Integers Lesson 1.4: Adding same signed numbers using number line

Created Feb. 7, 2024 by Susan Jones

Adding Signed Numbers using the number line

Links to Documents

Chapter One: Transitions Math (Microsoft document)

Chapter One: Transitions Math -- Open Office document

Chapter One: Transitions Math -- Google Document

Key with Teacher's Notes:

Chapter One Transitions Integers Key.docx

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

Abstract

For many adult students, positive and negative integers are an example of when math “keeps changing the rules.” This is the fourth 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. The previous lesson focused on “real life situations” and this will teach expressing those real life situations on a number line. The actual problems will still be adding integers of the same sign because of the prevalence of confusion with adding two negative numbers.

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: Middle school and up

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:

Apply previous knowledge (see lessons 1.1 to 1.3) with practical examples of adding the same signed amounts (e.g. starting at 5 below zero and “adding” a loss of 2 degrees, or losing 3 dollars and then losing 2 more) to modeling addition of integers with the same sign on a number line.

Language

English

Material Type

Instructional material

Student Text

Student practice

Lecture Notes

Learning Goals

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

Add positive to positive numbers

Add negative to negative numbers

Discern whether answers to these problems are greater than, less than, or equal to answers to similar problems

Show these ideas on a number line

Keywords

Adult Education

Integers

Math

Math Anxiety

Multisensory

Learning Disabilities

Developmental Math

CCRS Standard: RI.6.2

Time Required for Lesson

15-20 minutes (though this is somewhat variable; for some students this will be “review,” and for others, a new application of new knowledge).

Prior Knowledge

Learners should have counting skills and have completed lesson 1.1 and 1.2 and 1.3 This lesson explicitly teaches applying the knowledge of number lines learned in lesson 1.2 to the addition learned in lesson 1.3 . 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

License:

Creative Commons CC BY 4.0 license

LESSON

Instructional Strategies and Activities

Warm-Up (five minues )

This should be adapted to the learners. (In my idea of a blended course, the practice would be individually adapted and students would get instant feedback so they’d know right away if they correctly identified the larger quantity and had the right “greater than” or “less than” sign.)

The “warm-up” is longer for this lesson because we are including more practice and review to develop fluency.

One possible warm up is:

Integer size review - give students time to work on it, then review with class

Adding same signed integer review --

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 added numbers using images and stories and red and black counters. In this lesson, we’ll practice applying what we know to using a number line.

Presentation / Modeling / Demonstration

Time: 2 minutes

Use the text page 14 . Compare the pictures from the second “review” lesson to the number line -- note these properties of number lines:

Number lines are based on zero – but you can actually start anywhere.

The spaces have to be consistent – but they can be large or small.

We traditionally start small on the left and get bigger to the right.

The “origin” is zero – but now that we’re higher level thinkers, we can go backwards forever, too!

Guided Practice

Time: 5 minutes

Use text p.14-17 to have students practice illustrating addition of same-signed numbers on the number line.

Take a “break” and show (using textbook) the commutative property. An analogy that works for some students is that “commuting” is going back and forth to work, and it’s the same distance either way. This also helps students who might want to say or write “communative.”

Complete the next problems in the text.

Help students see the pattern that they can use as a rule for deciding what to do: If two numbers are the same sign, we add their (absolute) values and keep the sign.

It is worth clarifying that we are only adding the “number” part -- the absolute value at this point. “Set the sign aside for now and add them… then give them back their sign when you’re done.”