## Common Core State Standards for Mathematics

Grade(s) 3 resources related to the following standard:
Operations and Algebraic Thinking
Understand properties of multiplication and the relationship between multiplication and division.
5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

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This Flash game develops students' computational fluency and flexibility. It can be played alone or with others. Players choose 6 face-down number cards, and the applet provides a target number. Number cards include one each of 25, 50, 75, and 100, and multiple copies of 1 to 10. The goal is to use the selected numbers and the four basic operations (addition, subtraction, multiplication, division) to arrive at the target. Players can ask the applet to Show a Solution, although others may be possible. Several rule and scoring variations are suggested. A full screen option facilitates use on an interactive board. (This game is not self-checking.)
Activity, Game, Interactive Media
This interactive 100 grid has a variety of open-ended uses. Users can "make" as many counters as they choose from among three different kinds, and then drag them onto the grid, allowing any number to be covered by up to 3 different markers at one time. An Ideas page offers possible tasks and games suited to the applet.
Activity, Interactive Media
Grade Level: K, 1, 2, 3, 4, 5
With this flexible Flash applet students can explore a wide range of concepts, including addition and subtraction, factors and multiples, fractions, ratios, and combinations. Users place, move and rotate virtual Cuisenaire Rods on a grid which can be enlarged, reduced, moved or printed. It contains a link to page of challenges which can take advantage of this tool.
Activity, Interactive Media
Grade Level: 1, 2, 3, 4, 5
This Java applet shows the distributive property in action. Toggle to change the height and width of a rectangle, the side lengths of which represent two factors; click on any interior edge of the rectangle's unit squares to create a new re-grouping. An expression appears at the bottom displaying the numeric representation of the new groups, illustrating the distributive property.
Interactive Media
This Flash applet allows the user to explore the concept of a function using an input-output machine with two operations and options to set and hide or reveal all operations and numbers. A notepad is available for recording inputs and outputs, and a loop function takes the current output as the next input.
Activity, Interactive Media
Grade Level: 3, 4, 5, 6+
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 lesson plan provides the teacher with an activity for introducing the game Krypto, which helps to develop number sense, computational skill, and an understanding of the order of operations. Players are given five number cards. They combine them, using the standard arithmetic operations, to create a target number. As students investigate the game, they develop strategies for finding solutions efficiently. The plan includes learning objectives, materials needed, questions to ask students, assessment options, extensions, teacher self-reflection questions, and a link to the online version, Primary Krypto, (catalogued separately).
Activity, Game, Lesson Plans
Grade Level: 3, 4, 5, 6+