Why do some problems have

one solution and other problems have more than

one?

Bag the Beansby

Becky McCrawand

Suzanne Padgett

Objectives•Develop thinking skills

•Explore numerical relationships

•Solve equations

Directions•Make groups

of 4 students.•Sort the beans

into piles.•Discuss the

rule used to sort the beans.

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?

Steps to Solving Problems

• Understand the problem

• Plan a solution

• Carry out the plan

• Examine the solution

Understand the Problem

This bag contains one fewer Lima bean thanRed beans. There are four more Black beans than Lima beans. There are 11 beans in all.

Known

Total = 11 beansRed > Lima

Black > Lima

Unknown

How many of each bean are in the bag?

Plan a Solution

• Use a table.

Type of

BeanLima Red Black Total

Formula

Carry Out the PlanType

ofBean

Lima Red Black Total

Formula X X + 1 X + 4 11

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

Carry Out the Plan (cont.)4. Find the value of X by setting the addends

(formulas) equal to 11. (X) + (X + 1) + (X + 4) = 11

5. Combine like terms, X, and digits. (X + X + X) + (1 + 4) = 11

6. Add variables and digits. 3X + 5 = 11

7. Isolate the variable. 3X + 5 - 5 = 11 – 5

3X = 68. Divide both sides by the coefficient of X in

order to isolate the variable.3X ÷ 3 = 6 ÷ 3

X = 2

Examine the SolutionType of

BeanLima Red Black Total

Formula X X + 1 X + 4 11

Solution 2 2 + 1 = 3

2 + 4 = 6

2+3+6= 11

1.Substituted the variable, X, with the solution, 2.

2.Solve each formula with X = 2.

3.Check the total by adding the three solutions.

4.Does your answer check?

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?

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.htmlin order to practice sorting skills.

Benchmarks• 2C The Nature of Mathematics:

Mathematical Inquiry (3-5) #1

• 12B Computation and Estimation #1

• Retrieved from: http://www.sciencelinks.com/lessons/