Math at the Core: Middle School

Operations and Algebraic Thinking


  • Finding Patterns to Make Predictions

    Make predictions then explore the patterns found in everyday objects like stairs. This interactive exercise focuses on developing an equation to represent a mathematical rule and working with virtual manipulatives to visualize a concept, taking math out of the classroom and into the real world. This resource is part of the Math at the Core: Middle School collection.

    Grades: 3-8
  • Creating Numerical Patterns with Rules: Bianca Functions in the Wild

    In this Cyberchase video, Bianca and her friend go camping and soon realize that Bianca has left the food at home. They find a vending machine in the woods, but it doesn't dispense the food that corresponds with the numbers Bianca presses. After several attempts to get her favorite candy bar, Bianca discovers a pattern, or rule. Each time she enters a number, she gets a snack labeled with the number she pressed plus two (n + 2). In the accompanying classroom activity, students play a dice game in pairs in which one student applies a rule in secret that the other student must guess. Points are awarded for correct guesses, and students are penalized for incorrect guesses. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-6
  • Stop the Machine!

    In this interactive from WNET, shut down a series of creature-controlling machines by determining the solution to a function. When changing one quantity determines the value of another, they are connected by a rule you may not see. Find the rule and you can predict any outcome. In the accompanying classroom activity, students use a deck of playing cards to see if they can use what they learned in the interactive about rules, functions, and numbers in another game called "Mystery Envelope." This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5
  • Order of Operations

    Discover the importance of order of operations when solving an expression. This video focuses on implementing PEMDAS and demonstrates the reason we need order of operation by solving a single expression in three different, two incorrect, ways. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
    Grades: 4-6
  • Order of Operations: PEMDAS

    Watch and listen to a recitation of the order of operations set to hip-hop music. This video focuses on PEMDAS as the acronym for order of operations and demonstrates the concept by walking through a problem in the correct order. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers. This resource is part of the Math at the Core: Middle School collection.

    Grades: 5-6
  • Algebraic Expressions

    In this interactive From APT, write algebraic expressions and practice using mathematical terms relating to algebraic expressions. In the accompanying classroom activity, students begin with an introduction to mathematical terms relating to algebraic expressions. Then, they play a game in which they write expressions with numbers and variables generated randomly. Finally, they consolidate what they learned using the interactive. To get the most from the lesson, students should be comfortable using parentheses in numerical expressions and evaluating expressions with parentheses. They should also have some exposure to expressions involving one variable. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7,13+
  • Make It Math

    Solve the problems online and watch an image appear on the coordinate plane. This interactive exercise can be set up by you or your teacher to focus on a range of algebraic or computational skills.

    This activity was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

    Grades: 4-8
  • Super Stairs: Patterns of Ordered Pairs

    Try to find the numerical pattern to describe what happens when Dan runs stairs. This interactive exercise focuses on using what you know about pattern recognition and using data to write expressions in order for you to figure out the equation to model the situation given.
    Grades: 4-6
  • Toothpicks: Patterns in Geometric Shapes

    How can you describe the pattern made by a growing triangular shape? This interactive exercise focuses on using what you know about pattern recognition and completing a table so you have data you can use to graph the coordinates on a plane to make predictions about the ongoing pattern.
    Grades: 4-6
  • Gauss-Arithmetic Sequence Strategy

    Learn how mathematician Karl Friedrich Gauss figured out how to sum up any arithmetic sequence without having to add up each and every term. This video focuses on using your critical thinking to follow along as Gauss determines his formula for adding series of numbers and gives you the formula so you can test it on other number series.

    This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

    Grades: 4-7
  • Math in Fashion

    Following a profile of fashion designer and Project Runway winner Chloe Dao, students are prompted to alter garment designs, using their sense of style combined with their math skills to hit target price points. Algebra concepts explored include: linear relationships; rates (percents), ratios, and proportions; using multiple representations; algebraic and numeric expressions, equations, and inequalities. Please click the Display SPL link below to view. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-10
  • Math in Restaurants

    Students are introduced to Sue Torres, an accomplished chef and restaurant owner and learn how she uses math in her work. Sue presents teams with a mathematical restaurant challenge: find the best price point to charge for guacamole, a popular item in the restaurant by identifying what she should pay for avocados, the main ingredient. In this lesson, students focus on understanding the Big Ideas of Algebra: patterns, relationships, equivalence, and linearity; learn to use a variety of representations, including modeling with variables; build connections between numeric and algebraic expressions; and use what they have learned about number and operations, measurement, statistics, as applications of algebra. Please click the Display SPL link below to view. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-10
  • Math in Special Effects

    Using video and web interactives from Get the Math, students engage in an exploration of mathematics, specifically reasoning and sense making, to solve real world problems and learn how special effects designers use math in their work. In the challenge, students focus on understanding the Big Ideas of Algebra: patterns, relationships, equivalence, and linearity; learn to use a variety of representations, including modeling with variables; build connections between numeric and algebraic expressions; and use what they have learned previously about number and operations, measurement, proportionality, and discrete mathematics as applications of algebra. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-10

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