Pct 3b Traditional Math: Two-Step Equations with Distribution (Cont.)
Continued from previous post:
Word Problems. I use one of the word problems to launch this discussion. (If such a problem wasn’t included in the Warm-Ups, then I provide one.) Problem 1 was: “A bowling alley charges $3 to rent shoes. The cost of a game is $2. If Bob spends $13, how many games has he bowled?”
“Solving it, we know the constant (flat fee) is $3, and we want to know how many games bowled at $2 a game. So we have 3 + 2x = 13.”
“Now suppose I had the same information but that there were four people bowling at this same alley and the total cost was $60. How would I write the equation?”
I have them write in their notebooks and circulate around the room. I find a person who is doing it correctly, or I guide them to a correct answer and have that person present it on the board: 4(3+2x) = 60, which they know how to solve.
They know how to solve this by now, which I have them do. The answer is 6 games.
Examples (Written beforehand and projected on board using document camera):
I have them work in their notebooks, and walk around the room providing help and guidance.
1. At a banquet there are 7 identical flower arrangements at each table. Each arrangement contains some roses and 9 tulips. The total amount of flowers is 147 to make the arrangements. How many roses are in each arrangement?
Hints:
What are we trying to find? (The number of roses in each arrangement.)
How do I represent the number of roses in each arrangement? (x)
How do we write the expression for the number of flowers for one arrangement? (x + 9)
How many arrangements are there? (7).
What is the expression for the number of flowers for 7 arrangements? 7(x +9)
What is the equation for this problem? 7(x+9) = 147 Answer: x = 12
2. Tanya has coupons for $1.15 off the regular price of each box of cereal. She buys 4 boxes of cereal. The total cost is $8.40. Write and solve an equation to find the total price of the cereal.
Hints:
Regular price of the cereal: x
Expression for cost of one box of cereal: x – 1.15
Equation and solution:
3. Brady buys 5 T-shirts on sale for $4 off the regular price. His total cost is $55 before tax. Write and solve an equation to find the regular price of each T-shirt.
I let them solve this independently providing less guidance than previously.
Homework. Homework should be a mix of problems for which dividing by the multiplier is the easiest method, and those for which distribution is a better way. (I make it clear that it is up to them what to use; if they want to distribute all of them, that’s fine.) Also there should be some with a fractional multiplier, and four or five word problems.