Multiplication and Division Learning progressions Word problems Online resources

CCSS  Practice Standards Problem solving Reasoning Modeling  Content Standards Critical Areas at each grade

In Grade 4, instructional time should focus on three critical areas: (1)developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2)developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3)understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

In Grade 5, instructional time should focus on three critical areas: (1)extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; (2)developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (3)developing understanding of volume.

Curriculum Tools  C-R-A: An instructional approach  U-F-G: A theory of knowledge  Learning progressions  Types of problems  Visual representations

C-R-AConcrete Solve this with mental math. There are 47 children on the playground. 24 go home. How many are left on the playground. 47 – 24 = ____

C-R-AConcrete (objects) Now solve this with mental math. There are 53 children on the playground. 38 go home. How many are left on the playground. 53 – 38 = ____ You can use counters or a number line.

C-R-ARepresentational (pictures)

C-R-A Abstract (symbols)

U-F-G Framework Conceptual Understanding FluencyGeneralization Addition is putting together and adding to, subtraction is taking apart, taking from and comparing. Problems are solved using objects and drawings to represent situations. Fluency starts with strategies such as counting on, making ten, doubles plus one. By end of 2 nd grade, know all sums from memory. Addition is the foundation for multiplication through skip counting of arrays.

How would children solve these? 1. Chad had 5 bags of candy with 7 pieces of candy in each bag. How many pieces of candy did Chad have? 2. At Sally’s birthday party there were 15 children and 3 blankets. If the same number of children sat on each blanket, how many children sat on each blanket? 3. Lee collects stamps. He has 45 stamps. If he sticks 9 stamps on each page, how many pages would he fill with stamps? 4. Mr. Wong has 4 children. He wants his children to share 12 marbles so that they each get the same amount. How many marbles should Mr. Wong give each child? children are going to the circus. 5 children can ride in each car. How many cars are needed so that all the children can go to the circus? 6. Maria has 17 fish. If 3 fish can be put into one fish bowl, how many bowls does she need to hold her fish?

Types of multiplication and division problems  Grouping problems (Partitive and measurement division)  Rate problems  Price problems  Multiplicative Comparison problems  Array and Area problems

Three questions:  What does it mean to really know multiplication and division well?  How is multiplication of decimals related to multiplication of whole numbers?  How can I use these resources in my teaching? 1. C-R-A, U-F-G 2. Types of Problems 3. Learning Progressions 4. Virtual Manipulatives 5. Number Talks

Online Resources Find Out More About: Wiki Spaces 3. Elementary Math Resources 4. 4 th -5 th Grade