Kindergarten · Mathematics

Model the action of joining to represent addition and the action of separating to represent subtraction

Quarter 2 · Week 6 · TEKS

Standards Alignment

  • TEKS.MATH.K.03A primary
    model the action of joining to represent addition and the action of separating to represent subtraction;
  • TEKS.MATH.K.03B primary
    solve word problems using objects and drawings to find sums up to 10 and differences within 10; and

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Lesson Overview

This kindergarten mathematics lesson focuses on helping students understand addition and subtraction by modeling the actions of joining (for addition) and separating (for subtraction). Students will use objects and drawings to solve word problems involving sums up to 10 and differences within 10, developing foundational skills in number operations aligned with TEKS standards.

Learning Objectives

  • Model the action of joining to represent addition.
  • Model the action of separating to represent subtraction.
  • Solve word problems using objects and drawings to find sums up to 10.
  • Solve word problems using objects and drawings to find differences within 10.

Success Criteria

  • Students can demonstrate joining objects to show addition.
  • Students can demonstrate separating objects to show subtraction.
  • Students can solve simple word problems using drawings or objects to find sums up to 10.
  • Students can solve simple word problems using drawings or objects to find differences within 10.

Prerequisite Knowledge

Students should be familiar with counting objects up to 10 and recognizing numbers up to 10.

Key Vocabulary

  • Addition
  • Subtraction
  • Join
  • Separate
  • Sum
  • Difference
  • Objects
  • Drawings

Materials and Resources

  • Counters or small objects (e.g., blocks, buttons)
  • Paper and crayons or markers
  • Whiteboard and markers
  • Simple word problem cards

Teacher Preparation

  • Prepare sets of counters or small objects for each student or group.
  • Create simple word problem cards involving joining and separating with totals up to 10.
  • Prepare drawing templates or blank paper for students to illustrate problems.
  • Review the TEKS standards TEKS.MATH.K.03A and TEKS.MATH.K.03B to align instruction.

Detailed Lesson Notes

Understanding Addition as Joining

Addition is the action of putting groups of objects together to find out how many there are in all. When we join two groups, we combine them to make a bigger group. For example, if you have 3 blocks and then add 2 more blocks, you join them to find the total number of blocks. This action of joining is the foundation of addition.

Understanding Subtraction as Separating

Subtraction is the action of taking away or separating some objects from a group to find out how many are left. For example, if you have 5 blocks and take away 2 blocks, you separate them to find how many blocks remain. This action of separating helps us understand subtraction.

Using Objects and Drawings to Model Addition and Subtraction

Young learners can use physical objects like counters or blocks to model addition and subtraction. For addition, they physically join groups together and count the total. For subtraction, they remove some objects from a group and count what remains. Drawings can also represent these actions by showing groups of items joined or separated. This concrete representation helps students visualize and solve problems.

Solving Word Problems with Sums and Differences up to 10

Students will solve simple word problems that involve adding or subtracting numbers up to 10. For example, a problem might say, "You have 4 apples and get 3 more. How many apples do you have now?" Students can use objects or drawings to model the problem and find the sum or difference. This practice connects math to real-life situations and reinforces understanding.

Common Misconceptions and How to Address Them

Some students might confuse addition and subtraction actions or think subtraction always means 'smaller' without understanding the action of separating. Use clear language and physical modeling to show that addition means joining groups and subtraction means separating groups. Encourage students to explain their thinking to clarify understanding.

Worked Examples

Worked Example 1

Scenario

You have 4 red blocks and 3 blue blocks. If you put them together, how many blocks do you have?

Explanation

Joining the two groups means adding the number of red blocks and blue blocks. 4 blocks plus 3 blocks equals 7 blocks in total.

Answer Guide

7 blocks

Worked Example 2

Scenario

There are 6 apples on the table. You eat 2 apples. How many apples are left?

Explanation

Separating means taking away 2 apples from the 6 apples. 6 apples minus 2 apples equals 4 apples left.

Answer Guide

4 apples

Engage

Teacher Activity

Introduce the lesson by showing two small groups of counters (e.g., 2 and 3). Ask students how many counters there are if we put the groups together.

Student Activity

Observe the counters and respond to the question by counting all counters after joining the groups.

Explanation

This activity helps students see the action of joining as putting groups together to find a total, which is addition.

Examples

  • Students count all counters after joining and say the total is 5.
  • Students recognize that putting groups together is called addition.

Explore

Teacher Activity

Provide students with counters and simple word problems involving joining (addition) and separating (subtraction). Guide them to use objects or drawings to solve the problems.

Student Activity

Use counters or draw pictures to model the word problems and find the answers.

Explanation

Hands-on exploration with objects and drawings allows students to concretely understand addition as joining and subtraction as separating.

Examples

  • Students physically join or separate counters to solve problems.
  • Students create drawings that represent joining or separating groups.
  • Students find correct sums and differences up to 10.

Explain

Teacher Activity

Explain the terms addition and subtraction using the actions of joining and separating. Demonstrate with counters and drawings how these actions represent addition and subtraction.

Student Activity

Listen and watch the demonstration. Repeat the terms and explain the actions in their own words.

Explanation

Clarifying vocabulary and linking it to physical actions helps solidify conceptual understanding of addition and subtraction.

Examples

  • Students can define joining as putting groups together and separating as taking groups apart.
  • Students relate these actions to addition and subtraction.

Elaborate

Teacher Activity

Present real-world word problems involving joining and separating with sums and differences up to 10. Encourage students to solve them using objects or drawings and explain their reasoning.

Student Activity

Solve the problems using counters or drawings and explain how they found the answer.

Explanation

Applying skills to real-world problems deepens understanding and shows relevance of addition and subtraction.

Examples

  • Students use objects or drawings to solve problems.
  • Students explain their reasoning using joining or separating language.
  • Students find accurate sums and differences.

Evaluate

Teacher Activity

Ask students to demonstrate joining and separating with counters and solve a short word problem independently. Observe and ask them to explain their thinking.

Student Activity

Use counters to show addition and subtraction and solve a word problem. Explain the steps taken.

Explanation

This assessment confirms students' ability to model addition and subtraction and solve related problems.

Examples

  • Students correctly join and separate counters.
  • Students solve the problem using objects or drawings.
  • Students explain their reasoning clearly.

Classroom Activity

Use counters or draw pictures to model the word problems and find the answers.

Guided Practice

Guided Practice 1

Prompt

Show how to join 2 groups of counters: one group has 1 counter and the other has 2 counters. How many counters are there in all?

Teacher Answer Guide

There are 3 counters in all because 1 plus 2 equals 3.

Guided Practice 2

Prompt

If you have 5 blocks and take away 3 blocks, how many blocks do you have left? Use objects or drawings to find the answer.

Teacher Answer Guide

You have 2 blocks left because 5 minus 3 equals 2.

Guided Practice 3

Prompt

Solve this word problem: You see 4 birds on a tree. 3 more birds join them. How many birds are there now?

Teacher Answer Guide

There are 7 birds now because 4 plus 3 equals 7.

Guided Practice 4

Prompt

Explain how joining groups is different from separating groups using counters or drawings.

Teacher Answer Guide

Joining groups means putting two or more groups together to find the total (addition), while separating groups means taking some objects away from a group to find how many remain (subtraction).

Guided Practice 5

Prompt

Create your own word problem that uses joining to add and solve it using drawings or objects.

Teacher Answer Guide

Example: I have 3 toy cars. My friend gives me 4 more toy cars. How many toy cars do I have now? Answer: 7 toy cars because 3 plus 4 equals 7.

Independent Practice

  1. Foundational: Show how to join 2 groups of counters: one group has 1 counter and the other has 2 counters. How many counters are there in all?
  2. Developing: If you have 5 blocks and take away 3 blocks, how many blocks do you have left? Use objects or drawings to find the answer.
  3. Application: Solve this word problem: You see 4 birds on a tree. 3 more birds join them. How many birds are there now?
  4. Analysis: Explain how joining groups is different from separating groups using counters or drawings.
  5. Challenge: Create your own word problem that uses joining to add and solve it using drawings or objects.

