A Standards Progression 2.OA. Work with equal groups of objects to gain foundations for multiplication. 4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 3.OA. Understand properties of multiplication and the relationship between multiplication and division. 5. Apply properties of operations as strategies to multiply and divide. Examples: if 6x4 = 24 is known, then 4x6=24 is also known. (Commutative property of multiplication.) 3x5x2 can be found by 3x5=15, then 15x2=30, or 5x2=10, then 3x10-30. (Associative property of multiplication.) Knowing that 8x5=40 and 8x2=16, one can find 8x7 as 8x(5+2)=(8x5)+(8x2)=40+16=56. (Distributive property.) 4.NBT. Use place value understanding and properties of operations to perform multi-digit arithmetic. 5. Multiply a whole number of up to four digit by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 5.NBT. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5. Fluently multiply muli-digit numbers using ‘the’ standard algorithm. How does the idea of multiplication grow across grade levels? (include contexts, representations, equations, models, and number size) How does the work in each grade level build toward an understanding and use of the distributive property to justify strategies?