Activity: Smart Guessing

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Virgil Berry
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1 Activity: Smart Guessing GENERATE EQUIVALENT FORMS OF FRACTIONS & DECIMALS USE MULTIPLICATION & DIVISION TO SOLVE PROBLEMS INVOLVING FRACTIONS ESTIMATE TO APPROXIMATE REASONABLE RESULTS WHERE EXACT ANSWERS ARE NOT REQUIRED Prerequisites Number Studies Activity: Multiplying & Dividing Fractions Preparation Worksheet #1 & #2 for each student Overhead #1 Set of Playing Cards for each pair Calculators The Multiplying and Dividing Fractions exploration is a prerequisite for the Smart Guessing Activity. Students need to be familiar with the question being asked by multiplication and division problems in order to make their smart guesses. Start by displaying Overhead #1 to demonstrate how Smart Guessing works. For Smart Guessing you and your partner are going pull a card which will have a multiplication or a division problem on it. At the top it will give a range for where you want the answer to fall. What you need to do is guess a fraction to take the place of the square. Each pair will have a calculator to check to see if you hit the answer range. Let s do this one together. So 7 times something needs to fall between 4 and 6. Who has a first guess to start us off? I then take guesses and use a calculator to check the answer. I encourage students to discuss their thought process aloud. For instance a student might say If you multiply 7 times 1/2 you ll get 3.5 so it needs to be bigger than that. Let s try 3/4. This would be recorded: 7 x ¾ = In order for students to be able to check their answers on a calculator, they'll need to be familiar with the decimal equivalent. Hopefully by this time in the school years, students have already worked through all the number studies. The guess 7 x ¾ would be put into the calculator 7 x The answer is 5.25 which falls in the target range so no further guesses are needed. I only have 2 rules. First, student s guesses need to be recorded in fraction form (not as decimals), although the answers can be written as decimals. Second, the pair can discuss as long as they like, but as soon as they try a possible number on the calculator, they must record it as a guess. After students are comfortable with the rules, I have them get in pairs and pass out Worksheet #1 and a set of Smart Guessing multiplication cards. I circulate as students work. After they ve worked through a number of the cards, I call the class to attention to discuss how they are doing. I ask: Are your guesses improving with each card you do? Why? What strategies have you developed? If the card said 100 x = with an answer range of 55 to 65, how would you decide what number to guess first? Next students can work through division cards. You may want to demonstrate with another example or simply pass out the cards out and let pairs get to work. : pg. 1 of 10

2 ACTIVITY: SMART GUESSING LESSON PAGES On the surface this activity may seem to be rather easy since students get to use a calculator to check their guesses. However, the thought process involved in making smart guesses is rooted in an understanding of fractions, relative size of fractions, and the meaning of fraction multiplication and division questions. It actually requires a higher level of number sense than finding exact answers to fraction problems. Worksheet #2 could be used as an extension or a homework assignment. : pg. 2 of 10

3 Answer Range: 1 to 3 9 x = Answer Range: 15 to 16 ¾ x = ACTIVITY: SMART GUESSING PLAYING CARDS Answer Range: 400 to ½ x = Answer Range: 40 to x = Answer Range: 1 to 5 25 x = Answer Range: 2 to 4 6 x = Answer Range: 100 to 150 x = Answer Range: 500 to x = 100 pg. 3 of 10

4 Answer Range: 5 to 7 12 x = Answer Range: 1 to ¾ x = ACTIVITY: SMART GUESSING PLAYING CARDS Answer Range: 1 ½ to 2 1 x = Answer Range: 15 to 20 ⅔ x = Answer Range: 1 to 2 2 ½ x = Answer Range: 8 to x = Answer Range: 10 to 15 2 ½ x = Answer Range: 50 to x = 10 pg. 4 of 10

5 Answer Range: 4 to 10 3 = Answer Range: 6 to 10 1 = ACTIVITY: SMART GUESSING PLAYING CARDS Answer Range: 3 to 5 1 ½ = Answer Range: 0 to ½ 10 = Answer Range: ½ to 1 ½ 23 = Answer Range: 4 to 5 1 = Answer Range: 2 to 4 ⅔ = Answer Range: 7 to = 10 pg. 5 of 10

6 Answer Range: 2 to 4 ½ = Answer Range: 6 to 10 2 = ACTIVITY: SMART GUESSING PLAYING CARDS Answer Range: 0 to ⅞ 1 ½ = Answer Range: 2 to 4 = Answer Range: 0 to ¾ 5 = Answer Range: 4 to 6 1 ¼ = Answer Range: 4 to 7 3 = Answer Range: 8 to = 10 pg. 6 of 10

7 Name: Date: Smart Guessing ACTIVITY: SMART GUESSING WORKSHEET #1 pg. 7 of 10

8 ACTIVITY: SMART GUESSING WORKSHEET #1 pg. 8 of 10

9 Answer Range: 4 to 6 7 x = ACTIVITY: SMART GUESSING OVERHEAD #1 2. too high too low 3. too high too low 4. too high too low 5. too high too low 6. too high too low 7. too high too low 8. too high too low 9. too high too low pg. 9 of 10

10 Name: Do Not Solve :) 1. What question does 1 x 7 = ask? What question does 1 x 14 = ask? Since 1 x 7 = 10 can you find the answer to 1 x 14 = without solving? If so, give the answer and explain your reasoning. Date: ACTIVITY: SMART GUESSING WORKSHEET #2 2. What question does 3 ¾ = ask? What question does 9 ¾ = ask? Since 3 ¾ = 4 can you find the answer to 9 ¾ = without solving? If so, give the answer and explain your reasoning. 3. What question does 10 ⅔ = ask? What question does 10 ⅓ = ask? Since 10 ⅔ = 15 can you find the answer to 10 ⅓ = without solving? If so, give the answer and explain your reasoning. pg. 10 of 10

Statisticians deal with groups of numbers. They often find it helpful to use

Chapter 4 Finding Your Center In This Chapter Working within your means Meeting conditions The median is the message Getting into the mode Statisticians deal with groups of numbers. They often find it