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Why do some problems have one solution and other problems have more than one?

Why do some problems have one solution and other problems have more than one?. Bag the Beans. by Becky McCraw and Suzanne Padgett. Objectives. Develop thinking skills Explore numerical relationships Solve equations. Directions. Make groups of 4 students. Sort the beans into piles.

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Why do some problems have one solution and other problems have more than one?

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  1. Why do some problems have one solution and other problems have more than one?

  2. Bag the Beans by Becky McCraw and Suzanne Padgett

  3. Objectives • Develop thinking skills • Explore numerical relationships • Solve equations

  4. Directions • Make groups of 4 students. • Sort the beans into piles. • Discuss the rule used to sort the beans.

  5. Questions for Sorting Beans • How many piles of beans did you make? • How would you describe each of the piles you have made? • What was your rule? • Can you sort the beans using a different rule?

  6. Steps to Solving Problems • Understand the problem • Plan a solution • Carry out the plan • Examine the solution

  7. Understand the Problem This bag contains one fewer Lima bean than Red beans. There are four more Black beans than Lima beans. There are 11 beans in all.

  8. Plan a Solution • Use a table.

  9. Carry Out the Plan 1.Complete the table with known information. 2.Use a variable, X, in a formula corresponding to the known information. 3.Set: Lima bean = X, Red bean = X+1, Black bean = X +4

  10. Carry Out the Plan (cont.) • Find the value of X by setting the addends (formulas) equal to 11. (X) + (X + 1) + (X + 4) = 11 • Combine like terms, X, and digits. (X + X + X) + (1 + 4) = 11 • Add variables and digits. 3X + 5 = 11 • Isolate the variable. 3X + 5 - 5 = 11 – 5 3X = 6 • Divide both sides by the coefficient of X in order to isolate the variable. 3X ÷ 3 = 6 ÷ 3 X = 2

  11. Examine the Solution • Substituted the variable, X, with the solution, 2. • Solve each formula with X = 2. • Check the total by adding the three solutions. • Does your answer check?

  12. You Try! This bag contains at least eight beans. There are three times as many Red beans as Black beans. There is one more Lima bean than Red beans. What is your solution? Can there be a different solution?

  13. Assessment • Check for correct answers on student’s worksheet. Enrichment • Have students create his or her own Bag the Beans problem for classmates to solve. Remedial • Have students complete an additional on-line, interactive site, http://pbskids.org/lions/wolf/flood2.html in order to practice sorting skills.

  14. Benchmarks • 2C The Nature of Mathematics: Mathematical Inquiry (3-5) #1 • 12B Computation and Estimation #1 • Retrieved from: http://www.sciencelinks.com/lessons/

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