P.O.W. = Problem Of The Week (Grade 4) The kids on Abracadabra Street counted all of the Halloween candy. They had 18 pieces of candy in all. Abby had fewer than 4 pieces of candy. Billy had twice as much as Abby. Charlie had twice as much as Billy. David had 2 pieces more than Abby. How many pieces did each kid have? Rubric for Grading P.O.W. s 1. Write down what the problem is asking you to find out 2. List the important information form the problem. 3. Solve the problem. You must show your work with numbers, diagrams, pictures, tables, ect. 4. Explain your thinking (tell how you solved the problem). This will be a more than 2 or three sentence. 5. Write your answer in a complete sentence 6. Proofread your work. Check for correct punctuation, spelling (words that are in the problem) and neatness. * All Answers must be written in complete sentences **** You will be graded with one point for each of the above standards for a highest possible score of 6 An example of a 6-point answer. 1. The question is asking how many pieces of candy did each kid have? (Write down what the problem is asking you to find out) 2. The important information is: they have 18 pieces of candy in all, Abby had fewer than 4 pieces of candy, and Billy had twice as much as Abby. Charlie had twice as Billy. David had 2 pieces more than Abby. (List the important information form the problem.) 1
3. Working On Solving The Problem (You must show your work with numbers, diagrams, pictures, tables, ect. Try # 1 Abby 0 Billy 2 Charlie 2 David 4 Added together doesn t =18 Try #2 Name Number of Pieces Math steps Abby 2 Billy 4 2 + 2 = 4 Charlie 8 4+ 4 = 8 David 4 2+ 2 = 4 4+4+8+2 = 18 4. I solved this problem by first guessing that Abby had 0 pieces of candy, so that would mean Billy got 2 and David got 4. But that did not add up to 18. So then I tried Abby having 2 pieces of candy, so Billy had 4, Charlie had 4 and David had 4. That added up to 18 so that is my answer. (Explain your thinking (tell how you solved the problem). This will be a more than 2 or three sentence.) 5. Abby had 2 pieces of candy, Billy had 4 pieces of candy, Charlie had 8 pieces, and David had 4 pieces of candy. (Write your answer in a complete sentence) Word Problem Strategies There are many different strategies for solving word problems. You need to pick the strategy that fits the problem best. Below is a list of pages that will teach you some important word problem solving strategies. From (http://library.thinkquest.org/4471/learn.htm) Multiple Step Problems Extra Information Use Logical Reasoning Choosing a Calculation Method Problems with More Than One Answer Deciding When to Estimate Using Data from a Chart Work Backwards Guess and Check Look for a Pattern Draw a Picture 2
MULTIPLE STEP PROBLEMS You may need to use more than one operation to solve some problems. These are called multiple-step problems. The blacksmith could forge 6 swords in two days. How many swords could he forge in 9 days? First, divide 2 into 6 swords to see how many swords he could make in one day. 6 2 = 3 Then multiply your answer by 9 to see how many swords he could make in 9 days. 3 x 9 = 27 EXTRA INFORMATION Sometimes a problem has extra information that you do not need to solve the problem. At the tavern, Ralph bought a mug of mead for 1 shilling, bread for 2 shillings, meat for 2 shillings, and a souvenir for his children 5 shillings. How much did Ralph spend on food? First, find the information you need to solve the problem. Some information is extra. The extra information is: Ralph bought a souvenir toy for his children for 5 shillings. I'll solve the problem using only the information I need. 1 + 2 + 2 = 5 Ralph spent 5 shillings on food. LOGICAL REASONING - USE OF VENN DIAGRAMS TO SOLVE PROBLEMS To solve some problems a helpful strategy is LOGICAL REASONING. The Canterbury Dance Festival presented dances from many different countries. 32 children joined in the dances. 19 danced the Welsh Dance and 15 danced the Scottish Dance. How many children danced in both dances? I'll draw a Venn diagram. 3
I'll put 19 counters inside the Welsh circle. I'll put 15 counters inside the Scottish circle. To do this with only 32 counters. I must place 2 counters so that they are inside both circles. 2 children danced both dances. Choosing a Calculation Method When you solve a problem, you must choose which of these calculations methods is best to use: mental math, pencil and paper, or calculator. Tournament Records Spear throw 100 feet Fencing 4 hours Archery 600 feet Shot put 27 feet Which methods would you use to solve these Tournament Records problems? How many minutes did it take to reach the record for fencing? 1. 4 x 60 (I can do this using mental math.) 2. How many inches is the shot put record? 27 x 12 (I think I'll use paper and pencil.) Use these hints when you are choosing a calculation method. First try mental math... Look for easy computations. Then choose paper and pencil or a calculator. It is better to use a calculator when many steps are needed. Problems with More than One Answer Some problems have more than one answer. When you find an answer to a problem, don't stop there. Ask yourself if there might be other answers. The villagers were building a bridge. While working under the bridge Rodney could see only the legs of those walking by. He counted 10 legs in one group. What combination of sheep and children could have been in that group? Try 3 people and 2 sheep. I can use guess and check. 6 legs + 8 legs = 14 legs That's too many legs. Try 3 people and 1 sheep 6 legs + 4 legs = 10 legs Correct! Rodney saw 10 legs. 4
