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Mathematical Tasks: Monkey's Peaches Challenge and Problem-Solving Strategies

Explore math tasks involving peaches, fabric, and cakes to enhance cognitive demand and problem-solving skills. Reflect on solutions and engage with mathematical practices for a comprehensive learning experience.

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Mathematical Tasks: Monkey's Peaches Challenge and Problem-Solving Strategies

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  1. Welcome to …

  2. TODAY’S AGENDA • Hershey Bars • BREAK • Peaches Task & Cognitive Demand • LUNCH • Fabric Task, Tina and Tony’s Task, Little Cakes • Extending Children’s Mathematics • BREAK • Whole Matters • Young Mathematicians at Work • SMP Reflections

  3. The Standards for Mathematical PracticeStudent Reasoning and Sense Making about Mathematics • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

  4. Chocolate Bar Task

  5. Break Time

  6. Peaches Task A little monkey had 60 peaches. On the first day he decided to keep 3/4 of his peaches.He gave the rest away. Then he ate one. On the second day he decided to keep 7/11 of his peaches.He gave the rest away. Then he ate one. On the third day he decided to keep 5/9 of his peaches.He gave the rest away. Then he ate one. On the fourth day he decided to keep 2/7 of his peaches.He gave the rest away. Then he ate one. On the fifth day he decided to keep 2/3 of his peaches.He gave the rest away. Then he ate one. How many did he have left at the end?

  7. Peaches Task (ii) A little monkey had 75 peaches. Each day, he kept a fraction of his peaches, gave the rest away, and then ate one.These are the fractions he decided to keep: 1/2, 1/4, 3/4, 3/5, 5/6, 11/15 In which order did he use the fractions so that he was left with just one peach at the end?

  8. Peaches Task (iii)Peach RationingWhenever the monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. I wonder how long he could make his peaches last for? Here are his rules: Each fraction must be in its simplest form and must be less than 1. The denominator is never the same as the number of peaches left (for example, if there were 45 peaches left, he would not be allowed to keep 44/45 of them). Can you start with fewer than 100 peaches and choose fractions so that there is at least one peach left after a week?

  9. Lunch

  10. Preparing to Solve the Tasks • Solve all 3 tasks individually. • Try to solve each one in more than one way. • Keep track of your thinking and the strategies that you use in solving them.

  11. Tasks to Solve • It takes 2/3 of a yard of material to make a pillow. How many yards of material would it take to make 15 pillows? • Tina and Tony painted pictures today. Tina used half a jar blue paint for her picture. Tony used three-fourths of the same size jar of blue paint for his picture. How much blue paint did Tina and Tony use altogether for their paintings? • Each little cake take ¾ of a cup of frosting. If Betsy wants to make 20 little cakes for a party, how much frosting will she need?

  12. Reflecting on Tasks • Share you strategies and thinking with a partner. • Whole group discussion

  13. Math Notes • What SMP’s did you find yourself engaging in with the task? • What was mathematically significant for you as you interacted with the task, task strategies and videos? • What are the important mathematical ideas you want to remember about these tasks?

  14. Break Time

  15. Whole Matters Task • Spend time working on the task individually. • Make note of your strategies and thinking

  16. Analyzing the Task • Share your solution with a partner • Small group sharing • Whole group discussion

  17. Math Notes • What SMP’s did you find yourself engaging in with the task? • What was mathematically significant for you as you interacted with the task, task strategies and videos? • What are the important mathematical ideas you want to remember about this task?

  18. Young Mathemathematicans at Work • Whole Matters – Ready pages 55 -71 • Read the part assigned to your group # • Make note of significant ideas as you read.

  19. Reading Reflection • Form groups with #1 - #4 and take turns sharing the part you read. • Whole group discussion.

  20. Walk-Across Groups

  21. Develop a Walk-Across for Fractions K-5 Assignment: What is a “Walk Across for Fractions?” It’s a focused look at mathematical connections in the CCSSM: 1) You will demonstrate what connections you can see in the standards across the domains and grade levels. 2) You will explain how a standard connects with prior and/or subsequent standards regarding students’ development of fractional understanding?

  22. Develop a Walk-Across for Fractions K-5 FIRST: To begin, you should give attention to each standard, regardless of domain, and consider whether or not it pertains to ones understanding of fractions. You should only include standards that DO pertain to either development of pre-fraction ideas or directly to fractions themselves. You may find many standards not in the fraction specific CCSSM domain that also act to build fraction sense. SECOND: Once you find connections among standards, articulate an explanation of how they are connected. Do some standards prepare students for future standards? How so? Show what students would be doing and thinking in one standard and explain how that doing and thinking prepares them to do and think about future mathematics. When explaining connections among standards use the names (for example 3.G.2). THIRD: There is a large creative element to this task. You may display and explain the connections in any creative media you choose. It can be as formal as a word document, excel sheet, or power point. Or as informal as a large scale painting, video, or drawings. The only delimiters that must be satisfied are 1) and 2) above. That will most likely require text or comments in some form or another.

  23. Time of Reflection Take a few moments to reflect on SMP’s connected to the content tasks we did today. -- Name of the task and related SMP’s -- Evidence for the chosen SMP’s -- Jot down how you contributed to our shared community of professionals and what mathematical and/or pedagogical knowledge you are taking away from today.

  24. Stay Safe • Please help us put the room in proper order. • Please leave your name tags for next time.

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