Multiplication using place value understanding

The  exercise appears under the 4th Grade Math Mission. This exercise uses place value and properties of multiplication to discover some multiplication techniques.

Types of Problems
There are three types of problems in this exercise:


 * 1) Use the associativity property: This problem asks the student to multiply two numbers together. The student uses the associative property to fill in the blanks and arrive at the answer.Mupvu1.png
 * 2) Use the distributive property: This problem asks the student to perform a multiplication property by using the distributive property on it's individual place values.Mupvu2.png
 * 3) Use several multiplication properties: This problem provides a multiplication problem that can be viewed as using all of the "big three" multiplication properties.Mupvu3.png

Strategies
It is not necessary to know the names of the multiplication properties, but some familiarity could increase efficiency on this exercise.
 * 1) The three problem types repeat the same pattern with different numbers, so it is possible to develop an algorithm to recognize the numbers that need to be inserted quickly.
 * 2) The associative property of multiplication says that when multiplying numbers associate with each other, i.e., grouping does not matter. $$ a\times (b\times c)=(a\times b)\times c$$.
 * 3) The commutative property says order does not matter, i.e.,$$ a\times b=b\times a$$.
 * 4) The distributive property says that $$a(b+c)=ab+ac$$.

Real-life applications

 * 1) Efficiency in multiplication will increase the ability to work confidently in fractions which occur in real-life often.