I can check for other answers. I'll organize my work in a table. People Legs Sheep Legs Total 1 2 2 8 10 OK 2 4 2 8 12 not OK 3 6 1 4 10 OK 4 8 1 4 12 not OK There are two possible answers: 1 person and 2 sheep, or 3 people and 1 sheep. Deciding When to Estimate In some problems you only need an answer that is close to correct. You can estimate. In other cases, you need an exact answer. Decide which method to use by what you are going to do with the answer. 1. Gerald is on duty in the watchtower. It is 10:37 PM. He wants to stop at an inn on the way home. At what time shall he tell his friends he will arrive at the inn? Gerald does not need to arrive at the inn at an exact time. He can estimate the time needed. 2. Joan is practicing for a rowing competition. She wants to know how much greater her trial time is than the course record time of 23 minutes, 9 seconds. Joan needs to know exactly how many seconds faster she must go to beat the record. Joan needs to know her exact trial time. Data from a Chart To solve some problems, you need to sort through numbers in a chart to find the data you need. How much taller is the tallest knight than the shortest knight? Knight Statistics Name Height Weight Galahad 4' 11" 110 pounds Gawain 5' 1" 103 pounds Lancelot 5' 3" 107 pounds Hector 5' 4" 118 pounds 5
I'll find the data in the chart. Hector is 5 ' 4" tall. Galahad is 4' 11" tall. Now I'll solve the problem. 5' 4" = 64" 4' 11" = 59" 64-59 = 5 Hector is 5" is taller than Galahad. Work Backwards To solve some problems, you may need to undo the key actions in the problem. This strategy is called Work Backward. The castle kitchen servants brought in 4 pies left over from the feast. 12 pies were eaten at the feast. Queen Mab took 2 home with her. How many pies did the servants bring into the feast at the beginning? First, I'll account for all the pies that were eaten or taken home. 12 + 2 = 14 Then I'll add the 4 pies that were left over. 14 + 4 + 18 Therefore, there must have been 18 pies at the start of the feast. Guess and Check Some problems cannot be solved directly. You need to use a strategy called Guess and Check. Prince Carl divided 15 stone games into two piles: games he owns and games his brother owns. He owns 3 more games than his brother. How many games does his brother own? I'll guess his brother owns 8 games. That means Prince Carl owns 11 games. That's a total of 19 games. My guess is too high. I'll guess again. This time I'll guess his brother owns 6 games. That means Prince Carl owns 9 games. That's a total of 15 games. My guess is right. His brother owns 6 games. 6
Look for a Pattern Some problems can be solved by recognizing a pattern. Make a table to help you. Daniel arranged loaves of bread on 6 shelves in the bakery. He put 1 loaf on the top shelf, 3 loaves on the second shelf, and 5 loaves on the third shelf. If he continues this pattern, how many loaves did Daniel put on the 6th shelf? I'll make a table and look for a pattern. Shelf 1 2 3 4 5 6 Loaves 1 3 5 7 9 11 I see the pattern. There are 2 more loaves on each shelf. I've completed the table to shelf 6. Daniel put 11 loaves on shelf 6. Draw a Picture Draw a picture to help you solve some problems. Four pages were in line. Daniel was behind Timothy. James was between Daniel and Timothy. Daniel was in front of Colin. A mud puddle was near the page that was in the back of the line. Who was in the back of the line? First, I'll draw the line. Daniel is in back of Timothy. James is between Daniel and Timothy. Colin is behind Daniel. Colin is in the back of the line! 7
Name Date Problem Of The Week P.O.W Brain Frame For HWC Write down what the problem is asking you to do in complete sentences (Hints are we adding, subtracting, multiplying, dividing or doing multiple operations to solve the problem????) 1. 2. 3. What is the important Information from the problem? 1. 2. 3. 4. Try # 1 - Solve The Problem & Make Sure To Show All Of Your Work Explain why you used this particular method 8
Try #2 Explain why you used this particular method Try # 3 Explain why you used this particular method Please explain your thought process for the entire problem using the notes you made during in your attempts to solve the problem (Make sure to use complete sentences) Now Double Check & Copy All Of Your Work On To Your Teachers Format To Turn In For Full Credit FYI We all know that you are being graded on punctuation, spelling, neatness, and complete sentences so make it happen 9
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