Integers Lesson 1.3: Adding same signed numbers

Created Feb. 7, 2024 by Susan Jones

Part 1: Lesson Description

Lesson Title

1.3 Integers: Adding Signed Numbers

Links to Other Documents & Materials (student text, student practice)This lesson pertains to “Section 1.3: Adding Signed Numbers”

Download: Chapter one transitions integers_1.docx

as Open Document Format (draft)

Download: Chapter One Transitions Math April2016.odt

Google Doc link: Chapter One Transitions Math Google Doc

Key with Teaddiacher's Notes and Comments:

Download: Chapter One Transitions Integers Key.docx

Google Docs Link: Chapter One Transitions Math (Integers) Answer Key - Google Doc

https://www.youtube.com/watch?v=IkV-dHnDNAU -- 6:48 video version of lesson (which I’ll be re-working for better sound). (audience: students).

https://www.youtube.com/watch?v=hGVm2xs0HEA videos explaining different models for explaining adding and subtracting integers to students (audience: teachers)

Abstract

For many adult students, positive and negative integers are an example of when math “keeps changing the rules.” This is the third of six lessons guiding students in constructing the abstract concepts necessary to understand adding positive and negative integers.

This lesson will review previous knowledge about negative numbers and teach adding integers with the same sign, with connections to “real life” situations such as gains and losses in football yards or bank account overdraws.

Learner Audience / Primary Users

This lesson is part of a structured sequence of multisensory, conceptual lessons building basic math concepts for students who struggle with number sense and arithmetic, especially figuring out what to do with practical problems. It is taken from Parkland College's "Transitions" course for students whose placement test scores do not qualify them for Pre-algebra. In 4 semesters, fewer that 5% of students have questioned whether their placement was valid. They recognize the need for more than a quick review of math.

Educational Use

Curriculum / Instruction
Professional Development College & Career Readiness Standards (CCRS) Alignment

Level: Adult Education
Grade Level:
Subject: Mathematics
Domain or Strand:

Number Sense
Primarily Math Practices 1, 2
Level D (because it includes negative numbers -- It is not assumed that students are competent with the first three levels.)
Standard Description: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. (6.NS.6) • Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. (6.NS.6a)
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. (6.NS.6c) Understand ordering and absolute value of rational numbers. (6.NS.7)
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. (6.NS.7a)
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3º C > –7º C to express the fact that –3º C is warmer than –7º C. (6.NS.7b)
Apply this knowledge to adding integers of the same sign (with applications to practical situations such as cold temperatures and debt).

Language

English

Material Type

Instructional material
Student Text
Student practice
Lecture Notes
Video

Learning Goals

The purpose of this lesson is for learners to be able to:

Add positive to positive numbers
Add negative to negative numbers

Keywords

Adult Education
Integers
Math
Math Anxiety
Multisensory
Learning Disabilities
Developmental Math
CCRS
RI.6.2

Time Required for Lesson

20-30 minutes

Prior Knowledge

Learners should have counting skills and have completed lesson 1.1 and 1.2 This course is designed for students with minimal "prior knowledge" or math skills.

Required Resources

Text and paper and pencil.There are support videos that can be viewed online or downloaded for viewing with a device that can show MP4 videos (computer, tablet, telephone).

Lesson Author: Susan Jones using text by Kathy Wahl

download image

License: Creative Commons CC BY 4.0 license

Part 2: Lesson

Learning Objectives

By the end of this lesson, the ESL, ABE or GED learner should be able to:

Add integers of the same sign to each other

Lesson Topics

Key topics covered in this lesson include:

Applying negative and positive number concepts to debt and temperature
Adding numbers of the same sign to each other.
Addressing common misconception that “two negatives make a positive.”

This lesson is the initial entry into math for students whose math background is below what’s expected for adults. They may have been in special education settings in K-12. In our setting, they will have taken the Accuplacer math placement test and scored below the required score to place into “Pre-Algebra.” However, they need more than “test preparation’ and review. “

These students are usually degree- or certificate- seeking students who have significant gaps in their arithmetic and algebra skills.

Relevance to Practice

Understanding negative numbers is relevant because of their use in topics such as budgeting and science, as well as in required courses and placement tests. We have moved this chapter to the beginning of the course because we feel it will have the affective advantage of being an abstract, non-elementary math topic, while allowing the teacher to discern the students’ number sense with single-digit operations. Many students with this placement are still adding by “counting up” or even counting from zero, and we can address this here without the student having to do primary-level math. For example, students label number lines with positive and negative numbers “counting by fives,” or twos, or tens.

Key Terms and Concepts

Note: many of these terms will be “familiar” to learners, but we will be using and applying them in less familiar ways.

Addition

Integer

Negative

Opposite

Parentheses

Positive

Instructional Strategies and Activities

Warm-Up (a minute)

This should be adapted to the learners.

One possible warm up is:

Review the concept (relating it to real situations) that -10 is lower than -5.
Review that number lines go from smaller to larger going left to right and that spaces need to be consistent but can be of different sizes, so we can count by twos or fives or threes.
Ask students to remind you which sign means greater than and which sign means less than. You might want to put this poster up, or make smaller printouts of the images for students.

Introduction (1 minute)

We’ve learned what positive and negative numbers mean -- now we’re going to see what happens when we work with these numbers and “do math” with them. What math could we do?

Presentation / Modeling / Demonstration

Time: 6 minutes

Use the text pages 9-13. Begin with students drawing their own examples of “regular” addition with positive numbers. Talk about how we could “draw” the idea of adding negative amounts.

View the video https://www.youtube.com/watch?v=IkV-dHnDNAU -- pause periodically to see whether students have questions.

Guided Practice

Time: 15 minutes

Use text p.10 to have students “illustrate” the problems on page 10 (which include the answers).

Take a “break” and explain a common source of confusion to students -- parentheses. Do they mean multiply? (See textbook.)

Then have students illustrate *and solve* the next problems.

Finally, have students work together to create their own “negative plus negative” example.

Evaluation

Time: 5-10 minutes (will vary)

https://docs.google.com/document/d/1tEaqIao6cZ1LUmYkxyFk028NesjlbzsJVrsFhYidThA/edit?usp=sharing

Part 3: Supplementary Resources & References

Supplementary Resources

http://www.mathatube.com/pre-algebra-adding-integers-with-the-same-signs.html

http://www.mathsisfun.com/positive-negative-integers.html -- summary of adding

http://www.scholastic.com/teachers/top-teaching/2012/09/positive-approach-teaching-negative-numbers ideas for teachers for explaining negative numbers

References/Attribution Statements

Transitions, Chapter One contributed by Kathy Wahl and Sue Jones of Parkland College to this project.