Learning Activity

Adding Integers Using Two-Color Counters

Subject Area

Digital Literacy and Computer Science
Mathematics

Grade(s)

7

Overview

In this introductory activity, students will use two-color counters to explore adding integers. Students will also develop a working definition of the additive inverse. Using online two-color counters, students will discover algorithms for adding integers. Finally, students will develop addition integer rules based on the solutions to the mathematical sentences modeled using the two-color counters.

Adding Integers Using Two-Color Counters Student Response Page

Digital Literacy and Computer Science (2018) Grade(s): 7

DLCS18.7.6

Create and organize algorithms in order to automate a process efficiently.

Unpacked Content

UP:DLCS18.7.6

Vocabulary

  • algorithm

Knowledge

Students know:
  • algorithms can be used to automate a process efficiently.

Skills

Students are able to:
  • use search and sort algorithms to automate organizing a set.

Understanding

Students understand that:
  • algorithms organized and applied to the appropriate task can significant increase proficiency.
Mathematics (2019) Grade(s): 7

MA19.7.4

Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

Unpacked Content

UP:MA19.7.4

Vocabulary

  • Integers
  • Rational numbers
  • Additive inverses
  • opposite quantities
  • Absolute value
  • Terminating decimals
  • Repeating decimals

Knowledge

Students know:
  • a number and its opposite have a sum of 0.
  • A number and its opposite are called additive inverses.
  • Strategies for adding and subtracting two or more numbers.
  • Absolute value represents distance on a number line, therefore it is always non-negative.
  • Strategies for multiplying signed numbers.
  • Every quotient of integers (with non-zero divisor) is a rational number.
  • If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
  • The decimal form of a rational number terminates or eventually repeats.

Skills

Students are able to:
  • add rational numbers.
  • Subtract rational numbers.
  • Represent addition and subtraction on a number line diagram.
  • Describe situations in which opposite quantities combine to make 0.
  • Find the opposite of a number.
  • Interpret sums of rational numbers by describing real-world contexts.
  • Show that the distance between two rational numbers on the number line is the absolute value of their difference.
  • Use absolute value in real-world contexts involving distances.
  • Multiply and divide rational numbers.
  • Convert a rational number to a decimal using long division.

Understanding

Students understand that:
  • finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line.
  • Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
  • If a factor is multiplied by a number greater than one, the answer is larger than that factor.
  • If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
  • Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
  • Integers can be divided, provided that the divisor is not zero.
Mathematics (2019) Grade(s): 7

MA19.7.8

Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

Unpacked Content

UP:MA19.7.8

Vocabulary

  • Rational numbers
  • Integers
  • Estimation

Knowledge

Students know:
  • techniques for converting between fractions, decimals, and percents.
  • Techniques for estimation, mental computations, and how to assess the reasonableness of their answers.

Skills

Students are able to:
  • convert between different forms of a rational number.
  • Add, subtract, multiply and divide rational numbers.-translate verbal forms of problems into algebraic symbols, expressions, and equations.
  • Use estimation and mental computation techniques to assess the reasonableness of their answers.

Understanding

Students understand that:
  • One form of a number may be more advantageous than another form, based on the problem context.
  • Using estimation strategies helps to determine the reasonableness of answers.

Phase

Before/Engage
Learning Objectives

Learning Objectives

Students will develop number sentences involving adding integers.

Students will develop a working definition of the additive inverse.

Students will use the digital tool Didix Two Color Counters to model algorithms of adding integers.

Students will discover and write addition integer rules based on model solutions.

Activity Details

Students will explore adding integers using two-color counter digital manipulatives. To begin the activity learners step forward one step (+1) and backward one step (-1). This helps kinesthetic learners connect integer values to spaces on a number line in relation to zero. Next, students connect positive and negative values to two-color counters. Red counters are used to represent negative values and yellow counters are used to represent positive values. Students use this information to develop a working definition of additive inverse and create and organize algorithms (a set of rules to follow) for given problems. Using the online tool, students model number sentences using two-color counters to find the solutions to 10 addition integer problems. Answers are recorded on the “Adding Integers Using Two-Colored Counters” activity page. Next students will develop addition integer rules for the following problem types, negative + negative, positive + negative, and negative + positive. At this point, the teacher should conduct a Think-Pair-Share with the class. Each student should have a partner. Ask the students to work with their partners and compare their addition integer rules. On their activity page, they are asked to explain how their rules are alike, how they are different, and to write a statement about what they feel is important to share with the class. Allow the students to share their statements with the class and address any misconceptions students may have.

Assessment Strategies

Assessment Strategies

Assess student’s understanding by reviewing the student response page. 

The teacher will observe students using the digital tool Didix Two-Color Counters to assess organizing algorithms of adding integers.

Variation Tips

Students can write their own number sentences to use with the counter. These problems can be exchanged with classmates to solve.

Background and Preparation

Background / Preparation

Visit the Didix two-color counter online resource to become familiar with how to use the tool. 

Students will need online access to the two-colored counters manipulatives.

Copy the “Adding Integers Using Two-Colored Counters” student response page.

Digital Tools / Resources

Didix Two Color Counters
http://www.didax.com/apps/two-color-counters/

Approved Date

Owner (Author)

kdockery
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