## Friday, April 1, 2016

### Math problems of the week: Common Core-inspired word problems plus commentary and rationale

In the age of Common Core, wordiness reigns supreme: whether in Common Core-inspired word problems, Common Core-inspired commentaries on word problems, or Common Core-inspired rationales for word problems.

Here are two sample 4th grade problems from New York's Common Core-inspired EngageNY curriculum,  Each is accompanied by one commentary and one rationale. I've followed each problem, commentary and rationale with an edited counterpart.

Problem 1

Candy wants to buy herself a new bicycle that costs \$240. Candy has already saved \$32, but she needs to make a plan so she can save the rest of the money she needs. She decides to save the same amount of money, x dollars, each month for the next four months.

Part A: Write an equation that helps Candy determine the amount of money she must save each month.

Part B: Solve the equation to find the amount of money she must save each month to meet her goal of buying a bicycle.

[94 words]

Problem 1, edited

Candy wants to buy a \$240 bike. She has \$32 and will save x dollars each month for the next four months.

Write an equation that describes this situation. Solve the equation.

[32 words]

Commentary: This question aligns to CCLS 4.OA.3 and assesses a student’s ability to solve a multi-step word problem posed with whole numbers. It also assesses the ability to represent a problem using an equation with a letter standing for the unknown quantity.

[41 words]

Commentary, edited: This question assesses the ability to solve a word problem involving whole numbers using an equation involving one variable.

[19 words]

Rationale: In Part A the equation includes the subtraction of \$32 from \$240 to identify how much is needed to be saved in four months and the division of the remaining amount, \$208, by four to represent the amount to be saved each month. Likely errors may include dividing \$240 by four without subtracting the already saved amount of \$32 (…) or using \$32 dollars as the amount of money saved during the first month and dividing the remaining amount by three (…). In Part B errors may occur during the computation of the equation in Part A or may be the result of accurate computations based on an inaccurate equation from Part A.

[113 words]

Rationale, edited:

[0 words] (The rationale is obvious.)

Problem 2

Students from three classes at Hudson Valley Elementary School are planning a boat trip. On the trip, there will be 20 students from each class, along with 11 teachers and 13 parents.

Part A: Write an equation that can be used to determine the number of boats, b, they will need on their trip if 10 people ride in each boat.

Equation: b =______________________________________

Part B: How many boats will be needed for the trip if 10 people ride in each boat?

Part C: It will cost \$35 to rent each boat used for the trip. How much will it cost to rent all the boats needed for the trip?

[110 words]

Problem 2, edited:

Students from three classes will go on a boat trip. There will be 20 students from each class, along with 11 teachers and 13 parents.

a. Write an equation that describes the required number of boats, b, if 10 people ride in each boat.

Equation: b =______________________________________

b. How many boats will they need?

c. If each boat costs \$35 to rent, how much is the total cost?

[69 words]

Commentary: This question aligns to CCLS 4.OA.3 and assesses a student’s ability to solve a multi-step word problem posed with whole numbers. It also tests the student’s ability to represent the problem using an equation, with a letter standing for the unknown quantity. It tests a student’s ability to interpret the remainder of the division problem and use this interpretation properly to determine the number of boats as well as the total cost.

[72 words]

Commentary, edited: Same as in Problem 1, above. This question also assesses whether the student applies the fact that boats can’t be fractional.

[21 words]

Rationale: The equation in Part A includes a calculation for the number of students who went on the trip (20 × 3 = 60) plus the 11 teachers and 13 parents, bringing the total to 84 individuals on the trip. The number of boats, b, needed is the sum of all individuals divided by the number of people able to sit in a single boat. In Part B, students perform the calculation—84 is divided by 10, to get 8 R 4. The remainder of 4 indicates that an additional boat is needed, so the number of boats needed is 8 + 1 = 9 boats. In Part C, the total cost is the number of boats required multiplied by the cost per boat, \$35 × 9 = \$315.

Rationale:

[0 words]