1. Rewrite each rate or price so that it uses the word "per"
a. The weather got warmer at a rate of 3 degrees Fahrenheit each day.
The weather got warmer at a rate of 3 degrees Fahrenheit per day.
b. The train went 40 miles an hour
The train went 40 miles per hour
c. The chocolate costs $2 for a bar.
The chocolate costs $2 per bar.
2. Rewrite each rate or price so that it uses the word "each"
a. The car was driving at 45 miles per hour.
The car drove 45 miles each hour.
b. The price was $1.50 per hot dog.
Hot dogs cost $1.50 each.
c. Green beans cost $3 a pound.
Each pound of green beans costs $3.
3. For each rate or price problem, decide if it is a multiplication, measurement division or partitive division problem.
a. The toy train takes 3 minutes to go 18 feet. How far will the train go in 1 minute?
3 minutes and 18 feet. Those units (minutes and feet) don't match, and we need to divide the 18 feet into 3 equal amounts to find out how far in 1 minute, so this is a partitive division problem.
b. Finger puppets cost $4. How many finger puppets can you buy with $20?
$4 and $20. Those units match ($ and $), and we need to find how many 4's will fit in 20. Measurement division.
c. The bean plant grew 3 inches per day. How much did it grow in 7 days?
3 inches taken 7 times--multiplication.
d. Kelly bought 6 packs of Pokemon cards for $24. How much did each pack of cards cost?
6 packs and $24. The units (packs and $) don't match. Also, we need to split $24 into 6 equal groups to find out how much for 1 pack of cards. Partition division.
e. 2 ounces of water evaporates from the bucket each hour. How long will it take for 10 ounces of water to evaporate?
2 ounces and 10 ounces--those units match. Also, we need to find how many 2's are in 10. Measurement division.
f. A toy dragon costs $6. How much do 4 dragons cost?
4 sets of $6. Multiplication.
4. For each of these Cuisenaire rod problem solving strategies, decide if it's finding the solution to a multiplication, measurement division or partitive division problem.
a. Put out Cuisenaire rods to show the amount 32 (using 3 orange tens and 1 red 2), and then put purple (length four) rods next to them until the amounts are even. Finally, count how many purple rods there are to find the answer.
Measurement division (measure the length 32 using 4's. The number of groups is the answer)
b. Put out Cuisenaire rods to show the amount 32 (using 3 orange tens and 1 red 2). Then put 4 yellows out next to them, notice that the amounts are not even. Put out 4 blacks, and notice that the amounts are not even. Put out 4 browns, and notice that the amounts are even. Figure out/remember how long a brown is.
Partitive division (guess and check to find the amount that will give 32 when using 4 of them.)
c. First, put out 6 black (length 7) Cuisenaire rods, then figure out that the total length is 42.
Finding the total of 6 sevens. Multiplication.
5. True or false: Rate and Price problems should usually be solved with Cuisenaire rods.
False. Problems should be solved in a way that makes sense to the child and uses materials appropriate to their knowledge of number. It is a coincidence that Cuisenaire rods and Rate and Price problems are in the same lesson.