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Content Area: Math
Index: 4.4D Grade 4 CPI 1
Standard: 4.4 - Data Analysis, Probability, and Discrete Mathematics
Strand: D - Discrete Mathematics--Vertex-Edge Graphs and Algorithms
Cumulative Progress Indicator: 1 - The student will follow, devise, and describe practical sets of directions (e.g., to add two 2-digit numbers).
Grade: 4
Sample Activities:
· Students follow a recipe to make a cake or to assemble a simple toy from its component parts, and then write their own versions of those instructions.
· Students give written and oral directions for going from the classroom to another room in the school, and represent these directions with a diagram drawn approximately to scale.
· Students read Anno's Mysterious Multiplying Jar by Mitsumasa Anno. During a second reading they devise a method to record and keep track of the increasing number of items in the book and predict how that number will continue to grow. Each group explains its method to the class.
· Students write step-by-step directions for a simple task like making a peanut butter and jelly sandwich, and follow them to prove that they work.
· Students find and describe the shortest path from the computer to the door or from one location in the school building to another.
· Students find the shortest route from school to home on a map, where each edge has a specified numerical length in meters; students modify lengths to obtain a different shortest route.
· Students write a program which will create specified pictures or patterns, such as a house or a clown face or a symmetrical design. Logo software is well-suited to this activity. In Turtle Math, students use Logo commands to go on a treasure hunt, and look for the shortest route to complete the search.
· Working in groups, students create and explain a fair way of sharing a bagful of similar candies or cookies. (See also the vignette entitled Sharing A Snack in the Introduction to this Framework.) For example, if the bag has 30 brownies and there are 20 children, then they might suggest that each child gets one whole brownie and that the teacher divide each of the remaining brownies in half. Or they might suggest that each pair of children figure out how to share one brownie. What if there were 30 hard candies instead of brownies? What if there were 25 brownies? What if there were 15 brownies and 15 chocolate chip cookies? The purpose of this activity is for students to brainstorm possible solutions in the situations where there may be no solution that everyone perceives as fair.
· Students devise a strategy for never losing at tic-tac-toe.
· Students find different ways of paving just enough streets of a "muddy city" so that a child can walk from any one location to any other location along paved roadways. In "muddy city" none of the roads are paved, so that whenever it rains all streets turn to mud. The mayor has asked the class to propose different ways of paving the roads so that a person can get from any one location to any other location on paved roads, but so that the fewest number of roads possible are paved.
· Students divide a collection of Cuisenaire rods of different lengths into two or three groups whose total lengths are equal (or as close to equal as possible).
Kidspiration Activities
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