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The California Frog-Jumping Contest. Fosnot - Algebra Day Two: Jumping Buddies Minilesson : Keeping the ratio constant in division Target: More frog-jumping problems as a context for examining common multiples of 8 and 12. Equivalent expressions are represented on the open number line.
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The California Frog-Jumping Contest Fosnot- Algebra Day Two: JumpingBuddies Minilesson: Keeping the ratio constant in division Target: More frog-jumping problems as a context for examining common multiples of 8 and 12. Equivalent expressions are represented on the open number line.
Student Materials Needed • Tables need their CFJC Packet • Sticky notes- one per table • Large piece of paper- one per pair of students • Markers
Today’s learning target is to… • Practice a range of strategies as students solve a string of division problems • Represent your thinking on a number line • Determine all possible points made by frog jumps • Highlight the different ways to determining and representing equivalence
Mental Math MinilessonKeeping the Ratio Constant in Division Give a thumbs-up when you know the answer…. 36 72 6 = 72 12 = 144 24 = 42 6 = 126 18 = 425 25 = Explain your reasoning, and represent the strategy on an open number line.
Team Roles & Responsibilities For each team, select a role and responsibility for each person at your table. • The Recorder’s job: to write the solutions for each problem in the Team packet and to listen to the Speaker’s to check the accuracy of the team’s solutions • The Artist’s job: to create a visual model or poster of the solutions and clearly display the team’s knowledge of the investigation • The Speaker’s job: to present the poster created by Artist to the entire class and explain the team’s reasoning for each solution during the Gallery Walk
Frog & Toad – Appendix D • Frog’s Jump Problem: Frog jumps 8 times. Every time he jumps, he travels the same distance. After 8 jumps, he has traveled 96 steps. How long are his jumps? • Toad’s Jump Problem: It takes Toad the same amount of time to get to 96, but he does it differently. Each of his jumps is equal to 8 of Frog’s steps. How many jumps does Toad make?
The Investigation • Represent both problems on one diagram showing jumping amounts, and explain how they are different and how they are similar. • Marking the Meeting Points! • Where do Frog and Toad both land? Clearly, 96 is one answer. Are there other places where they both land?
Need Help? • I encourage you to draw an open number line or double number line to represent your thinking • At what points on the track do Frog and Toad both land? • Try marking off all 96 steps on the number line • Try skip-counting and identify common multiples • Try using multiplication to derive common points • Once you have solved the problems, can you determine all the possible points where Frog’s and Toad’s jumps meet?
Preparing for the Math Congress Gallery Walk • Sticky notes are for comments or to ask questions about each other’s posters • Conduct a gallery walk to give students a chance to review and comment on each other’s posters. • Plan for a congress discussion that will highlight the different ways of determining and representing equivalence
Teacher Notes about the Math Congress • The purpose of the Math Congress is to allow students to discuss their thinking about equivalence. • Discussion should center on the idea of the various equivalences given by common multiples • At the end, students should note that all the common multiples (24, 48, 72, 96) are multiples of the least common multiple, which is 24.
Teacher Notes aboutFacilitating the Math Congress • Have students share the equivalence relationships they used in finding common landing points. • Focus the conversation on the distance between those points to highlight how common multiples and common factors are related • Have students consider the distance between the points • Have students reflect on why they are equally spaced
Reflections on the Day • The work today focused on equivalent expressions and their representation on the number line. • In the minilesson, students explored division. • The investigation of Frog’s and Toad’s jumps provided a context for students to think about common multiples and equivalent expressions. • The number line used to represent unknown jump lengths became a tool for considering the relationships among different common multiples.
