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Grade 3

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Confidential2 Step 1: Read Read the problem to: See what you need to find. Identify information that will help you find it. What do you know? What do you need to find? Step 2: Plan What strategy will you use? logical reasoning; drawing a picture or diagram; making a graph; acting it out; making a table or list; looking for a pattern; guessing and checking; writing an equation; working backwards; solving a simpler problem Step 3: Solve Solve the problem. Step 4: Look Back Check your answer Does your answer make sense?

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A problem-solving strategy is a plan for solving a problem. Different strategies work better for different types of problems. Sometimes you can use more than one strategy to solve a problem. As you practice solving problems, you will discover which strategies you prefer and which work best in various situations. Confidential3

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You can use logical reasoning to solve problems. Example: Coach Paul wants 11 liters of water in a cooler. He has a 5-liter bottle and an 8-liter bottle. How can he use them to measure exactly 11 liters? ◦ What do you know? Coach Paul wants 11 liters of water in a cooler. Coach Paul has bottles that hold 5 liters and 8 liters. ◦ What do you need to find? You need to find how to use the bottles to measure exactly 11 liters. Confidential4 Step 1: Read

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Choose a strategy Use Logical Reasoning to solve the problem You can use the difference of the amount of water in the bottles to measure exactly 11 liters. Confidential5 Step 2: Plan

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Carry out your plan Follow the steps Confidential6 Step 3: Solve Fill the 8-L bottle800 Fill the 5-L bottle from the 8-L bottle350 Pour what is left in the 8-L bottle into the cooler 053 Refill the 8-L bottle803 Pour the water from the 8-L bottle into the cooler 0011 Add 8 + 3 = 11. There are 11 liters in the water cooler. 8-L bottle 5-L bottle Water cooler

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Is the solution reasonable? Reread the problem. How can you check your answers? Possible answer: use water containers to check your answer. Confidential7 Step 4: Look Back

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Jack has a 6-oz cup and an 8-oz cup. How can he use the cup to measure 10 ounces of water? Confidential8

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You can solve problems by drawing diagrams. Example: There are 22 students in Mrs. Diane’s class. Ten students have sisters. Five students have brothers. Seven students have sisters and brothers. How many students have sisters? ◦ What do you know? There are 22 students. 10 students have sisters. 5 students have brothers, and 7 students have both. ◦ What do you need to find? How many students have sisters? Confidential9 Step 1: Read

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Choose a strategy You can make a diagram to solve the problem Confidential10 Step 2: Plan Students who have sisters 10 Students who have brothers 5 Both 7 Mrs. Diane’s class This is a Venn Diagram

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Carry out your plan You know that there are 10 students who have sisters. You know that there are 7 students who have sisters and brothers. Write an addition sentence that shows the number of students who only have sisters and the number of students who have sisters and brothers. 10 + 7 = 17 There are 17 students who have sisters. Confidential11 Step 3: Solve

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Is the solution reasonable? Reread the problem. Does your answer make sense? Yes Did you answer the question? Yes What other strategies could you use to solve the problem? Confidential12 Step 4: Look Back

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There are 8 students in a math group using pattern blocks. Three students have squares. Two have triangles. Three have both squares and triangles. How many have triangles? Confidential13

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You can solve problems by making graphs. Example: Which collection is largest? Smallest? Use data from the table to solve. ◦ What do you know? You know how many items are in each collection. ◦ What do you need to find? You need to find which collection has the greatest and fewest number of items. Confidential14 Step 1: Read Largest Collection in Our School CollectionNumber of Items Records225 Toy Robots75 Comics175 Game Cards350 Dolls150

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Choose a strategy A graph can help you compare data quickly. Make a pictograph to solve the problem. Confidential15 Step 2: Plan

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Carry out your plan Make a pictograph. Confidential16 Step 3: Solve CollectionNumber of items Records Toy Robots Comics Game Cards Dolls Each represents 50 items. Each represents 25 items. Compare the number of symbols for each item. Game cards has the most symbols. Toy Robots has the fewest symbols. So, Game Cards is the largest and Toy Robots the smallest collection.

