Swimming Swamp Monkeys - Using an Open Number Line to Solve Word Problems

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Objective

SWBAT identify factors in word problems and use an open number line to model the problem. They will be methodical in the use of the open number line in order to attend to the precision of their answers.

Big Idea

Open number lines are another tool that can be used to make models to solve multiplication story word problems.

Opener

5 minutes

Explain to the students that today they are going to get another chance to explore one of the many ways that scientists use math in their research!  The animal we will study today is an old world monkey named the Allen's Swamp Monkey.

Possible side questions:  Where is the "old world"? How did it get the name "the old world"?

Do you think everyone agrees with that term?  Why or why not?  (What does it imply?)

Optional:

Explain what a swamp is (this is necessary in Tucson, where I teach).

swamp

(Science: ecology) spongy landlow ground filled with water, a wooded area having surface water much of the time. Low land that is seasonally flooded; has more woody plants than a marsh and better drainage than a bog.A type of environment consisting of a wooded area that is often flooded, or at least very damp.

Definition taken directly from:  www.biology-online.org.  I did not link to the site because there is an ad that isn't especially appropriate for children in the sidebar.

Direct Instruction

6 minutes

Quickly review how to represent multiplication problems on an open number line.  

Show Me Video

Do this with the following problems - note, the students will be stepping up from using easily represented factors of 1 2, 5 and 10 to factors of 3, 4, 6 and 7.  

Draw open number lines and teacher talk the following equations:

3 x 5 =

4 x 6 =

3 x 8 =

Teach students how to make certain they are counting accurately when they are using these numbers. 

Show Me

Contextually Based Guided Practice

30 minutes

SWBAT apply their new knowledge of open number lines in multiplication to solving simple word problems based on some facts about the Allen's Swamp Monkey in central Africa.  

As the students follow along with the Swimming Swamp Monkey Guided Practice and work on the equations on whiteboards or scrap paper, I monitor and adjust. Here are a few examples of the problems in the guided practice:

 After we finish the guided practice, I have students discuss the following questions with a partner.  If I notice that students are struggling with any of the concepts I bring the conversation back to the whole group.

"How are open number lines the same as repeated addition with numerals only?"

"How are open number lines different than repeated addition?"

'How do those similarities (differences) matter? " (How do they relate to a student's ability to solve the equation?)

As the class reads the information, there are opportunities for extending the science content by asking critical thinking questions.

For example, "Why would scientists want to know how many times a day Allen's Swamp Monkeys use a leaf to catch fish?"

"Why would scientists want to know how many invertebrates (of different types) an Allen's Swamp Monkey eats on a daily or weekly basis?"

"How can information about how an animals hunts and how much it consumes help people trying to protect it?"

"Do you think different individuals of this species eat different invertebrates, or do you think they all eat the same animals?  Explain your thinking."

Contextually Based Partner of Independent Practice

20 minutes

Present the students with the following word problems:

  • If a Swamp Monkey eats 9 True Bugs (Order Hemiptera) every day for 6 days, how many Hemipterans did they eat in all?
  • 6 Swamp Monkeys climb up 6 different trees in one day.  How many trees did they climb that day?
  • 4 scientists each observe 8 Swamp Monkeys on their daily walk.  How many Swamp Monkeys have they observed in all?

One of the reasons using open numbers lines is an important practice is that it not only is a strategy, it is an actual representation of mathematical thinking.

My students are required to show their open number line on scrap paper or whiteboards, and explain the steps on the open number line to solve a word problem to someone else (partner or teacher).

Wrap-up

3 minutes

To close the lesson, students are either selected or volunteer (depends on what works best for your class) and show/share the steps for solving a simple multiplication equation using an open number line.