STANDARDS OF MATHEMATICAL PRACTICE (SMP) 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. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. ***Mathematical Practices 1 and 6 should be evident in EVERY lesson. *** Background Knowledge (Information quoted from Van de Walle and Lovin, Teaching Student-Centered Mathematics: Grades 3-5, page 62) the beginning, students will be able to use the same models sets and number lines for all “In – – four operations. A model not generally used for addition but extremely important and widely used for multiplication and division is the array. An array is any arrangement of things in rows and columns, such as a rectangle of square tiles or blocks. To make the connection to addition, early multiplication activities should also include writing and addition sentence for the same model.” COMMON MISCONCEPTIONS Traditionally multiplication tables are emphasized when students begin learning about multiplication. Students are sent home with flash cards without a true understanding of what multiplication is. This way of learning multiplication can be difficult for students to understand. Naturally, students make groups and groups of groups. The creation of groups is a way to find the total of something in the most efficient way. The following activity allows students to build on their natural ability to form groups and learn multiplication without memorizing facts in isolation, but as number facts that can be related to each other in a multitude of ways (Frans van Galen and Catherine Twomey Fosnot, 2007, Context for Learning Mathematics). ESSENTIAL QUESTIONS How can we use arrays to help develop an understanding of the commutative property? How does drawing an array help us think about different ways to decompose a number? MATERIALS
STANDARDS OF MATHEMATICAL PRACTICE (SMP) 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. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. ***Mathematical Practices 1 and 6 should be evident in EVERY lesson. *** Background Knowledge (Information quoted from Van de Walle and Lovin, Teaching Student-Centered Mathematics: Grades 3-5, page 62) “In the beginning, students will be able to use the same models – sets and number lines – for all four operations. A model not generally used for addition but extremely important and widely used for multiplication and division is the array. An array is any arrangement of things in rows and columns, such as a rectangle of square tiles or blocks. To make the connection to addition, early multiplication activities should also include writing and addition sentence for the same model.” COMMON MISCONCEPTIONS Traditionally multiplication tables are emphasized when students begin learning about multiplication. Students are sent home with flash cards without a true understanding of what multiplication is. This way of learning multiplication can be difficult for students to understand. Naturally, students make groups and groups of groups. The creation of groups is a way to find the total of something in the most efficient way. The following activity allows students to build on their natural ability to form groups and learn multiplication without memorizing facts in isolation, but as number facts that can be related to each other in a multitude of ways (Frans van Galen and Catherine Twomey Fosnot, 2007, Context for Learning Mathematics). ESSENTIAL QUESTIONS How can we use arrays to help develop an understanding of the commutative property? How does drawing an array help us think about different ways to decompose a number? MATERIALS
CCGPS_Math_3_Unit2Framework.docx