In this activity, students will compute real-world problems with rational numbers while using a digital number line. Students are provided a sample problem to work through to become familiar with the digital number line. Since problems can be solved using multiple methods, students are asked to provide a number sentence to represent their number line model as well as the solution to the problem. Through the online digital tool, students can also share a link to their work with their teacher or classmates. This provides a great opportunity for students to investigate how to solve problems using multiple methods.
Using Number Lines to Model Real-World Problems Student Response Page
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
In this learning activity, students are introduced to the concept of adding and subtracting positive and negative numbers through an animated free math video from GCFLearnFree.org. In the video, a bird demonstrates how to move up and down the number line based on the operation and integers in the equation. It is a clever way to remember which direction to move based on the positive and negative numbers in the equation. Students then practice the tricks they learned using an interactive game.
This activity was created as a result of the ALEX Resource Development Summit.
In this free learning activity from Illustrative Mathematics, students will be presented with a real-world problem involving Evan and his school bookstore account. Students will need to use the tricks they have learned about adding and subtracting positive and negative numbers to help Evan with his school bookstore account and justify their reasoning.
In this free interactive math learning activity from Math is Fun, students gain an understanding of adding and subtracting positive and negative numbers by “playing” with an interactive tool.
This activity results from the ALEX Resource Development Summit.
This YouTube video will help explain how to teach adding rational numbers using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of three videos to fully teach this concept. The videos are labeled Adding Rational Numbers Part 1, Adding Rational Numbers Part 2, and Adding Rational Numbers Part 3. This video can be played to introduce a lesson on adding rational numbers. This video is 11 minutes and 35 seconds in length.
This YouTube video will help explain how to teach adding rational numbers using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of three videos to fully teach this concept. The videos are labeled Adding Rational Numbers Part 1, Adding Rational Numbers Part 2, and Adding Rational Numbers Part 3. This video can be played as a continuation of a lesson on adding rational numbers. This video is 10 minutes and 36 seconds in length.
This YouTube video will help explain how to teach adding rational numbers using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of three videos to fully teach this concept. The videos are labeled Adding Rational Numbers Part 1, Adding Rational Numbers Part 2, and Adding Rational Numbers Part 3. This video can be played as a continuation of a lesson on adding rational numbers. This video is 7 minutes and 34 seconds in length.
In this video lesson, students recognize that the difference between two numbers can be positive or negative, but the distance between two numbers is always positive. Using the geometry of the number line, they see that if you switch the order in which you subtract two numbers, the difference becomes its opposite. By observing the outcome of several examples, students conjecture that this is always true.
In this video lesson, students will learn how to add signed numbers to build fluency. They see that adding a number and its opposite gives a sum of 0. They contrast adding numbers with the same sign with numbers with different signs. In addition, the students will learn that using the structure of opposites on the number line, they see that when adding two numbers with different signs, the sign of the sum will match the sign of the addend with a greater magnitude. Students are also introduced to using negative numbers in the context of money to represent debts or debits.
Using a mathematical structure (the signed numbers) to represent a context (a checking account balance) is an example of modeling with mathematics.
In this video lesson, students investigate different ways to represent the addition of signed numbers on a number line. They review what they know about negative numbers including placing them on the number line, comparing and ordering them, and interpreting them in the contexts of temperature and elevation.
Using the context of temperature helps students make sense of the addition equations. Students see that an increase in temperature can be represented as adding a positive value and a decrease in temperature can be represented as adding a negative value. When students use quantitative contexts like temperature to aid in abstract reasoning about numeric expressions with signed numbers.
The purpose of this lesson is to develop the rules for multiplying two negative numbers. Students use the familiar fact that distance = velocity x time to make sense of this rule. They interpret negative time as the time before a chosen starting time and then determine the position of an object moving with a negative velocity at a negative time. An object moving with a negative velocity is moving from right to left along the number line. At a negative time, it has not yet reached its starting point of zero, so it is to the right of zero, and therefore its position is positive. So a negative velocity times a negative time gives a positive position. When students connect reasoning about quantities with abstract properties of numbers.
The purpose of this video lesson is to help students make sense of expressions, and reason about their position on the number line— whether the number is positive or negative, which of two numbers is larger, or whether two expressions represent the same number. They work through common misconceptions that can arise about expressions involving variables. They also reason about expressions in a and b, given the positions of a and b on a number line without a given scale. This helps develop the idea that the letters in an algebraic expression can be thought of as numbers, even if you don't know the value of a.
Students connect ideas about rational number arithmetic and the interpretation of negative quantities, such as negative time or negative rates of change. They solve problems with rational numbers in various contexts by making tables or numerical calculations. As students reason about the meaning of negative quantities, they engage in MP2.
This resource includes the Expressions with Rational Numbers and Solving Problems with Rational Numbers lesson printout and a Practice Problems handout.
Deepen your understanding of multiplication and division of rational numbers. This interactive exercise focuses on the rules for finding the products and quotients of positive numbers, negative numbers, and fractions and then finding the solutions on a number line.
This animated Math Shorts video from the Utah Education Network explains the term additive inverse and provides several examples that demonstrate the concept. In the accompanying classroom activity, students create equations and solve problems that involve adding groups of negative and positive integers that sum to zero. To get the most out of this activity, students should be familiar with plotting positive and negative integers on a number line. This resource is part of the Math at the Core: Middle School Collection.
In Topic C, students problem-solve with rational numbers and draw upon their work from Grade 6 with expressions and equations. They perform operations with rational numbers, incorporating them into algebraic expressions and equations. They represent and evaluate expressions in multiple forms, demonstrating how quantities are related. The Integer Game is revisited as students discover “if-then” statements, relating changes in players’ hands (who have the same card-value totals) to changes in both sides of a number sentence. Students translate word problems into algebraic equations and become proficient at solving equations of the form px + q = r and p(x + q) = r, where p, q, and r, are specific rational numbers. As they become fluent in generating algebraic solutions, students identify the operations, inverse operations, and order of steps, comparing these to an arithmetic solution. The use of algebra to represent contextual problems continues in Module 3.
Students will use the Quizizz response system to complete an Adding and Subtracting Rational Numbers Assessment. Quizizz allows the teacher to conduct student-paced formative assessments through quizzing, collaboration, peer-led discussions, and presentation of content in a fun and engaging way for students of all ages.
