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Guess and Check, Work Backward

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Have you ever wondered about different types of elephants? Well, different elephants have different characteristics for example, what they eat or where they live. Let's think about what they weigh.

There are two elephants at the city zoo, and they are also two different kinds of elephants. One is an African Elephant and the other is an Indian Elephant. An African elephant is larger than an Indian elephant. One of the fun jobs that city zookeepers get to do is to weigh in the elephants. It is always interesting to see how much each elephant weighs. Tara Jonsen gets the fun job of weighing Jojo, a male African Elephant and Junas, an Indian Elephant. She wonders if just this once Junas will weigh more than Jojo. Jojo weighs 4,000 pounds more than Junas. Their combined weight is 26,000 pounds. Tara leads them both back to their habitats. When she returns to the log book, she realizes that she forgot to write down each specific weight. She remembers two things. That Jojo weighs 4,000 pounds more than Junas. That their combined weight was 26,000 pounds. Given this information, can Tara figure out what each elephant weighed?

Using the strategy guess, check and revise, you can help Tara figure out what each elephant weighed.

Guidance

In our last Concept, we worked on reading and understanding a given problem situation. We used this first step of the four-part problem-solving plan as we worked with Tyler and his orangutan adoption problem.

Now we are going to apply this first step to the elephant problem.

Let’s look at the problem once again so that we can determine the given information and identify what information we are looking for.

Here is the problem.

There are two elephants at the city zoo, and they are also two different kinds of elephants. There is an African Elephant and an Indian Elephant. An African elephant is larger than an Indian elephant. One of the fun jobs that city zookeepers get to do is to weigh in the elephants. It is always interesting to see how much each elephant weighs. Tara Jonsen gets the fun job of weighing Jojo, a male African Elephant and Junas, an Indian Elephant. She wonders if just this once Junas will weigh more than Jojo. Jojo weighs 4,000 pounds more than Junas. Their combined weight is 26,000 pounds. Tara leads them both back to their habitats. When she returns to the log book, she realizes that she forgot to write down each specific weight. She remembers two things. That Jojo weighs 4,000 pounds more than Junas. That their combined weight was 26,000 pounds. Given this information, can Tara figure out what each elephant weighed?

Our given information is:

Jojo weighs 4,000 pounds more than Junas.

Their combined weight is 26,000 pounds.

To understand this problem, we need to figure out two unknowns. We need to figure out what Junas weighed and what Jojo weighed. There is a relationship between the two weights.

We can work on figuring out the weights of the two elephants by using guess, check and revise. Guess, check and revise has us guess numbers that we think might work and try them out. Since we don’t know a lot about what the two elephants weighed, this is probably a good strategy for this problem.

Jojo-let’s call his weight x

Junas-let’s call his weight y

x + 4000 + y = 26,000

Here is an equation that represents our problem. Let’s guess a few numbers that might work in this problem.

What if Junas weighed 10,000 pounds? We can say that Junas weight +\ 4000 = Jojo’s weight. Here is our new equation. Let’s see if it works.

10,000 + 4000 = 14,000 & = \text{Jojo's weight}\\10,000 & = \text{Junas weight}\\14,000 + 10,000 & = 24,000

Uh oh, our number is too small. We need to revise. We could keep guessing numbers until we find ones that work.

Let's practice with a few examples.

Example A

Kyle caught 15 fish in one day. In his first bucket he put 1 more fish than his second. How many fish were in his first bucket?

Solution: 8 fish

Example B

How many fish were in his second bucket?

Solution: 7

Example C

If he put double the amount of fish in his first bucket, how many more did he add? What is the new total in the first bucket?

Solution: 8 more fish for a total of 16 fish

If Tara keeps on guessing, checking her work and revising, eventually she will figure out that Jojo weighs 15,000 pounds and Junas weighs 11,000 pounds.

Vocabulary

Product
the answer to a multiplication problem
Quotient
the answer to a division problem
Word Problem
A problem that uses verbal language to explain a mathematical situation.
Sum
the answer in an addition problem
Difference
the answer in a subtraction problem

Guided Practice

Here is one for you to try on your own.

Betsy picked a bunch of apples. She wanted to give some to her neighbor. She kept a bowl of apples for herself and gave her neighbor five more apples than she kept herself.

If the total number of apples picked was 25, how many did Betsy keep for herself?

Answer

To solve this problem, we can write the following.

 x + (x + 5) = 25

Now we can guess until we get the correct answer.

Let's use x for Betsy's apples. What about if she kept 10 apples? Does that work?

 10 + (10 + 5) = 25

This works!

Betsy kept 10 apples and gave her neighbor 15 apples.

Video Review

Khan Academy: Word Problem Solving Plan 1

Practice

Directions: Solve each of the following problems using the four part problem solving plan.

A small lion weighs in at 330 pounds. A large lion weighs in at 500 pounds.

1. If there are four large lions in the habitat, how much do the lions weigh in all?

2. If there are five small lions in the habitat, what is the total weight of the small lions?

3. If a lion can sleep 20 hours in one day, how many hours is a lion asleep over a period of five days?

4. If a lion sleeps this much, how many hours is the lion awake over a period of three days?

5. A Burchell’s zebra is smaller than a Grevy’s zebra, the Burchell’s zebra weighs about 550 pounds. What is the difference between the small zebra and the large Grevy's zebra weighing 990 pounds?

6. What is the weight difference between a small Grevy’s zebra and a zebra weighing 880 pounds?

7. What is the weight difference between a small Grevy’s zebra and a large zebra weighing 900 pounds?

8. An adult African male elephant weighs 15,400 pounds. What is the difference between its weight and the weight of a large Grevy’s zebra?

9. What is the difference between the African elephant’s weight and the weight of the small Burchell's zebra?

10. Dana caught twenty-eight fish. She wants to divide the fish into four baskets. If she does this, how many fish will be in each basket? Can she put the same number of fish in each basket?

11. Carl also went fishing. He caught five fish on the first day and four fish on the next day. If he continues this pattern on what day will he not catch any fish?

12. Jessie loves to cook fish after she catches them. She is having ten people over for dinner. If each person eats a half of a fish, how many fish will she need to cook to feed all ten people?

13. Cass takes people out on a fishing boat to go deep sea fishing. With his strategies, people often catch double the amount of fish that they do regularly. If someone normally catches three fish in a day, how many fish will they catch using Cass’ strategy?

14. If you were someone who usually caught thirty-five fish in one week, how many fish would you catch on average per day?

15. if you caught thirty - five fish in one week, how much would that be in one month?

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