Algebra: Algebra II

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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 4: Multiplication and Division of Fractions and Decimal Fractions

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Grade 5’s Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions.  Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication.  The module proceeds to fraction by fraction multiplication in both fraction and decimal forms.  An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa.  Students are introduced to the work of division with fractions and decimal fractions.  Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers.  Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients.  Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams.

Material Type: Module

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

5.MD Using Volume to Understand the Associative Property of Multiplication

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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: Make sure you have plenty of snap cubes. Build a rectangular prism that is 2 cubes on one side, 3 cubes on another, and 5 cubes on the third side. We w...

Material Type: Activity/Lab

Author: Illustrative Mathematics

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

Making a Ten

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This task requires students to study the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Naked Egg Drop

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Student pairs experience the iterative engineering design process as they design, build, test and improve catching devices to prevent a "naked" egg from breaking when dropped from increasing heights. To support their design work, they learn about materials properties, energy types and conservation of energy. Acting as engineering teams, during the activity and competition they are responsible for design and construction planning within project constraints, including making engineering modifications for improvement. They carefully consider material choices to balance potentially competing requirements (such as impact-absorbing and low-cost) in the design of their prototypes. They also experience a real-world transfer of energy as the elevated egg's gravitational potential energy turns into kinetic energy as it falls and further dissipates into other forms upon impact. Pre- and post-activity assessments and a scoring rubric are provided. The activity scales up to district or regional egg drop competition scale. As an alternative to a ladder, detailed instructions are provided for creating a 10-foot-tall egg dropper rig.

Material Type: Activity/Lab

Author: Lauren Jabusch

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