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**The California Frog-Jumping Contest**

Fosnot- Algebra Day One: Frog Jumping! The frog-jumping context is used to generate the open number line model that will be used throughout the unit to explore and represent equivalence of algebraic expressions.

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**Student Materials Needed**

Student recording sheet for the frog-jumping investigation- one per pair of students Large piece of paper- one per pair of students Markers

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**Today’s learning target is to…**

Develop the context of the California Frog-Jumping Contest Introduce a bullfrog named MT Investigate the length of MT’s jumps Generate an open number line model

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**California Frog-Jumping Contest**

In California, in Calaveras County, a new sport was introduced more than 100 years ago; the frog jump. As many as 2,000 frogs compete each May at the Frogtown Fairgrounds in Calaveras County, Angel Camp, California. The world’s frog jump record was set by Rosie the Ribiter in She jumped 21 Feet & inches! The contest was inspired by Mark Twain’s 1865 fictional short story, The Celebrated Jumping Frog of Calaveras County. Over the years, the contest has become the most popular attraction at the Angel Camp annual fair, which also includes music, a craft show, and local talent. Today, some of the sidewalks of the city are lined with painted green frogs and bronze plaques, modeled on the Hollywood Walk of Fame.

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**California Frog-Jumping Contest**

Calaveras County, Angel Camp, California Rosie the Ribiter Jumped 21 Feet & 5 ¾ inches!

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**Mark Twain’s Famous Short Story**

The Celebrated Jumping Frog of Calaveras County

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**Frog on the Jumping Track**

Frogs spend most of their day sitting still. They catch flies or other insects with their tongues while they sit. Only occasionally do they jump, and that is usually to get to the water. So when they are placed on a jumping track, they usually sit and wait. When you command a frog, “JUMP!” usually it sits still and waits. To get frogs to jump, you usually need to encourage them with a slight touch on the back or maybe a few gentle touches before they get annoyed and decide to jump.

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**When they do jump, they don’t jump just once**

When they do jump, they don’t jump just once. Usually they take two, three, or more jumps and walk a little bit (a few steps in one direction or another). So the behavior of frogs when they jump presents a special problem in competitions where you want to find out which frog has the biggest jump. This is because you have to figure out the length of a frog’s jump when you know the length of several jumps and several steps combined. Referees of frog-jumping contests often use this rule…..

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**The Referee’s Frog-Jumping Rule**

Whenever a frog jumps in an event, if the frog takes more than one jump, all jumps are assumed to be equal in length and all steps are assumed to be equal in length. Why would this rule be used in frog-jumping contests?

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**The Referee’s Frog-Jumping Rule**

A Bullfrog Named MT MT is a bullfrog. He is world-famous for his long jump. When he takes 4 jumps and 8 steps, it is the same as 52 steps. Use the referee’s frog-jumping rule below to figure out the following: How many steps are equal to 2 jumps and 4 steps made by MT? How many steps are equal to each jump made by MT? The Referee’s Frog-Jumping Rule Whenever a frog jumps in an event, if the frog takes more than one jump, all jumps are assumed to be equal in length. All steps are also assumed to be equal in length.

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Need some help? Do you think you could answer the 1st question without knowing the answer to the 2nd? How might you do that? I encourage you to draw jumps on a number line to represent your thinking and compare your sequences. Try to represent what you know! YOU CAN DO IT!

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**Preparing for the Math Congress**

Explain how the two questions are related Make a draft explaining the relationship between the two jumping sequences on a large piece of paper Present your draft to Mrs. Burgess Complete your final poster for the Math Congress

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**The Math Congress Presentation of Student Posters**

A discussion of the usefulness of the number line representation in determining the equivalence

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Behind the Numbers What would happen if MT took one jump and two steps? How is this jump sequence related to the other jump sequence? What about three jumps and six steps? What other jumping sequences can we find values for without first finding the jump length?

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Reflections on the Day Today was devoted to developing representations. The context of frog jumps led to the use of the open number line and established the fact the algebraic expressions can be operated on to make other equivalent expressions, without always having to solve for the unknown. The work today developed the terrain for the journey ahead. As we continue with this unit, you will be encouraged and supported in substituting equivalent expressions as you solve for unknowns and work with simultaneous equations.

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