How Do You Turn a Longer Verbal Phrase into an Algebraic Expression?

'a', 'b', and 'm' are variables
Break up the descriptions into manageable phrases that will be easier to translate
We can translate words like 'two' or 'three' into 2 and 3
'Times' means we multiply 2 by whatever comes after 'times'
Taking the sum of two things will always mean that you add them together
Plus always means we are adding
'Of' means multiplication
Something 'squared' is just something raised to the second power

1. 'a', 'b', and 'm' are variables
1. 'a' and 'b' are variables
1. 'b' is a variable
1. There are four pieces:
2. 1) Two times the sum of a and two b
3. 2) Plus half of b squared
4. 3) Plus twice the sum of a and three b
5. 4) Equals m.
6. 'a', 'b', and 'm' are variables
1. 'a' and 'b' are variables
1. 'a' and 'b' are variables
1. 'a' and 'b' are variables
1. 'a' and 'b' are variables
2. Since we are multiplying 2 by the entire sum of a+2b, we need to use parentheses
1. 'a' and 'b' are variables
2. Since we want to multiply 2 by the SUM of a and 2b, we have to add a and 2b FIRST
3. Parentheses have to be done first in the order of operations, so if a+2b is inside parentheses they have to be added first
1. 'The first phrase is 2•(a+2b)
2. 'a' and 'b' are variables
1. 'b' is a variable
1. 'b' is a variable
1. 'b' is a variable
1. 'a' and 'b' are variables
1. 'a' and 'b' are variables
1. 'a' and 'b' are variables
1. 'a' and 'b' are variables
2. Since we want to multiply 2 by the SUM of a and 3b, we have to add a and 3b FIRST
3. Whatever is inside parentheses is done FIRST, so put them around a+3b
1. 'a' and 'b' are variables
1. 'b' is a variable
1. 'a' and 'b' are variables
1. 'm' is a variable

Translate the following description into an equation:Two times the sum of a and two b, plus half of b squared, plus twice the sum of a and three b equals m.