1. Since multiplication is just repeated addition, students may use a grid to repeatedly add the same number over and over. Ex: .35 x 3 --- the student would shade .35 two times to show the final product of .70.
The first image shows that when we multiply by 10, 100, or 1000 the place value increases or "a zero is added" -
However, when we multiply by 0.1, 0.01, .001 - the opposite happens, it is the inverse. When we multiply these numbers we are essentially dividing by 10, 100, and 1000.
This is meant to show that when we multiply a number by 1, we get the original number, but when we multiply a number by LESS than 1, we will always get a smaller number.
this stands for.. P-problem, E-estimate, A-actual, C-check, E- evaluate
P- what is the problem asking us? Write it out
E- We estimate to determine what our answer should be around.
A- Solve the actual, real answer using a model.
C- Check - do a check using the standard algorithm
E- evaluate - compare this with your estimate and ask yourself - Does this make sense? If she filled 4.5 ounce bottles, does it make sense that she would use around 15 ounces? Often times when students have a crazy answer, this is where they can catch it.
Using these steps helps to avoid what we often refer to as, "Careless mistakes" - when we do ALL of the steps (yes they may seem tedious) - we rarely make mistakes. Skipping steps is when we mess up!
Below is the area model... Area models just break apart the numbers into smaller sections. See the model below.
Once they have found each section, they add the partial products together to get the final answer.