Core Decisions of Teaching
What?
Students will build on their understanding of addition and subtraction by working with combinations of the numbers 1 through 20. They will enhance their understanding of numeric combinations by adding quantities ranging from 1 to 10 to sum 20 or less. Students will build upon their knowledge of the landmark numbers 10 and 15, and of combining single digits to make multiple combinations. Students will work towards developing computational fluency through number compositions, which “is an integral part of learning with depth and rigor about numbers and operations” (Russell, 2000, p. 158). By providing a familiar framework using the concept of making pizzas, an objective is to steer students from “growing evidence” that suggests students “have difficulty learning to bring meaning to their work” once they practice “procedures without understanding” (Russell, 2000, p. 156). Students will work towards improving the ideas of efficiency, accuracy and flexibility of fluency by “applying knowledge about the structure of the base-ten system” as they create multiple combinations of pizza toppings and engage their understanding of procedures (Russell, 2000, p. 155).
How?
Students will work in pairs to create numeric combinations of pizza toppings with assigned values of 1 to 10 in order to sum 20 or less. Each student will select one combination and create a personalized pizza that will represent their choices. These pizzas engage individual interests and allow students to “use what they already know, including understandings they have already constructed” in order to problem solve (Hiebert et al). They will learn to construct their own methods by discovering what works in order to create combinations up to 20. Working in pairs, students will visualize addition methods by recording their combinations on a graphic organizer, and will refer to the enlarged graphic organizer with pictures as a tool for visualizing the numerals. Culminating the lesson, I will facilitate a group discussion where students share their pizzas and engage in a discussion of the various combinations with which one can make a pizza for $20.
Why?
My focusing question is about how we can incorporate prior knowledge and individual interests into curriculum design. By asking students to incorporate mathematical methods in the practice of building a pizza, they will be engaging their interests while drawing on prior knowledge of food prices and combining numbers up to twenty. Reflective of the CCSS and the Investigations curriculum, students will build upon their current knowledge of the landmark numbers of 10 and 15 and will continue to develop an understanding of addition and subtraction up to twenty. By incorporating pictures with prices, a graphic organizer, and the kinesthetic activity of building a personalized pizza, the lesson will be reflective of this pedagogical focus: Selecting and using representations to make mathematics meaningful and draw connections between mathematical concepts. Students will create their own connections through active engagement with the tools and through discussion of these mathematical representations, increasing fluency and understanding of the possible numeric combinations up to twenty.
Students will build on their understanding of addition and subtraction by working with combinations of the numbers 1 through 20. They will enhance their understanding of numeric combinations by adding quantities ranging from 1 to 10 to sum 20 or less. Students will build upon their knowledge of the landmark numbers 10 and 15, and of combining single digits to make multiple combinations. Students will work towards developing computational fluency through number compositions, which “is an integral part of learning with depth and rigor about numbers and operations” (Russell, 2000, p. 158). By providing a familiar framework using the concept of making pizzas, an objective is to steer students from “growing evidence” that suggests students “have difficulty learning to bring meaning to their work” once they practice “procedures without understanding” (Russell, 2000, p. 156). Students will work towards improving the ideas of efficiency, accuracy and flexibility of fluency by “applying knowledge about the structure of the base-ten system” as they create multiple combinations of pizza toppings and engage their understanding of procedures (Russell, 2000, p. 155).
How?
Students will work in pairs to create numeric combinations of pizza toppings with assigned values of 1 to 10 in order to sum 20 or less. Each student will select one combination and create a personalized pizza that will represent their choices. These pizzas engage individual interests and allow students to “use what they already know, including understandings they have already constructed” in order to problem solve (Hiebert et al). They will learn to construct their own methods by discovering what works in order to create combinations up to 20. Working in pairs, students will visualize addition methods by recording their combinations on a graphic organizer, and will refer to the enlarged graphic organizer with pictures as a tool for visualizing the numerals. Culminating the lesson, I will facilitate a group discussion where students share their pizzas and engage in a discussion of the various combinations with which one can make a pizza for $20.
Why?
My focusing question is about how we can incorporate prior knowledge and individual interests into curriculum design. By asking students to incorporate mathematical methods in the practice of building a pizza, they will be engaging their interests while drawing on prior knowledge of food prices and combining numbers up to twenty. Reflective of the CCSS and the Investigations curriculum, students will build upon their current knowledge of the landmark numbers of 10 and 15 and will continue to develop an understanding of addition and subtraction up to twenty. By incorporating pictures with prices, a graphic organizer, and the kinesthetic activity of building a personalized pizza, the lesson will be reflective of this pedagogical focus: Selecting and using representations to make mathematics meaningful and draw connections between mathematical concepts. Students will create their own connections through active engagement with the tools and through discussion of these mathematical representations, increasing fluency and understanding of the possible numeric combinations up to twenty.