A different way to look at integers is on this number line with variables in place of numbers. Learners are to look at different expressions and describe why they think the answer would be positive or negative, depending on the location...

The ninth installment of a 21-part module has pupils compare integers and rational numbers in decimal and fraction form. They match stories to number lines and compare values in the stories.

This resource sneaks in the math so your learners will be adding and subtracting positive and negatives on a number line while thinking they are mapping out houses. The activity starts by putting houses the appropriate distance away from...

Four inequality statements are given for the same two negative numbers. The resource is a good practice for pupils to interpret statements of inequalities relative to the position on the number line. The objective is for pupils to...

Experiment with integer relationships. Young scholars consider integers that have a sum of 10. They begin with two integers, then three, four, and more. As they consider each situation, they discover patterns in the possible solutions.

How many ways can you make 10? Class members tackle three problems to find all possible ways three numbers add to be 10. The first is with positive integers, secondly with non-negative integers, and finally with real numbers. Pupils also...

Make your own number line ... using a compass. The first installment of a 21-part series has scholars investigate positive and negative integers on a number line by using a compass to construct points that are the same distance from zero...

Learners demonstrate their ability to operate with rational numbers through a five-question assessment that includes questions ranging from simple operations with integers to solving two-step equations with rational coefficients.

Ensure your class has a solid understanding of positive and negative integers before moving on. The 14th installment of a 21-part series is a mid-module assessment. Scholars solve problems on positive and negative integers, on...

Subtracting negative numbers can be confusing to your middle schoolers. Here, they are able to draw a number line and put their answer in sentence form to check their understanding of negative numbers. 

Mathematics involves a study of patterns. The exploratory lesson has learners consider the addition pattern in different sets of numbers. Each set has a different pattern that pupils describe mathematically. The patterns involve...

Mathematics minors consider the magnitude of a jumping flea as he hops from place to place. Through this exercise, they will investigate absolute values, as well as positive and negative rational numbers on a number line. The first page...

A rational number is a ratio of two integers. Discuss with your class how to convert the rational numbers of repeating decimals to fractions. A good commentary on letting x equal the repeating decimal and multiplying each side of...

Scholars learn how to write number theory proofs by viewing a video reviewing techniques for proofs on divisibility, parity, and consecutive integers. They then write proofs for a handful of conjectures on a worksheet.

Continuing from the previous lesson in the series, scholars learn to use positive and negative integers to describe real-world situations. In groups, they come up with their own situations for given positive and negative integers. 

Access the instructional counting level of your class by prompting them to recall consecutive numbers within a given number range. Working one-on-one with your students and starting with the number range of 1-10, and working toward the...

During a walk-a-thon your learners must determine the walking rate of Julianna's progress. Using tables, graphs, and an equation, they must be able to calculate the time it took her to walk one mile and predict her distance based on the...

Time to see what they've learned. Seventh graders solve a set of seven short problems in the ratios and proportional relationships domain. Applications include photo negatives, washing machines, coffee powder, sleep, stamps, etc.

AP exams don't have to be a mystery. Scholars look at the free-response questions for the 2015 AP Computer Science A exam. They get a chance to see actual AP questions involving one- and two-dimensional arrays of integers and the design...

The best way to familiarize yourself with a test's format is to look at past tests. The free-response questions for the 2018 AP Computer Science A are available for instructors to reference. Topics include simulation methods, word pairs,...

It's opposite day! The fourth installment of a 21-part module teaches scholars about opposites of integers and of zero. Number lines and real-world situations provide an entry point to this topic.

It's said that opposites attract, but what about opposites of opposites? Individuals learn about the opposite of opposites using number lines. They complete a group activity in which members determine the opposite of opposites of...

What is the meaning of sea level? This resource helps your class understand the meaning of elevations above, below, and at sea level. Provides for good discussion on using positive and negative numbers to represent quantities in the real...

Class members investigate how positive and negative numbers are useful in the real world. Individuals first read a short passage and identify terms indicating positive and negative numbers. They consider situations involving positive...