Independent Practice Teacher Answer Key

  1. 1. There are 3 counters in all because 1 plus 2 equals 3.
  2. 2. You have 2 blocks left because 5 minus 3 equals 2.
  3. 3. There are 7 birds now because 4 plus 3 equals 7.
  4. 4. Joining groups means putting two or more groups together to find the total (addition), while separating groups means taking some objects away from a group to find how many remain (subtraction).
  5. 5. Example: I have 3 toy cars. My friend gives me 4 more toy cars. How many toy cars do I have now? Answer: 7 toy cars because 3 plus 4 equals 7.

Guiding Questions

  • What does it mean to join groups?
  • How do you find the total when you join groups?
  • What does it mean to separate groups?
  • How do you find how many are left after separating?
  • Can you show me with objects or drawings?

Common Misconceptions

  • Students may think subtraction means only 'smaller' without understanding the action of separating objects.
  • Students might confuse the terms joining and separating or the operations addition and subtraction.
  • Students may count objects incorrectly when joining or separating groups if not guided carefully.

Differentiation

Support and Intervention

Provide extra counters and one-on-one guidance for students who need help counting and modeling. Use simpler word problems with smaller numbers for students who struggle. Allow students to work in pairs to support each other.

English-Language Learner Support

Use clear, simple language and gestures when explaining joining and separating. Show pictures and physical objects to support vocabulary understanding. Repeat key vocabulary and use sentence frames like 'I join ___ and ___ to get ___.'

Advanced and Extension

Challenge students to solve word problems with sums and differences close to 10 independently. Encourage students to explain their reasoning in complete sentences. Have students create their own word problems involving joining and separating.

Assessment

  • Observe students as they join and separate counters during guided practice.
  • Ask students to explain the actions of joining and separating in their own words.
  • Check students' drawings to see if they represent addition and subtraction correctly.
  • Show me how to join two groups of objects and tell me the total.
  • Show me how to separate some objects from a group and tell me how many are left.
  • Solve a simple word problem using objects or drawings and explain your answer.
  • Give a short quiz with word problems requiring addition and subtraction up to 10 using drawings or objects.
  • Have students write or draw their own addition and subtraction problems and solve them.

Answer Guide

  • Show how to join 2 groups of counters: one group has 1 counter and the other has 2 counters. How many counters are there in all?
    Answer: There are 3 counters in all because 1 plus 2 equals 3.
  • If you have 5 blocks and take away 3 blocks, how many blocks do you have left? Use objects or drawings to find the answer.
    Answer: You have 2 blocks left because 5 minus 3 equals 2.
  • Solve this word problem: You see 4 birds on a tree. 3 more birds join them. How many birds are there now?
    Answer: There are 7 birds now because 4 plus 3 equals 7.
  • Explain how joining groups is different from separating groups using counters or drawings.
    Answer: Joining groups means putting two or more groups together to find the total (addition), while separating groups means taking some objects away from a group to find how many remain (subtraction).
  • Create your own word problem that uses joining to add and solve it using drawings or objects.
    Answer: Example: I have 3 toy cars. My friend gives me 4 more toy cars. How many toy cars do I have now? Answer: 7 toy cars because 3 plus 4 equals 7.

Real-Life Application

Encourage families to practice addition and subtraction at home using everyday objects like toys or snacks. Ask students to explain how they join or separate groups to find answers.

Homework or Home Connection

  • Encourage families to practice addition and subtraction at home using everyday objects like toys or snacks. Ask students to explain how they join or separate groups to find answers.

Lesson Summary

Students learned to model addition as joining groups of objects and subtraction as separating groups. They practiced solving word problems using objects and drawings to find sums and differences up to 10. This foundational understanding supports their development of number operations and problem-solving skills aligned with TEKS standards.

Teacher Notes

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

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