1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE (Information quoted from Van de Walle and Lovin, Teaching Student-Centered Mathematics: Grades 3-5, page 113) For multiplication, the ability to break numbers apart in flexible ways is even more important than in addition or subtraction. The distributive property is another concept that is important in multiplication computation. For example, to multiply 43 x 5, one might think about breaking 43 into 40 and 3, multiplying each by 5, and then adding the results. Children require ample opportunities to develop these concepts by making sense of their own ideas and those of their classmates. Third grade students will not be required to use the distributive property for products greater than one hundred. COMMON MISCONCEPTIONS When using the distributive property to solve problems, students will partition numbers and arrays at different points. It is important for students to decide the appropriate way to partition a number, instead of the teacher, so that the problem makes sense to them. ESSENTIAL QUESTIONS How does understanding the distributive property help us multiply large numbers? What are strategies for leaning multiplication facts? MATERIALS Connecting cubes (bags of 100) Graph paper Making the Hard Facts Easy Recording Sheet Crayons or colored pencils Scissors Glue
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE (Information quoted from Van de Walle and Lovin, Teaching Student-Centered Mathematics: Grades 3-5, page 113) For multiplication, the ability to break numbers apart in flexible ways is even more important than in addition or subtraction. The distributive property is another concept that is important in multiplication computation. For example, to multiply 43 x 5, one might think about breaking 43 into 40 and 3, multiplying each by 5, and then adding the results. Children require ample opportunities to develop these concepts by making sense of their own ideas and those of their classmates. Third grade students will not be required to use the distributive property for products greater than one hundred. COMMON MISCONCEPTIONS When using the distributive property to solve problems, students will partition numbers and arrays at different points. It is important for students to decide the appropriate way to partition a number, instead of the teacher, so that the problem makes sense to them. ESSENTIAL QUESTIONS How does understanding the distributive property help us multiply large numbers? What are strategies for leaning multiplication facts? MATERIALS Connecting cubes (bags of 100) Graph paper Making the Hard Facts Easy Recording Sheet Crayons or colored pencils Scissors Glue
3rd-Math-Unit-2.docx