## Common Core State Standards for Mathematics

Grade(s) 3 resources related to the following standard:
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

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This narrative document describes the progression of Counting and Cardinality and Operations and Algebraic Thinking across the K-5 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary students that of understanding and using numbers. The focus is on the basic operations—the kinds of quantitative relationships they model and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships.
Reference Materials, Article
Grade Level: K, 1, 2, 3, 4, 5
This interactive applet allows a student to visually explore the concept of factors by creating different rectangular arrays for a number. The user constructs the array by clicking and dragging on a grid. The length and width of the array are factors of the number. A student can elect an option of a randomly selected number or the student selects his own number between 2 and 50. Exploration questions are included to promote student discovery of mathematical concepts with factors.
Activity, Interactive Media
Resource is part of a PD collection
This Sketchpad activity, which opens on Geometer's Sketchpad as well as on iOS with Sketchbook Explorer (cataloged separately), allows students to be informally introduced to a rectangular array model of multiplication in this series of three games. Learners subdivide a rectangular array into strips of size 1, 2, and 5 squares and then skip count to determine the total number of squares in the array. A three-minute movie provides detailed instructions and downloadable PDF of teacher notes and student worksheets are also included.
Activity, Instructor Guide/Manual, Tutorial, Video
This virtual manipulative is a Java applet that allows students to explore concepts in whole number operations and fractions, just as they would with a physical manipulative such as Cuisinaire Rods. The user can add bars of length 1 to 10 to the workspace, change their color, and move, duplicate, or remove them. Instructions for using the applet and teaching ideas for parents/teachers are available through the links at the top of the page.
Activity
Grade Level: K, 1, 2, 3, 4, 5, 6+
In this 28-minute professional development video, teachers focus on geometry and spatial relations by having students explore shapes that tessellate and have the same area. Teachers from different grade levels collaborate on what they want their students to be able to understand and accomplish. Viewers can watch how a 3rd-grade teacher guides his students in understanding area through the application of tessellations. Support Materials includes a Sidewalk Capers Lesson Plan.
Activity, Lesson Plans, Video
This activity tool for the interactive white board (free access with registration) displays all the factor pairs a number has in an organized list after users choose a number and then press 'set'. When the numerical expression is clicked, an array of dots is shown to the left. Learners can relate the arrays to the times table by looking at the multiplication expressions shown at the side.
Activity, Interactive Media
This brief article advocates the use of arrays to model the commutative and distributive properties as well as the inverse relationship between multiplication and division. The author explains how arrays also help children form mental pictures that support their memory and reasoning.
Instructional Strategy, Reference Materials, Article
Grade Level: 2, 3, 4, 5
Resource is part of a PD collection