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Enhancing Collaborative Learning through Personal Group Expectations in Mathematics

This lesson focuses on developing higher-order multiplication and division skills through collaborative learning. Students are encouraged to set personal group expectations that will enhance their success and engagement in class. Through investigations and hands-on activities, they will collect data, create graphs, and interpret relationships between variables. Reflection on their group rules will reinforce their understanding of effective collaboration. This process seeks to foster an environment conducive to mathematical exploration and teamwork, strengthening both individual and collective skills.

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Enhancing Collaborative Learning through Personal Group Expectations in Mathematics

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  1. Warm UpHigher Order Multiplication Skills 10

  2. Class Group Expectations Collaborative Learning……… Personal Group Expectations • Reflection:Write a minimum of a 5-6 sentence paragraph on how your group rules will help you be successful in class.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 11

  3. Investigationsand Mathematical Reflections What have I learned? Why did we do this?

  4. Warm UpHigher order Division Skills 12

  5. Investigation 1.1Collect the DataCollect information on left sideReflection:How would you organize the data collected today? Minimum of 1 paragraph_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

  6. Variables What are some examples? What are some nonexamples? Definition Sentence or Picture/Equation/Symbol For all of the following vocabulary create a frayer model using the example above: Variables Coordinate Graph Dependent Variable Y-Axis Independent Variable X-axis, Scale Coordinate Pair Relationship

  7. Investigation 1.2 Making Graphs Is the relationship you found between the jumping jacks and the time easier to see in the table or graph? Explain ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Write reflection on the left side of notebook

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  9. Investigation 1.3 Interpreting Graphs 1. Give the coordinate pair for the third point on your graph. (_____, ______) 2. Use a ruler to connect the point on your graph to help you determine intervals between points. Next use your line segments to estimate the distance traveled after ¾ of an hour (0.75 hours). Justify your answer. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Write reflection on left side

  10. 9/10 Warm-Up - Fractions 1. 3/4 + 4/5 2. 11/8 - 6/7 3. 22/3 + 13/4 Explain in complete sentences how to solve this problem • Right Side...now try these... • 4. 31/4 + 45/7 5. 12/3 + 7/8 • 6. 12/3 - 7/8 18

  11. Answer Questions on the Left Side….in complete sentences 19

  12. 9/11 Warm-Up - Fractions 1. 42/5 + 11/9 2. 21/2 - 32/5 3. 3/8 • 4/5 Explain in complete sentences how to solve this problem Right Side...now try these... 4. 2/9 • 3/12 5. 1/6 • 3/8 6. 11/2 • 32/5 7. 3/8 • 2 6 5

  13. Investigation 1.5a Finding Average Speed Make a table to reasonably represent the information from their journal. They traveled 80 miles in 7.5 hours. Suppose they traveled at a constant speed for the entire trip, is this the same as their average speed? _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

  14. Investigation 1.5b Finding Constant Speed Make a table to represent a rider that completed the entire trip at the average speed represented in the previous investigation? Describe the similarities and differences represented in the graph / table. _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

  15. 9/12 Warm-Up - Fractions 1. 2/3 • 6/7 2. 3/8 • 8/9 3. 3/8 ÷ 4/5 Explain in complete sentences how to solve this problem Right Side...now try these... 4. 11/8 ÷ 6/7 5. 2/5 ÷ 4/9 6. 3/8 ÷ 2 7. 11/2 ÷ 32/5 7 6 5

  16. Investigation 2.1 Analyzing Tables and Graphs Which bike shop should ocean tour use? Explain _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

  17. 9/13 Warm-Up - Fractions 1. 2/3 • 1/4 2. 4/5 - 2/6 3. 22/3 ÷ 1/8 4. 5/9 + 13/8 Assessment tomorrow 5. 4/8 - 6/7 6. 33/7 ÷ 4/9 7. 11/3 + 4/5 + 3/4 8. 2/3 • 41/2 •5/8 8 7 6 5

  18. Investigation 2.2 Making and Analyzing Graphs When constructing this graph, how did you determine which variable would be the x and y axis? Explain. _______________________________________________________ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________

  19. Investigation 2.2b Making and Analyzing Graphs ____________________________________________________________________________________________________________________________________________________

  20. 9/14 Mini-Assessment - Fractions 6/10• 3/8 2. 22/3 + 4 1/6 3. 4/6 ÷ 2/15 4. 31/4 • 43/5 bonus #5 51/8 ÷ 2

  21. Investigation 2.3 Interpreting Graphs Team work: Each member is responsible for explaining one of the following: Claimer– Announce the team decisions for each match. Defender – Have at least 3 reasons and use the diagram to confirm. Prover– Describe which words matched numerical patterns and trends. Explainer– Explain how you decided which graph matched each scenario.

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