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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

Authors: Pranit Samarth, Riaz Helfer, Sachin Nair, Satish S. Nair

Grade 1 Module 4:  Place Value, Comparison, Addition and Subtraction to 40

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Module 4 builds upon Module 2’s work with place value within 20, now focusing on the role of place value in the addition and subtraction of numbers to 40.  Students study, organize, and manipulate numbers within 40.  They compare quantities and begin using the symbols for greater than (>) and less than (<).  Addition and subtraction of tens is another focus of this module as is the use of familiar strategies to add two-digit and single-digit numbers within 40.  Near the end of the module, the focus moves to new ways to represent larger quantities and adding like place value units as students add two-digit numbers.

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

Comparisons 1

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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

Grade 2 Module 4:  Addition and Subtraction Within 200 with Word Problems to 100

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In Module 4, students develop place value strategies to fluently add and subtract within 100; they represent and solve one- and two-step word problems of varying types within 100; and they develop conceptual understanding of addition and subtraction of multi-digit numbers within 200.  Using a concrete to pictorial to abstract approach, students use manipulatives and math drawings to develop an understanding of the composition and decomposition of units, and they relate these representations to the standard algorithm for addition and subtraction.

Material Type: Module

1.OA Fact Families with Pictures

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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: Write as many equations for each picture as you can. Use the numbers 4, 1, and 5. Here are some equations for this picture. 4+1=5 \hskip4em 5 = 4+1 5-1...

Material Type: Activity/Lab

Author: Illustrative Mathematics

What's Missing?

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The words compose and decompose are used to describe actions that young students learn as they acquire knowledge of small numbers by putting them together and taking them apart. This understanding is a bridge between counting and knowing number combinations. It is how instant recognition of small numbers develops and leads naturally to later understanding of fact families. This task helps them develop an understanding of number combinations.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Grade 5 Module 5: Addition and Multiplication with Volume and Area

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In this 25-day module, students work with two- and three-dimensional figures.  Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms.  The second half of the module turns to extending students’ understanding of two-dimensional figures.  Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths.  They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifying the shapes by reasoning about their attributes.  This module fills a gap between Grade 4’s work with two-dimensional figures and Grade 6’s work with volume and area.

Material Type: Module

Grade 3 Module 4: Multiplication and Area

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In this 20-day module students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. Students conceptualize area as the amount of two-dimensional surface that is contained within a plane figure.  They come to understand that the space can be tiled with unit squares without gaps or overlaps.  They make predictions and explore which rectangles cover the most area when the side lengths differ.  Students progress from using square tile manipulatives to drawing their own area models and manipulate rectangular arrays to concretely demonstrate the arithmetic properties. The module culminates with students designing a simple floor plan that conforms to given area specifications.

Material Type: Module

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