## Year 1 Lesson 15 - - Year 2 Lesson 10 How to solve a Problem

This lesson discusses the steps involved in solving problems, and some of the strategies that kids can use. The lesson has four parts:

A. DISCUSSION WITH KIDS (10 minutes)
B. WORK A PROBLEM TOGETHER (10 minutes)
C. WORK THE MANGO PROBLEM (20 minutes)
D. EVALUATE A RESPONSE TO THE MANGO PROBLEM (10 minutes)

The problem will be graded in the five areas specified by the Math Olympiad Scoring Guide (Rubric). They are:
1. UNDERSTAND THE PROBLEM
2. CHOOSE A STRATEGY
3. CHECK YOUR RESULT
4. COMMUNICATE YOUR WORK
5. GETTING THE RIGHT ANSWER

### A. DISCUSSION WITH KIDS (10 minutes)

Begin the conversation with the kids. Ask them for ideas for each step: How can you show that you really understand the problem? What are some strategies that you can use? How can you check your result to see if it is reasonable? Here are some ideas that they might come up with in each area:

• UNDERSTAND THE PROBLEM
• Read the problem carefully.
• What facts are you given?
• What are you asked to find?
• What patterns did you observe?

• CHOOSE A STRATEGY
• Have you solved a similar problem before?
• What strategies can you think of that might work? Usually there will be more than one.
• Here are some strategies:
• Draw a picture or sketch
• Use a formula or equation
• Make a table or list
• Guess, check and revise
• Work backwards from information that you are given
• Solve a simpler problem
• Eliminate possibilities
• Look for patterns
• Use a strategy that seems to work to solve the problem

• CHECK YOUR RESULT
• Re-read the problem.
• Did you answer the question asked?
• Did you include correct units and labels?
• Does your answer seem reasonable?
• Can you get the same answer using a different strategy?

• COMMUNICATE YOUR WORK
• Have you shown your work?
• Are your pictures neat, with labels?
• Are your tables clear and logical?
• Do the steps in your solution follow logically with no gaps?
• Do you use sentences to explain your work?
• Are your spelling and grammar good?

• GETTING THE RIGHT ANSWER
• If you have done all of the steps above, you will probably get the right answer. But if you do not get the right answer, you can still get a lot of credit (at Math Olympiad and in High School and College) if you show your work. A lot of the time the person grading your work will give you partial credit if they can follow your thoughts and see where you went wrong.

### B. WORK A PROBLEM TOGETHER (10 minutes)

Let's try a simple problem:

Jake bought a pony for \$50. After a week he sold it for \$60. Two weeks later, he bought it back for \$70. A week after that he sold it for \$80. How much did Jake make or lose on the pony?

1. UNDERSTAND THE PROBLEM
What are we asked to find? We are asked to find out if Jake made money or lost money and how much he made or lost. We are given the prices at which he bought and sold the pony.

2. CHOOSE A STRATEGY
Lets draw a picture. It might look something like this:
Each \$ represents ten dollars.

 Spent: Week 1: \$\$\$\$\$ Week 3: \$\$\$\$\$\$\$

 Received: Week 2: \$\$\$\$\$\$ Week 4: \$\$\$\$\$\$\$\$

By comparing the dollar signs above the line with those below the line, you can see that Jake received \$20 more than he spent.

3. CHECK THE RESULT
Let's try a different strategy to check the result. Let's make an equation. Every time Jake buys a pony, we subtract the amount. Every time he sells a pony, we add that amount. So Jake ends up with:

-50 +60 -70 +80 = +20 dollars.

Does the answer seem reasonable? Yes it does. Does it match the answer we got before? Yes, again. What exactly were we asked to find? How much Jake made or lost.

4. COMMUNICATING
Okay, this is the hard part. We are asked to write about what we did. First we draw the picture that we came up with. It could be dollar bills, or bags of gold, each representing \$10. We clearly put the labels on indicating what was SPENT and what was RECEIVED. We explain our steps:

Every time Jake SPENT \$10, we put a \$ above the line. Every time Jake RECEIVED \$10, we put a \$ below the line. We noticed that every time Jake bought the pony and sold it again, he made \$10. If he had kept this pattern up, he would have made \$50 after 5 sales. By counting the \$ signs above the line and subtracting them from the \$ below the line, we see that he MADE \$20. We checked our work by writing an equation. Using the equation we got the same answer.

5. GETTING THE RIGHT ANSWER We are pretty sure we got the right answer, because we worked it two different ways, and because we checked back with the orgininal problem to make sure we answered the question they asked.

### C. WORK THE MANGO PROBLEM (20 minutes)

Now it is time for the kids to try one on their own. Kids can work as individuals or as teams. If you have fewer than 6 kids, it's best to let them work as individuals so that you can have more than one answer to compare. If there are more kids, you can have them work in teams of 3 or 4. It is still a good idea for each kid to do the entire problem, and then the team can choose which paper to submit. Give the kids about 20 minutes to work the mango problem.

### D. EVALUATE A RESPONSE TO THE MANGO PROBLEM (10 minutes)

Hand out the scoring guide (rubric) to the students, and put a copy on the board of the scoring grid. Ask for one person to volunteer a paper to be graded. Using the scoring guide, quickly evaluate the responses and average the 5 scores to come up with an overall score between 0 and 4.