to 20 using concrete objects, drawings, and number sentences. They explored the meaning of the equal sign as a relationship between two expressions and practiced finding unknown numbers in equations. These skills build foundational algebraic reasoning by helping students understand number relationships and operations in flexible ways.

Teacher Notes

Use the exact standards alignment and retrieved-source provenance stored with this enrichment.

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