Foundations Sampler 2024

45 Problem Solving Lesson Plans 38 ©MathTeachersPress, Inc. Reproduction by anymeans is strictly prohibited. 38 Mount Everest in Asia is 28,028 feet high.Mount McKinley in Alaska is 20,320 feet high.How much higher is Mount Everest than Mount McKinley? Steps for Problem Solving Mt.Everest 29,028 ft. Mt.McKinley 20,320 ft. I know that I need these facts: Mt.Everest= 28,028 ft. Mt.McKinley= 20,320 ft. Steps 1& 2 “Howmuch higher” means to compare by subtraction. Step 3 1.Read. 2.Find. 3.Decide. 4.Estimate. 5.Solve and check back. 28,028 rounds to 28,000 and 20,320 rounds to 20,000. A good estimate is about8,000 feet. Step 4 7708 is close to8000, somy answer is reasonable. Step 5 Use the problem solving steps to answer the following problems. 1. The deepest spot in all the oceans of theworld is 35,640 ft.in theMariana Trench nearGuam. The greatest depth in theAtlanticOcean is 30,246 ft.near PuertoRico.Find the difference in these depths. Est.__________ Actual __________ 3. How many more square miles did the United States acquire through the Louisiana Purchase of 827,192 square miles than through the purchase of Alaska with 586,400 square miles? Est.__________ Actual __________ 5. A basketball court is 94 feet long from end line to end line.A football field is 300 feet long from goal line to goal line.How much longer is a football field than a basketball court? Est.__________ Actual __________ 2. Find the area of the Pacific States if the area of California is 155,959 square miles, Oregon is 95,996 square miles andWashington is 66,544 square miles. Est.__________ Actual __________ 4. The distance from the earth to the moon is 238,857 miles and the distance from the earth to the sun is 92,897,416 miles.How much farther away is the sun from the earth? Est.__________ Actual __________ 6. The length of the Nile River in Africa is 4145 miles.TheYangtze River in China is 3964 miles long.How much longer is the Nile than theYangtze ? Est.__________ Actual __________ 28,028 – 20,320 7708 will vary 5394 ft. will vary 318,499 sq. mi. will vary 240,792 sq. mi. will vary 92,658,559 miles will vary 206 ft. will vary 181 miles Objective: To use the five-step problem solving model to solve problems involving addition and subtraction. Materials: Steps in Problem Solving (Master 11) Vocabulary: reasonable solution, estimate The Five-Step Plan In this activity, students will discover the five steps in problem solving. Be sure to write each step on the board as it is discovered. It is important that students understand clearly you believe they are capable of solving most problems you pose. Good problem solvers need strong self- concepts to become confident risk takers. Write the following problem on the board: In an online poll, 11,896 students said they completed their homework on Saturday and 17,143 students said they completed their homework on Sunday. How many more students completed their homework on Sunday? Today, we are going to find steps to help solve word problems. What is the first thing we must do to solve this problem? (Read it.) Have a volunteer read the problem and restate it in her own words. When the story is retold correctly, acknowledge that the student has shown she understands the problem. What is the next step in solving the problem? (Find the question and needed facts.) What is the question? Underline the question. What are the facts? Have a volunteer circle the facts in the problem on the board. What is the next thing we must do to solve this problem? (Decide on a process to solve the problem.) What ideas or strategies can we use to help decide how to solve this problem? Discuss the various problem-solving strategies (Master 11) together. Have students model the strategies as they are discussed. Can we use a model? (Yes, students can use base ten blocks to build each number. Discuss which operation is needed to solve the problem.) Can we simplify the problem? (Yes, smaller numbers can be used to model the problem. For example, 11 students do homework on Saturday and 17 do homework on Sunday. Discuss which operation is needed to solve this problem.) Can we act out the problem? (Students can combine acting it out and simplifying the numbers by showing 11 students on Saturday and 17 students on Sunday. Discuss which operation is needed to solve.) Ask students to explain the strategies they used and justify their selections. This process helps to clarify their thoughts and make them aware that they are making their own choices and becoming independent problem solvers. What process should we use to solve the problem? (Subtraction.) How do you know to use subtraction? (We are comparing one number to another.) Ask a volunteer to estimate the solution. (17,000 – 12,000 = 5000) After estimating the answer, what should we do? (Solve the problem.) Have a volunteer solve the problem. (17,143 – 11, 896 = 5247) How do we know if the answer is reasonable? (Compare the answer to the estimate.) How do we decide if the answer is correct? (Check the problem by adding and by putting the answer back into the problem.) Check for understanding and reinforce skills by using a second word problem. Allow time for students in small groups to discuss the steps as they solve the problem. It is important to have students restate the problem in their own words to be sure the problem has meaning to the student. Walk the students through the steps in the example at the top of the page. Draw students’ attention to the graphic on the page containing the five problem-solving steps. Have students complete the page on their own. MH1 Lesson Plan Students use a 5-step plan. Sample of Scripting (Bold Type) Today, we are going to find steps to help solve word roblems. What is the first thing we must do to s lve thi problem? (Read it.) Have a volunteer read the problem and restate it in her own words. When the story is retold correctly, acknowledge that the student has shown she understands the problem. What is the next step in solving the problem? (Find the question and needed facts.) What is the question? Underline the question. What are the facts? Have a volunteer circle the