Systematic Thinking The 4 Step Method for Problem

Systematic Thinking: The 4 -Step Method for Problem Solving STEP 1: Understand the problem. STEP 2: Analyze important information. STEP 3: Plan and solve. STEP 4: Check your work. This method… • standardizes the language of problem solving. • helps teachers model “expert” problem solving. • provides students with a systematic approach. 1

Using the 4 -Step Method Mark buys a set of 3 tennis balls. The tennis balls are packaged in a cylindrical container. The container has a height of 10 inches and the top of the container has a diameter of 6 inches. How much space is inside the container? A 30 cubic inches B 60 cubic inches C 60 cubic inches D 90 cubic inches 2

STEP 1: Understand the problem. Mark buys a set of 3 tennis balls. The tennis balls are packaged in a cylindrical container. The container has a height of 10 inches and the top of the container has a diameter of 6 inches. How much space is inside the container? § Scan the problem; what is it basically about? What kind of math is involved? This problem is about the volume of a cylinder. It involves geometry. § Restate the question in your own words. What is the volume of a cylinder with a height of 10 inches and a diameter of 6 inches? Alternative: There is ____ space inside the container. 3

STEP 2: Analyze important information. Mark buys a set of 3 tennis balls. The tennis balls are packaged in a cylindrical container. The container has a height of 10 inches and the top of the container has a diameter of 6 inches. How much space is inside the container? 10 in. • Underline the clues. • Rewrite the important information in a helpful way. Draw, list, chart, graph, symbols, or words. I can draw it. 6 in. 3 in. 4

STEP 3: Plan (strategy) and solve. What do you KNOW? I know the dimensions of the cylinder. What do you NEED? I need to figure out the volume of the canister. My work: V r 2 h (3)2(10) (9)(10) I will use the formula V r 2 h 90 in 2 How can you and substitute the correct use what you values. Can I solve with an Label all variables and KNOW to equation, a list, a graph, a find what you chart, or a verbal description? answers NEED? 5

STEP 4: Check your work. § Did you answer the right question? Yes, I figured out the volume of the cylinder. § Is your answer reasonable? Yes. 90 is about 270. That’s a reasonable volume. Formula Values § Can you solve the problem another way? Yes, I can use a chart instead. d r 6 3 r 2 h 9 10 V r 2 h V (9)(10) 90 6

Try It Out! The Environmental Club receives a certain amount of money from the school to host a teach-in. They budget 40% of the funds for a guest speaker, 25% for books, 20% for use of the auditorium, and the remainder for lunch. If the club plans to spend $90 on lunch for the participants, how much do they plan to spend on the guest speaker? (A) $40 (B) $120 (C) $150 (D) $240 (E) $600 7

4 -Step Method for Problem Solving STEP 1: Understand the problem. STEP 2: Analyze important information. STEP 3: Plan and solve. STEP 4: Check your work. 8