# Algebra Explorations, Pre-K through Grade 7

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CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.

Material Type: Activity/Lab, Teaching/Learning Strategy

# Linear Equations Game

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Students groups act as aerospace engineering teams competing to create linear equations to guide space shuttles safely through obstacles generated by a modeling game in level-based rounds. Each round provides a different configuration of the obstacle, which consists of two "gates." The obstacles are presented as asteroids or comets, and the linear equations as inputs into autopilot on board the shuttle. The winning group is the one that first generates the successful equations for all levels. The game is created via the programming software MATLAB, available as a free 30-day trial. The activity helps students make the connection between graphs and the real world. In this activity, they can see the path of a space shuttle modeled by a linear equation, as if they were looking from above.

Material Type: Activity/Lab

Author: Stanislav Roslyakov

# Grade 8 Module 4: Linear Equations

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In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs.  Students understand the connections between proportional relationships, lines, and linear equations in this module.  Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.

Material Type: Module

# Grade 7 Module 3: Expressions and Equations

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This module consolidates and expands upon students understanding of equivalent expressions as they apply the properties of operations to write expressions in both standard form and in factored form.  They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers.  Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities.  They interpret solutions within the context of problems.  Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms.

Material Type: Module

# Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions

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In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.

Material Type: Module

# A-REI Reasoning with linear inequalities

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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The following is a student solution to the inequality \frac{5}{18} - \frac{x-2}{9} \leq \frac{x-4}{6}. \begin{align} \frac{5}{18} - \frac{x-2}{9} & \le...

Material Type: Activity/Lab

Author: Illustrative Mathematics

# Dimes and Quarters

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This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.

Material Type: Activity/Lab

Author: Illustrative Mathematics

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This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. The progression of the content standards is 6.EE.8 to 7.EE.4 to A-REI.12.

Material Type: Activity/Lab

Author: Illustrative Mathematics

# Are They Similar?

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In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.

Material Type: Activity/Lab

Author: Illustrative Mathematics

# Sum of Angles in a Polygon

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This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180_.

Material Type: Activity/Lab

Author: Illustrative Mathematics

# Robot Design Challenges

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Through the two lessons and five activities in this unit, students' knowledge of sensors and motors is integrated with programming logic as they perform complex tasks using LEGO MINDSTORMS(TM) NXT robots and software. First, students are introduced to the discipline of engineering and "design" in general terms. Then in five challenge activities, student teams program LEGO robots to travel a maze, go as fast/slow as possible, push another robot, follow a line, and play soccer with other robots. This fifth unit in the series builds on the previous units and reinforces the theme of the human body as a system with sensors performing useful functions, not unlike robots. Through these design challenges, students become familiar with the steps of the engineering design process and come to understand how science, math and engineering including computer programming are used to tackle design challenges and help people solve real problems. PowerPoint® presentations, quizzes and worksheets are provided throughout the unit.

Material Type: Full Course, Unit of Study

# Grade 1 Module 6: Place Value, Comparison, Addition and Subtraction to 100

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In this final module of the Grade 1 curriculum, students bring together their learning from Module 1 through Module 5 to learn the most challenging Grade 1 standards and celebrate their progress. As the module opens, students grapple with comparative word problem types. Next, they extend their understanding of and skill with tens and ones to numbers to 100. Students also extend their learning from Module 4 to the numbers to 100 to add and subtract. At the start of the second half of Module 6, students are introduced to nickels and quarters, having already used pennies and dimes in the context of their work with numbers to 40 in Module 4. Students use their knowledge of tens and ones to explore decompositions of the values of coins. The module concludes with fun fluency festivities to celebrate a year's worth of learning.

Material Type: Module

# Grade 2 Module 3: Place Value, Counting, and Comparison of Numbers to 1,000

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In this 25-day Grade 2 module, students expand their skill with and understanding of units by bundling ones, tens, and hundreds up to a thousand with straws. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana?1 hundred, 2 hundred, 3 hundred, etc. A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones. The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart.

Material Type: Module

# Grade 2 Module 1: Sums and Differences to 20

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Module 1 sets the foundation for students to master the sums and differences to 20 and to  subsequently apply these skills to fluently add one-digit to two-digit numbers at least through 100 using place value understandings, properties of operations and the relationship between addition and subtraction.

Material Type: Module

# Grade 1 Module 2:  Introduction to Place Value Through Addition and Subtraction Within 20

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Module 2 serves as a bridge from students' prior work with problem solving within 10 to work within 100 as students begin to solve addition and subtraction problems involving teen numbers. Students go beyond the Level 2 strategies of counting on and counting back as they learn Level 3 strategies informally called "make ten" or "take from ten."

Material Type: Module

# Counting Stamps

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This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred.

Material Type: Activity/Lab

Author: Illustrative Mathematics

# Comparisons 2

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In this task students are required to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.

Material Type: Activity/Lab

Author: Illustrative Mathematics