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Is the solution reasonable? Reread the problem. Does your answer match the data given in the problem? Confidential17 Step 4: Look Back

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Morris School has 48 stamp collectors, 54 toy collectors, and 66 coin collectors. Which type of collecting is most popular? Least popular? Make a graph to solve this. Confidential18

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You can act out the problem to solve it. Example: Marvin has 10 pictures of Moon. He gives the same number of pictures to 2 friends. How many pictures does each friend get? ◦ What do you know? Marvin has 10 pictures. He gives pictures to 2 friends. ◦ What do you need to find? How many pictures does each friend get? Confidential19 Step 1: Read

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Choose a strategy You can act out the problem. Use counters to show the number of pictures. How many counters will you need? 10 Use plates to show the number of friends. How many plates will you need? 2 Confidential20 Step 2: Plan

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Carry out your plan Draw a counter to show each picture of Moon. Draw two plates to show the two friends. Place an equal number of counters on each plate. Confidential21 Step 3: Solve There are 5 counters on each plate. Each friend gets 5 pictures.

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Is the solution reasonable? Reread the problem. Does your answer make sense? Yes What other strategies could you use to solve the problem? Use a division sentence; 10 ÷ 2 = 5 Confidential22 Step 4: Look Back

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Each of 4 children is wearing 4 bangle bracelets. How many bracelets are there in all? Confidential23

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You can solve problems by making tables. Example: Which day the most sign-ups? Use data from the table to solve. ◦ What do you know? There are 3 days for after school tutoring. There is a list of names for each day. ◦ What do you need to find? You need to find out which day had the most sign-ups To do this you need to know how many sign-ups there were each day. Confidential24 Step 1: Read Sign-Up: After School Tutoring DayName MondayNatalie; Natasha; Chris; Rohan; Eli; Taylor; Ron; Tiffany; Josh; Donna; Bryan TuesdayAnn; Steve; Tara; Pete; Lily; Harry; Warren; Craig; Sebeka; Ian WednesdayTodd; Bailey; Carty; Sumit; Sonya; Joni; Beth

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Choose a strategy A table can help you organize what you know. Make a table to solve the problem. Confidential25 Step 2: Plan

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Carry out your plan Make a table. Tally the names for each day. Write the number of tallies for each day. Compare the tallies for each day. Complete the table. Confidential26 Step 3: Solve Sign-Up: After School Tutoring DayTallyNumber Monday11 Tuesday10 Wednesday7 There are 11 sign-ups for Monday, 10 for Tuesday, and 7 for Wednesday. Monday had the most sign-ups.

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Is the solution reasonable? Reread the problem. Does your answer match the data given in the problem? Yes What other strategies could you use to solve the problem? Write a number sentence. Or make a bar graph. Confidential27 Step 4: Look Back

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Which game got the most votes? Confidential28 My Favorite Game Computer: John, Chuck, Leon, Kim, Rebecca, Sara, Tom, Bill Board: Alan, Steve, Pete, David, Jared Card: Arlyn, Frank, Ashley, Kathy My Favorite Game Computer: John, Chuck, Leon, Kim, Rebecca, Sara, Tom, Bill Board: Alan, Steve, Pete, David, Jared Card: Arlyn, Frank, Ashley, Kathy

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You can solve problems by making tables. Example: The 24 dancers in a show dance in one long chorus line. Every third dancer wears a red costume. All of the others wear blue. Mary is the 14 th dancer. What color costume does she wear? ◦ What do you know? There are 24 dancers in a chorus line. Every third dancer wears a red costume. All of the other dancers wear blue costumes. Mary is the 14 th dancer in the line. ◦ What do you need to find? You need to find out what color costume the 14 th dancer wears. Confidential29 Step 1: Read

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Choose a strategy Finding a pattern will help you solve the problem. Find the pattern for the first three dancers in the line. Continue the pattern to find the color costume that the 14 th dancer wears. Confidential30 Step 2: Plan

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Carry out your plan There are 24 dancers in a line. Every third dancer wears a red costume. All the other dancers wear blue. Use a number chart to help you find the pattern. ◦ Color every third number red. ◦ Color each of the other numbers blue. Confidential31 Step 3: Solve 123456789101112 131415161718192021222324 Is the number 14 colored in red or blue? Blue The 14 th dancer is wearing a blue costume.

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Is the solution reasonable? Reread the problem. Does your answer make sense? Yes Did you answer the question? Yes Did you find a pattern and continue it? Yes What other strategies could you use to solve the problem? Confidential32 Step 4: Look Back

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Jennifer is playing the drums. In one performance she hits the drums on each of the first 3 beats, then rests for 2 beats. If this pattern continues, will she hit the drums on the 15 th beat? Confidential33

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