Many of us were taught math by memorizing “how to do it” but didn’t really have the understanding as to why we are doing it that way. That way of teaching has caused HUGE gaps in understanding. Decomposing numbers helps to bridge that gap and explains why we are working mathematical problems a certain way.
There are many reasons that decomposing numbers at all grade levels is important. First of all, it’s important that students understand the basic composition of numbers meaning that 7 is made up of a 5+2 or 3+3+1 or the idea that 13 is made up of a ten and 3 ones. Decomposing is the basic building block of understanding numeracy.
As students math skills develop, they will understand that division can be understood by the number of groups. For example, 44/11=4 BECAUSE there are 4 groups of 11’s that compose 44. Likewise, 4x11=44 BECAUSE students understand that 11 can be thought of as 10+1…so 4x10 is 40 and 4x1=4 so….40+4=44. NOW, students can build on that understanding to see that 24 x 32 can be thought of as (20 x 30) + (20 x 2) + (4 x 30) + (4 x 2) = 600 + 40 + 120 + 8. That’s just an example.
Decomposing numbers allows students to make sense of the problem in many different ways. It’s about STUDENTS UNDERSTANDING NUMBERS and the OPERATIONS with them, and BUILDING ON THEIR PRIOR KNOWLEDGE instead of just memorizing facts and spitting them back out.
http://www.math-play.com/adding-decimals-game.html
http://www.math-play.com/baseball-math-subtracting-decimals/subtracting-decimals.html
http://www.math-play.com/subtracting-decimals-game.html
http://www.math-play.com/multiplying-decimals-game.html
http://www.math-play.com/Decimals-Jeopardy/decimals-jeopardy.html
http://www.mathnook.com/math/alien-math-decimal-multiplication.html
http://www.coolmath.com/prealgebra/02-decimals/decimals-cruncher/multiplication
http://www.funbrain.com/football/
http://mrnussbaum.com/decimals-workshop/ (type in 10 problems, select divide decimals, select 1 and 2, select 2 and 2)