Math 247 Unit 2: Base 10 numbers and algorithms

Section 7: Multiplication and division algorithms.

Goal: The goals this week are for you to

• Know some ways of mentally computing with 2 digit numbers
  
• Know some common alternate and scaffolding algorithms for multiplication and division
  
• Know how to show the standard algorithms for multiplication and division using manipulatives and make connections between manipulatives and the pencil and paper work.

Resources

Multiplication

Paths to the standard algorithm:

Read and watch this discussion of breaking down multidigit multiplication using arrays and the distributive law, and recording multiplication using the expanded and the standard algorithm. (note: this page includes links to several videos, and hence is longer than it appears).

Assignment 33: Expanded and standard algorithms assignment 

Mental math and the lattice algorithm:

Read and watch this discussion of mental multiplication strategies and the lattice algorithm.

Assignment 34: Mental arithmetic multiplication and the lattice algorithm

Error patterns

Assignment 35: Figure out the error patterns and identify the alternate algorithms in the assignment Multiplication error patterns and algorithms

 

Division

Partitive division and long division

Do first: open the base 10 blocks Smart notebook (see resources), and use them to divide 860 ÷ 6 using a partitive interpretation (make 6 groups)

Watch:

• dividing by a 1-digit number
• dividing by a 2-digit number
  

Assignment 36: Manipulatives and partitive long division assignment (video)

Measurement division and the scaffolding algorithm

Watch:

• Scaffolding
• Using scaffolding to transition to the standard algorithm

Assignment:

Assignment 37: Scaffolding division assignment

Why can't you divide by 0?

Watch:

Read: Bassarear 4th ed pg 193 (3rd ed. pg. 188)

Assignment: