Question

How are the strategies the same and how are they different

Answer 1

Diagram 1.

Strategy 1.

`A_(Total)=253\cdot31=(200+50+3)\cdot(30+1)`

If we add all the areas together we get:

`\begin{gathered} A_(Total)=A_1+A_2+A_3+A_4+A_5+A_6 \\ =(200\cdot30)+(50\cdot30)+(3\cdot30)+(200\cdot1)+(50\cdot1)+(3\cdot1) \\ =6000+1500+90+200+50+3 \\ =7843 \end{gathered}`

Diagram 2.

Strategy 2.

`A_(Total)=253\cdot31=(253)\cdot(30+1)`

If we add all the areas together we get:

`A_(Total)=A_1+A_2=253\cdot30+253\cdot1=7590+253=7843`

We can see that we got the same answer: Total area = 7843 quare units

The strategies are similar because they are dividing the total area into smaller ones and then add them together.

However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.