Human Number Line

Students extend their knowledge of number to the negatives by building on prior knowledge of ordering positive rational numbers and plotting them on a number line. Students learn that opposite on a number line means to reflect over the origin. They also learn that the negative sign is used as notation for opposites. Students explain the meaning of 0, positive numbers, and negative numbers in a variety of contexts.

Magnificent Magnitude

Students formalize the idea that opposites are the same distance from zero and call this distance the absolute value of a number. Students continually revisit the meaning of absolute value, focusing on distance from 0. Students evaluate absolute value statements and compare numbers using absolute values. Students solve problems using absolute value statements.

What’s in a Name?

Students formally classify numbers as rational numbers and understand that all numbers they have studied so far are subsets of the rational numbers. Students sort and classify numbers. They investigate the density of rational numbers by locating rational numbers between other rational numbers.

Four Is Better Than One

Students build from working with rational numbers on a number line to rational numbers on a coordinate plane. They identify the four quadrants, identify points, and make generalizations about points located in given quadrants. Students determine distances between two points that have a common coordinate.

Math Football

A math football game is used to model the sum of positive and negative integers. Rules for the game and a game board are provided. Students use number cubes to generate the integers. They then take that same information and write integer number sentences

Walk the Line

A number line is used to model the sum of two integers. Students begin the lesson by walking a number line on the floor of the classroom. Through a series of activities, students will notice patterns for adding integers. After the kinesthetic activity, students examine a Worked Example and then practice calculating sums of positive and negative numbers using a number line model. Questions focus students on the distance an integer is from 0 on the number line, or the absolute value of the integer, to anticipate writing a rule for the sum of two integers having different signs. Students demonstrate their understanding of the patterns by writing informal rules for adding integers. Finally, they use a number line model to determine unknown values in equations.

Two-Color Counters

Through a series of activities with two-color counters, students will develop rules for adding integers. Students determine that to have a sum of zero, two integers must have opposite signs but the same absolute value. Examples of modeling the sum of two integers with opposite signs using two-color counters are provided. The counters are paired together, one positive counter with one negative counter, until no possible pairs remain. The resulting counters determine the sum of the integers. Several models are given and students write a number sentence to represent each model. Students critique reasoning about using the two-color counters to model adding integers. They draw models for given number sentences and create number sentences for given models. They create a graphic organizer to represent the sum of additive inverses using a variety of representations.

What’s the Difference?

Number lines and two-color counters are used to model subtraction of signed numbers. Through a series of activities, students will develop rules for subtracting integers. As in the lesson on adding signed numbers, the number line method is used to model the difference between two integers. Students then learn how to use zero pairs when performing subtraction using the two-color counter method. Students analyze real-world situations that require calculating the distance between two signed numbers. They build on what they already know about absolute value to determine the distance.

Equal Groups

Two-color counters and number lines are used to model the product of two integers. Through a series of activities, students develop rules to determine the sign of a product or quotient of two integers. They conclude that multiplying or dividing two positive integers or two negative integers always results in a positive product or quotient, and that multiplying or dividing a positive integer by a negative integer always results in a negative product or quotient. Questions focus students on the sign of a product resulting from the multiplication of two positive integers, two negative integers, and one positive and one negative integer. Students apply this knowledge to determine the sign of the product that results from multiplying three or more integers.